a default file name is generated in the directory for permanent files (File directories) by prepending \u201c.movecs\u201d with the file prefix, i.e., \u201c.movecs\u201d. The name of this file is stored in the database so that a subsequent SCF calculation will automatically restart from these MO vectors.
Applications of this directive are illustrated in the following examples.
Example 1:
vectors output h2o.movecs\n
Assuming a start-up calculation, this directive will result in use of the default atomic density guess, and will output the vectors to the file h2o.movecs.
Example 2:
vectors input initial.movecs output final.movecs\n
This directive will result in the initial vectors being read from the file \u201cinitial.movecs\u201d. The results will be written to the file final.movecs. The contents of \u201cinitial.movecs\u201d will not be changed.
Example 3:
vectors input project \"small basis\" small.movecs\n
This directive will cause the calculation to start from vectors in the file \u201csmall.movecs\u201d which are in a basis named \u201csmall basis\u201d. The output vectors will be written to the default file \u201c\u201c."},{"location":"Hartree-Fock-Theory-for-Molecules.html#vectors-swap-keyword","title":"VECTORS SWAP keyword","text":"
Once starting vectors have been obtained using any of the possible options, they may be reordered through use of the SWAP keyword. This optional keyword requires a list of orbital pairs that will be swapped. For UHF calculations, separate SWAP keywords may be provided for the alpha and beta orbitals, as necessary.
An example of use of the SWAP directive:
vectors input try1.movecs swap 173 175 174 176 output try2.movecs\n
This directive will cause the initial orbitals to be read from the file \u201ctry1.movecs\u201d. The vectors for the orbitals within the pairs 173-175 will be swapped with those within 174-176, so the resulting order is 175, 176, 173, 174. The final orbitals obtained in the calculation will be written to the file \u201ctry2.movecs\u201d.
The swapping of orbitals occurs as a sequential process in the order (left to right) input by the user. Thus, regarding each pair as an elementary transposition it is possible to construct arbitrary permutations of the orbitals. For instance, to apply the permutation (6 7 8 9) we note that this permutation is equal to (6 7)(7 8)(8 9), and thus may be specified as
vectors swap 8 9 7 8 6 7\n
Another example, now illustrating this feature for a UHF calculation, is the directive
vectors swap beta 4 5 swap alpha 5 6\n
This input will result in the swapping of the 5-6 alpha orbital pair and the 4-5 beta orbital pair. (All other items in the input use the default values.)
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#vectors-lock-keyword","title":"VECTORS LOCK keyword","text":"The LOCK keyword allows the user to specify that the ordering of orbitals will be locked to that of the initial vectors, insofar as possible. The default is to order by ascending orbital energies within each orbital space. One application where locking might be desirable is a calculation where it is necessary to preserve the ordering of a previous geometry, despite flipping of the orbital energies. For such a case, the LOCK directive can be used to prevent the SCF calculation from changing the ordering, even if the orbital energies change.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#vectors-reorder-keyword","title":"VECTORS REORDER keyword","text":"The mapping of the MO\u2019s to the nuclei can be changed using the REORDER keyword. Once starting vectors have been obtained using any of the possible options, the REORDER keyword moves the MO coefficients between atoms listed in the integer list. This keyword is particularly useful for calculating localized electron and hole states.
This optional keyword requires a list containing the new atom ordering. It is not necessary to provide separate lists for alpha and beta orbitals.
An example of use of the REORDER keyword:
vectors input try1.movecs reorder 2 1 output try2.movecs\n
This directive will cause the initial orbitals to be read from the file \u201ctry1.movecs\u201d. The MO coefficients for the basis functions on atom 2 will be swapped with those on atom 1. The final orbitals obtained in the calculation will be written to the file \u201ctry2.movecs\u201d.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#vectors-rotate-keyword","title":"VECTORS ROTATE keyword","text":"The following example shows how the ROTATE keyword can be used to rotate MO vectors calculated at geometry geom1 to geometry geom2, which has a different rotational orientation:
set geometry geom1\ndft\n vectors input atomic output geom1.mo\nend\ntask dft\nset geometry geom2\ndft\n vectors input rotate geom1 geom1.mo output geom2.mo\nend\ntask dft\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#vectors-fragment-superposition-of-fragment-molecular-orbitals","title":"VECTORS FRAGMENT: Superposition of fragment molecular orbitals","text":"The fragment initial guess is particularly useful in the following instances:
- The system naturally decomposes into molecules that can be treated individually, e.g., a cluster.
- One or more fragments are particularly hard to converge and therefore much time can be saved by converging them independently.
- A fragment (e.g., a metal atom) must be prepared with a specific occupation. This can often be readily accomplished with a calculation on the fragment using dummy charges to model a ligand field.
- The molecular occupation predicted by the atomic initial guess is often wrong for systems with heavy metals which may have partially occupied orbitals with lower energy than some doubly occupied orbitals. The fragment initial guess avoids this problem.
VECTORS [input] fragment <string file1> [<string file2> ...]\n
The molecular orbitals are formed by superimposing the previously generated orbitals of fragments of the molecule being studied. These fragment molecular orbitals must be in the same basis as the current calculation. The input specifies the files containing the fragment molecular orbitals. For instance, in a calculation on the water dimer, one might specify
vectors fragment h2o1.movecs h2o2.movecs\n
where h2o1.movecs contains the orbitals for the first fragment, and h2o2.movecs contains the orbitals for the second fragment.
A complete example of the input for a calculation on the water dimer using the fragment guess is as follows:
start dimer\ntitle \"Water dimer SCF using fragment initial guess\"\ngeometry dimer\n O -0.595 1.165 -0.048\n H 0.110 1.812 -0.170\n H -1.452 1.598 -0.154\n O 0.724 -1.284 0.034\n H 0.175 -2.013 0.348\n H 0.177 -0.480 0.010\nend\ngeometry h2o1\n O -0.595 1.165 -0.048\n H 0.110 1.812 -0.170\n H -1.452 1.598 -0.154\nend\ngeometry h2o2\n O 0.724 -1.284 0.034\n H 0.175 -2.013 0.348\n H 0.177 -0.480 0.010\nend\nbasis\n o library 3-21g\n h library 3-21g\nend\nset geometry h2o1\nscf; vectors input atomic output h2o1.movecs; end\ntask scf\nset geometry h2o2\nscf; vectors input atomic output h2o2.movecs; end\ntask scf\nset geometry dimer\nscf\nvectors input fragment h2o1.movecs h2o2.movecs \\\n output dimer.movecs\nend\ntask scf\n
First, the geometry of the dimer and the two monomers are specified and given names. Then, after the basis specification, calculations are performed on the fragments by setting the geometry to the appropriate fragment (SET) and redirecting the output molecular orbitals to an appropriately named file. Note also that use of the atomic initial guess is forced, since the default initial guess is to use any existing MOs which would not be appropriate for the second fragment calculation. Finally, the dimer calculation is performed by specifying the dimer geometry, indicating use of the fragment guess, and redirecting the output MOs.
The following points are important in using the fragment initial guess:
- The fragment calculations must be in the same basis set as the full calculation.
- The order of atoms in the fragments and the order in which the fragment files are specified must be such that when the fragment basis sets are concatenated all the basis functions are in the same order as in the full system. This is readily accomplished by first generating the full geometry with atoms for each fragment contiguous, splitting this into numbered fragments and specifying the fragment MO files in the correct order on the
VECTORS directive. - The occupation of orbitals is preserved when they are merged from the fragments to the full molecule and the resulting occupation must match the requested occupation for the full molecule. E.g., a triplet ROHF calculation must be comprised of fragments that have a total of exactly two open-shell orbitals.
- Because of these restrictions, it is not possible to introduce additional atoms (or basis functions) into fragments for the purpose of cleanly breaking real bonds. However, it is possible, and highly recommended, to introduce additional point charges to simulate the presence of other fragments.
- MO vectors of partially occupied or strongly polarized systems are very sensitive to orientation. While it is possible to specify the same fragment MO vector file multiple times in the
VECTORS directive, it is usually much better to do a separate calculation for each fragment. - Linear dependencies which were present in a fragment calculation may be magnified in the full calculation. When this occurs, some of the fragment\u2019s highest virtual orbitals will not be copied to the full system, and a warning will be printed.
A more involved example is now presented. We wish to model the sextet state of Fe(III) complexed with water, imidazole and a heme with a net unit positive charge. The default atomic guess does not give the correct d5 occupation for the metal and also gives an incorrect state for the double anion of the heme. The following performs calculations on all of the fragments. Things to note are:
- The use of a dummy +2 charge in the initial guess on the heme which in part simulates the presence of the metal ion, and also automatically forces an additional two electrons to be added to the system (the default net charge being zero).
- The iron fragment calculation (charge +3, d5, sextet) will yield the correct open-shell occupation for the full system. If, instead, the d-orbitals were partially occupied (e.g., the doublet state) it would be useful to introduce dummy charges around the iron to model the ligand field and thereby lift the degeneracy to obtain the correct occupation.
- Cs symmetry is used for all of the calculations. It is not necessary that the same symmetry be used in all of the calculations, provided that the order and orientation of the atoms is preserved.
- The unset scf:* directive is used immediately before the calculation on the full system so that the default name for the output MO vector file can be used, rather than having to specify it explicitly.
start heme6a1\ntitle \"heme-H2O (6A1) from M.Dupuis\"\n############################################################\n# Define the geometry of the full system and the fragments #\n############################################################\ngeometry full-system\n symmetry cs\n H 0.438 -0.002 4.549\n C 0.443 -0.001 3.457\n C 0.451 -1.251 2.828\n C 0.452 1.250 2.828\n H 0.455 2.652 4.586\n H 0.461 -2.649 4.586\n N1 0.455 -1.461 1.441\n N1 0.458 1.458 1.443\n C 0.460 2.530 3.505\n C 0.462 -2.530 3.506\n C 0.478 2.844 1.249\n C 0.478 3.510 2.534\n C 0.478 -2.848 1.248\n C 0.480 -3.513 2.536\n C 0.484 3.480 0.000\n C 0.485 -3.484 0.000\n H 0.489 4.590 2.664\n H 0.496 -4.592 2.669\n H 0.498 4.573 0.000\n H 0.503 -4.577 0.000\n H -4.925 1.235 0.000\n H -4.729 -1.338 0.000\n C -3.987 0.685 0.000\n N -3.930 -0.703 0.000\n C -2.678 1.111 0.000\n C -2.622 -1.076 0.000\n H -2.284 2.126 0.000\n H -2.277 -2.108 0.000\n N -1.838 0.007 0.000\n Fe 0.307 0.000 0.000\n O 2.673 -0.009 0.000\n H 3.238 -0.804 0.000\n H 3.254 0.777 0.000\nend\ngeometry ring-only\n symmetry cs\n H 0.438 -0.002 4.549\n C 0.443 -0.001 3.457\n C 0.451 -1.251 2.828\n C 0.452 1.250 2.828\n H 0.455 2.652 4.586\n H 0.461 -2.649 4.586\n N1 0.455 -1.461 1.441\n N1 0.458 1.458 1.443\n C 0.460 2.530 3.505\n C 0.462 -2.530 3.506\n C 0.478 2.844 1.249\n C 0.478 3.510 2.534\n C 0.478 -2.848 1.248\n C 0.480 -3.513 2.536\n C 0.484 3.480 0.000\n C 0.485 -3.484 0.000\n H 0.489 4.590 2.664\n H 0.496 -4.592 2.669\n Bq 0.307 0.0 0.0 charge 2 # simulate the iron\nend\ngeometry imid-only\n symmetry cs\n H 0.498 4.573 0.000\n H 0.503 -4.577 0.000\n H -4.925 1.235 0.000\n H -4.729 -1.338 0.000\n C -3.987 0.685 0.000\n N -3.930 -0.703 0.000\n C -2.678 1.111 0.000\n C -2.622 -1.076 0.000\n H -2.284 2.126 0.000\n H -2.277 -2.108 0.000\n N -1.838 0.007 0.000\nend\ngeometry fe-only\n symmetry cs\n Fe .307 0.000 0.000\nend\ngeometry water-only\n symmetry cs\n O 2.673 -0.009 0.000\n H 3.238 -0.804 0.000\n H 3.254 0.777 0.000\nend\n############################\n# Basis set for everything #\n############################\nbasis nosegment\n O library 6-31g*\n N library 6-31g*\n C library 6-31g*\n H library 6-31g*\n Fe library \"Ahlrichs pVDZ\"\nend\n##########################################################\n# SCF on the fragments for initial guess for full system #\n##########################################################\nscf; thresh 1e-2; end\nset geometry ring-only\nscf; vectors atomic swap 80 81 output ring.mo; end\ntask scf\nset geometry water-only\nscf; vectors atomic output water.mo; end\ntask scf\nset geometry imid-only\nscf; vectors atomic output imid.mo; end\ntask scf\ncharge 3\nset geometry fe-only\nscf; sextet; vectors atomic output fe.mo; end\ntask scf\n##########################\n# SCF on the full system #\n##########################\nunset scf:* # This restores the defaults\ncharge 1\nset geometry full-system\nscf\n sextet\n vectors fragment ring.mo imid.mo fe.mo water.mo\n maxiter 50\nend\ntask scf\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#example-of-projecting-smaller-basis-into-larger-basis","title":"Example of projecting smaller basis into larger basis","text":"Key ingredient needed: definition of both the smaller and the larger basis set, plus mention of the small basis set in the \u201cinput project\u201d line.
start he\n\n geometry\n he 0 0 0\n symmetry oh\n end\n\n basis small\n * library sto-3g\n end\n basis large\n * library 3-21g\n end\n\n set \"ao basis\" small\n scf\n vectors input atomic output small.mos\n end\n task scf \n\n set \"ao basis\" large\n scf\n vectors input project small small.mos output large.mos\n end\n task scf\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#atomic-guess-orbitals-with-charged-atoms","title":"Atomic guess orbitals with charged atoms","text":"As noted above, the default guess vectors are based on superimposing the density matrices of the neutral atoms. If some atoms are significantly charged, this default guess may be improved upon by modifying the atomic densities. This is done by setting parameters that add fractional charges to the occupation of the valence atomic orbitals. Since the atomic SCF program does not have its own input block, the SET directive (SET) must be used to set these parameters.
The input specifies a list of tags (i.e., names of atoms in a geometry, see GEOMETRY) and the charges to be added to those centers. Two parameters must be set as follows:
set atomscf:tags_z <string list_of_tags> \n set atomscf:z <real list_of_charges>\n
The array of strings atomscf:tags_z should be set to the list of tags, and the array atomscf:z should be set to the list of charges which must be real numbers (not integers). All atoms that have a tag specified in the list of tags will be assigned the corresponding charge from the list of charges.
For example, the following specifies that all oxygen atoms with tag O be assigned a charge of -1 and all iron atoms with tag Fe be assigned a charge of +2
set atomscf:z -1 2.0 \n set atomscf:tags_z O Fe\n
There are some limitations to this feature. It is not possible to add electrons to closed shell atoms, nor is it possible to remove all electrons from a given atom. Attempts to do so will cause the code to report an error, and it will not report further errors in the input for modifying the charge even when they are detected.
Finally, recall that the database is persistent (Data persistence) and that the modified settings will be used in subsequent atomic guess calculations unless the data is deleted from the database with the UNSET directive (UNSET).
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#accuracy-of-initial-guess","title":"Accuracy of initial guess","text":"For SCF, the initial Fock-matrix construction from the atomic guess is performed to a default precision of 1e-7. However, other wavefunctions, notably DFT, use a lower precision. In charged, or diffuse basis sets, this precision may not be sufficient and could result in incorrect ordering of the initial orbitals. The accuracy may be increased with the following directive which should be inserted in the top-level of input (i.e., outside of the SCF input block) and before the TASK directive.
set tolguess 1e-7\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#thresh-convergence-threshold","title":"THRESH \u2013 convergence threshold","text":" THRESH <real thresh default 1.0e-4>\n
This directive specifies the convergence threshold for the calculation. The convergence threshold is the norm of the orbital gradient, and has a default value in the code of 10-4.
The norm of the orbital gradient corresponds roughly to the precision available in the wavefunction, and the energy should be converged to approximately the square of this number. It should be noted, however, that the precision in the energy will not exceed that of the integral screening tolerance. This tolerance (Integral screening threshold) is automatically set from the convergence threshold, so that sufficient precision is usually available by default.
The default convergence threshold suffices for most SCF energy and geometry optimization calculations, providing about 6-8 decimal places in the energy, and about four significant figures in the density and energy derivative with respect to nuclear coordinates. However, greater precision may be required for calculations involving weakly interacting systems, floppy molecules, finite-difference of gradients to compute the Hessian, and for post-Hartree-Fock calculations. A threshold of 10-6 is adequate for most such purposes, and a threshold of 10-8 might be necessary for very high accuracy or very weak interactions. A threshold of 10-8 should be regarded as the best that can be attained in most circumstances.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#maxiter-iteration-limit","title":"MAXITER \u2013 iteration limit","text":" MAXITER <integer maxiter default 8>\n
The maximum number of iterations for the SCF calculation defaults to 20 for both ROHF/RHF and UHF calculations. For most molecules, this number of iterations is more than sufficient for the quadratically convergent SCF algorithm to obtain a solution converged to the default threshold (see Convergence threshold above). If the SCF program detects that the quadratically convergent algorithm is not efficient, then it will resort to a linearly convergent algorithm and increase the maximum number of iterations by 10.
Convergence may not be reached in the maximum number of iterations for many reasons, including input error (e.g., an incorrect geometry or a linearly dependent basis), a very low convergence threshold, a poor initial guess, or the fact that the system is intrinsically hard to converge due to the presence of many states with similar energies.
The following sets the maximum number of SCF iterations to 50:
maxiter 50\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#profile-performance-profile","title":"PROFILE \u2013 performance profile","text":"This directive allows the user to obtain timing and parallel execution information about the SCF module. It is specified by the simple keyword
PROFILE\n
This option can be helpful in understanding the computational performance of an SCF calculation. However, it can introduce a significant overhead on machines that have expensive timing routines, such as the SUN.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#diis-diis-convergence","title":"DIIS \u2013 DIIS convergence","text":"This directive allows the user to specify DIIS convergence rather than second-order convergence for the SCF calculation. The form of the directive is as follows:
DIIS\n
The implementation of this option is currently fairly rudimentary. It does not have level-shifting and damping, and does not support open shells or UHF. It is provided on an \u201cas is\u201d basis, and should be used with caution.
When the DIIS directive is specified in the input, the user has the additional option of specifying the size of the subspace for the DIIS extrapolation. This is accomplished with the DIISBAS directive, which is of the form:
DIISBAS <integer diisbas default 5>\n
The default of 5 should be adequate for most applications, but may be increased if convergence is poor. On large systems, it may be necessary to specify a lower value for diisbas, to conserve memory.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#direct-and-semidirect-recomputation-of-integrals","title":"DIRECT and SEMIDIRECT: recomputation of integrals","text":"In the context of SCF calculations direct means that all integrals are recomputed as required and none are stored. The other extreme are disk- or memory-resident (sometimes termed conventional) calculations in which all integrals are computed once and stored. Semi-direct calculations are between these two extremes with some integrals being precomputed and stored, and all other integrals being recomputed as necessary.
The default behavior of the SCF module is
- If enough memory is available, the integrals are computed once and are cached in memory.
- If there is not enough memory to store all the integrals at once, then 95% of the available disk space in the scratch directory (see File directories) is assumed to be available for this purpose, and as many integrals as possible are cached on disk (with no memory being used for caching). Some attempt is made to store the most expensive integrals in the cache.
- If there is not enough room in memory or on disk for all the integrals, then the ones that are not cached are recomputed in a semidirect fashion.
The integral file is deleted at the end of a calculation, so it is not possible to restart a semidirect calculation when the integrals are cached in memory or on disk. Many modern computer systems clear the fast scratch space at the end of each job, adding a further complication to the problem of restarting a parallel semidirect calculation.
A fully direct calculation (with recomputation of the integrals at each iteration) is forced by specifying the directive
DIRECT\n
Alternatively, the SEMIDIRECT directive can be used to control the default semidirect calculation by defining the amount of disk space and the cache memory size. The form of this directive is as follows:
SEMIDIRECT [filesize <integer filesize default disksize>] \n [memsize <integer memsize default available>] \n [filename <string filename default $file_prefix.aoints$]\n
The keyword FILESIZE allows the user to specify the amount of disk space to be used per process for storing the integrals in 64-bit words. Similarly, the keyword MEMSIZE allows the user to specify the number of 64-bit words to be used per process for caching integrals in memory. (Note: If the amount of storage space specified by the entry for memsize is not available, the code cuts the value in half and checks again for available space. This process is repeated until the request is satisfied.)
By default, the integral files are placed into the scratch directory (see File directories). Specifying the keyword FILENAME overrides this default. The user-specified name entered in the string filename has the process number appended to it, so that each process has a distinct file but with a common base-name and directory. Therefore, it is not possible to use this keyword to specify different disks for different processes. The SCRATCH_DIR directive (see File directories) can be used for this purpose.
For example, to force full recomputation of all integrals:
direct\n
Exactly the same result could be obtained by entering the directive:
semidirect filesize 0 memsize 0\n
To disable the use of memory for caching integrals and limit disk usage by each process to 100 megawords (MW):
semidirect memsize 0 filesize 100000000\n
The integral records are typically 32769 words long and any non-zero value for filesize or memsize should be enough to hold at least one record.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#integral-file-size-and-format-for-the-scf-module","title":"Integral File Size and Format for the SCF Module","text":"The file format is rather complex, since it accommodates a variety of packing and compression options and the distribution of data. This section presents some information that may help the user understand the output, and illustrates how to use the output information to estimate file sizes.
If integrals are stored with a threshold of greater than 10-10, then the integrals are stored in a 32-bit fixed-point format (with appropriate treatment for large values to retain precision). If integrals are stored with a threshold less than 10-10, however, the values are stored in 64-bit floating-point format. If a replicated-data calculation is being run, then 8 bits are used for each basis function label, unless there are more than 256 functions, in which case 16 bits are used. If distributed data is being used, then the labels are always packed to 8 bits (the distributed blocks always being less than 256; labels are relative to the start of the block).
Thus, the number (W) of 64-bit words required to store N integrals, may be computed as
no. 64-bit words labels values N 8-bit 32-bit 1.5N 16-bit 32-bit 1.5N 8-bit 64-bit 2N 16-bit 64-bit Table 1: number (W) of 64-bit words required to store N integrals
The actual number of words required can exceed this computed value by up to one percent, due to bookkeeping overhead, and because the file itself is organized into fixed-size records.
With at least the default print level, all semidirect (not direct) calculations will print out information about the integral file and the number of integrals computed. The form of this output is as follows:
Integral file = ./c6h6.aoints.0\nRecord size in doubles = 32769 No. of integs per rec = 32768\nMax. records in memory = 3 Max. records in file = 5\nNo. of bits per label = 8 No. of bits per value = 32\n#quartets = 2.0D+04 #integrals = 7.9D+05 direct = 63.6% cached = 36.4%\n
The file information above relates only to process 0. The line of information about the number of quartets, integrals, etc., is a sum over all processes.
When the integral file is closed, additional information of the following form is printed:
------------------------------------------------------------\nEAF file 0: \"./c6h6.aoints.0\" size=262152 bytes\n------------------------------------------------------------\n write read awrite aread wait\n ----- ---- ------ ----- ----\n calls: 6 12 0 0 0\n data(b): 1.57e+06 3.15e+06 0.00e+00 0.00e+00\n time(s): 1.09e-01 3.12e-02 0.00e+00\nrate(mb/s): 1.44e+01 1.01e+02\n------------------------------------------------------------\n Parallel integral file used 4 records with 0 large values\n
Again, the detailed file information relates just to process 0, but the final line indicates the total number of integral records stored by all processes.
This information may be used to optimize subsequent calculations, for instance by assigning more memory or disk space.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#scf-convergence-control-options","title":"SCF Convergence Control Options","text":"Note to users: It is desired that the SCF program converge reliably with the default options for a wide variety of molecules. In addition, it should be guaranteed to converge for any system, with sufficient iterations.
The SCF program uses a preconditioned conjugate gradient (PCG) method that is unconditionally convergent. Basically, a search direction is generated by multiplying the orbital gradient (the derivative of the energy with respect to the orbital rotations) by an approximation to the inverse of the level-shifted orbital Hessian. In the initial iterations (see Controlling the Newton-Raphson), an inexpensive one-electron approximation to the inverse orbital Hessian is used. Closer to convergence, the full orbital Hessian is used, which should provide quadratic convergence. For both the full or one-electron orbital Hessians, the inverse-Hessian matrix-vector product is formed iteratively. Subsequently, an approximate line search is performed along the new search direction. If the exact Hessian is being employed, then the line search should require a single step (of unity). Preconditioning with approximate Hessians may require additional steps, especially in the initial iterations. It is the (approximate) line search that provides the convergence guarantee. The iterations required to solve the linear equations are referred to as micro-iterations. A macro-iteration comprises both the iterative solution and a line search.
Level-shifting plays the same role in this algorithm as it does in the conventional iterative solution of the SCF equations. The approximate Hessian used for preconditioning should be positive definite. If this is not the case, then level-shifting by a positive constant (\u0394) serves to make the preconditioning matrix positive definite, by adding \u0394 to all of its eigenvalues. The level-shifts employed for the RHF orbital Hessian should be approximately four times (only twice for UHF) the value that one would employ in a conventional SCF. Level-shifting is automatically enabled in the early iterations, and the default options suffice for most test cases.
So why do things go wrong and what can be done to fix convergence problems? Most problems encountered so far arise either poor initial guesses or from small or negative eigenvalues of the orbital Hessian. The atomic orbital guess is usually very good. However, in calculations on charged systems, especially with open shells, incorrect initial occupations may result. The SCF might then converge very slowly since very large orbital rotations might be required to achieve the correct occupation or move charge large distances in the molecule. Possible actions are
- Modify the atomic guess by assigning charges to the atoms known to carry substantial charges (Atomic guess)
- Examining an analysis of the initial orbitals (Printing) and then swapping them to attain the desired occupation (VECTORS).
- Converging the calculation in a minimal basis set, which is usually easier, and then projecting into a larger basis set (VECTORS).
- Using the fragment orbital initial guess (Fragment molecular orbitals).
Small or negative Hessian eigenvalues can occur even though the calculation seem to be close to convergence (as measured by the gradient norm, or the off-diagonal Fock matrix elements). Small eigenvalues will cause the iterative linear equation solver to converge slowly, resulting in an excessive number of micro-iterations. This makes the SCF expensive in terms of computation time, and it is possible to exceed the maximum number of iterations without achieving the accuracy required for quadratic convergence \u2013 which causes more macro-iterations to be performed.
Two main options are available when a problem will not converge: Newton-Raphson can be disabled temporarily or permanently (see Controlling the Newton-Raphson), and level-shifting can be applied to the matrix (see Level-shifting). In some cases, both options may be necessary to achieve final convergence.
If there is reason to suspect a negative eigenvalue, the first course is to disable the Newton-Raphson iteration until the solution is closer to convergence. It may be necessary to disable it completely. At some point close to convergence, the Hessian will be positive definite, so disabling Newton-Raphson should yield a solution with approximately the same convergence rate as DIIS.
If temporarily disabling Newton-Raphson is not sufficient to achieve convergence, it may be necessary to disable it entirely and apply a small level-shift to the approximate Hessian. This should improve the convergence rate of the micro-iterations and stabilize the macro-iterations. The level-shifting will destroy exact quadratic convergence, but the optimization process is automatically adjusted to reflect this by enforcing conjugacy and reducing the accuracy to which the linear equations are solved. The net result of this is that the solution will do more macro-iterations, but each one should take less time than it would with the unshifted Hessian.
The following sections describe the directives needed to disable the Newton-Raphson iteration and specify level-shifting.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#nr-controlling-the-newton-raphson","title":"NR: controlling the Newton-Raphson","text":" NR <real nr_switch default 0.1>\n
The exact orbital Hessian is adopted as the preconditioner when the maximum element of the orbital gradient is below the value specified for nr_switch. The default value is 0.1, which means that Newton-Raphson will be disabled until the maximum value of the orbital gradient (twice the largest off-diagonal Fock matrix element) is less than 0.1. To disable the Newton-Raphson entirely, the value of nr_switch must be set to zero. The directive to accomplish this is as follows:
nr 0\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#level-level-shifting-the-orbital-hessian","title":"LEVEL: level-shifting the orbital Hessian","text":"This directive allows the user to specify level-shifting to obtain a positive-definite preconditioning matrix for the SCF solution procedure. Separate level shifts can be set for the first-order convergent one-electron approximation to the Hessian used with the preconditioned conjugate gradient (PCG) method, and for the full Hessian used with the Newton-Raphson (NR) approach. It is also possible to change the level-shift automatically as the solution attains some specified accuracy. The form of the directive is as follows:
LEVEL [pcg <real initial default 20.0> \\\n [<real tol default 0.5> <real final default 0.0>]] \\\n [nr <real initial default 0.0> \\\n [<real tol default 0.0> <real final default 0.0>]]\n
This directive contains only two keywords: one for the PCG method and the other for the exact Hessian (Newton Raphson, or NR). Use of PCG or NR is determined by the input specified for nr_switch on the NR directive, Controlling the Newton-Raphson above.
Specifying the keyword pcg on the LEVEL directive allows the user to define the level shifting for the approximate (i.e., PCG) method. Specifying the keyword nr allows the user to define the level shifting for the exact Hessians. In both options, the initial level shift is defined by the value specified for the variable initial. Optionally, tol can be specified independently with each keyword to define the level of accuracy that must be attained in the solution before the level shifting is changed to the value specified by input in the real variable final. Level shifts and gradient thresholds are specified in atomic units.
For the PCG method (as specified using the keyword pcg), the defaults for this input are 20.0 for initial, 0.5 for tol, and 0.0 for final. This means that the approximate Hessian will be shifted by 20.0 until the maximum element of the gradient falls below 0.5, at which point the shift will be set to zero.
For the exact Hessian (as specified using the keyword nr), the defaults are all zero. The exact Hessian is usually not shifted since this destroys quadratic convergence. An example of an input directive that applies a shift of 0.2 to the exact Hessian is as follows:
level nr 0.2\n
To apply this shift to the exact Hessian only until the maximum element of the gradient falls below 0.005, the required input directive is as follows:
level nr 0.2 0.005 0\n
Note that in both of these examples, the parameters for the PCG method are at the default values. To obtain values different from the defaults, the keyword pcg must also be specified. For example, to specify the level shifting in the above example for the exact Hessian and non-default shifting for the PCG method, the directive would be something like the following:
level pcg 20 0.3 0.0 nr 0.2 0.005 0.0\n
This input will cause the PCG method to be level-shifted by 20.0 until the maximum element of the gradient falls below 0.3, then the shift will be zero. For the exact Hessian, the level shifting is initially 0.2, until the maximum element falls below 0.005, after which the shift is zero.
The default options correspond to
level pcg 20 0.5 0 nr 0 0 0\n
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#orbital-localization","title":"Orbital Localization","text":"The SCF module includes an experimental implementation of orbital localization, including Foster-Boys and Pipek-Mezey which only works for closed-shell (RHF) wavefunctions. There is currently no input in the SCF block to control this so the SET directive (SET) must be used.
The directive
set scf:localize t\n
will separately localize the core, valence, and virtual orbital spaces using the Pipek-Mezey algorithm. If the additional directive
set scf:loctype FB\n
is included, then the Foster-boys algorithm is used. The partitioning of core-orbitals is performed using the atomic information described in the section describing how to freeze the orbitals .
In the next release, this functionality will be extended to included all wavefunctions using molecular orbitals.
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#printing-information-from-the-scf-module","title":"Printing Information from the SCF Module","text":"All output from the SCF module is controlled using the PRINT directive described in Print control. The following list describes the items from SCF that are currently under direct print control, along with the print level for each one.
Name Print Level Description \u201catomic guess density\u201d debug guess density matrix \u201catomic scf\u201d debug details of atomic SCF \u201cmo guess\u201d default brief info from mo guess \u201cinformation\u201d low results \u201cinitial vectors\u201d debug \u201cintermediate vectors\u201d debug \u201cfinal vectors\u201d debug \u201cfinal vectors analysis\u201d default \u201cinitial vectors analysis\u201d never \u201cintermediate evals\u201d debug \u201cfinal evals\u201d default \u201cschwarz\u201d high integral screening info stats at completion \u201cscreening statistics\u201d debug display stats after every Fock build \u201cgeometry\u201d high \u201csymmetry\u201d debug detailed symmetry info \u201cbasis\u201d high \u201cgeombas\u201d debug detailed basis map info \u201cvectors i/o\u201d default report vectors I/O \u201cparameters\u201d default convergence parameters \u201cconvergence\u201d default info each iteration \u201cmulliken ao\u201d never Mulliken population of basis functions Table 2: SCF Print Control Specifications
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#hartree-fock-or-scf-mcscf-and-mp2-gradients","title":"Hartree-Fock or SCF, MCSCF and MP2 Gradients","text":"The input for this directive allows the user to adjust the print control for the SCF, UHF, ROHF, MCSCF and MP2 gradients. The form of the directive is as follows:
GRADIENTS \n [print || noprint] ... \n END\n
The complementary keyword pair print and noprint allows the user some additional control on the information that can be included in the print output from the SCF calculation. Currently, only a few items can be explicitly invoked via print control. These are as follows:
Name Print Level Description \u201cinformation\u201d low calculation info \u201cgeometry\u201d high geometry information \u201cbasis\u201d high basis set(s) used \u201cforces\u201d low details of force components \u201ctiming\u201d default timing for each phase Table 3: Gradient Print Control Specifications
"},{"location":"Hartree-Fock-Theory-for-Molecules.html#references","title":"References","text":" -
Wong, A. T. and Harrison, R. J. (1995) \u201cApproaches to large-scale parallel self-consistent field calculation\u201d, J. Comp. Chem. 16, 1291-1300, DOI: 10.1002/jcc.540161010 \u21a9
-
Foster, I. T.; Tilson, J. L.; Wagner, A. F.; Shepard, R. L.; Harrison, R. J.; Kendall, R. A. and Littlefield, R. J. (1996) \u201cToward high-performance computational chemistry: I. Scalable Fock matrix construction algorithms\u201d, J. Comp. Chem. 17, 109-123, DOI: 10.1002/(SICI)1096-987X(19960115)17:1<109::AID-JCC9>3.0.CO;2-V \u21a9
"},{"location":"Hessians-and-Vibrational-Frequencies.html","title":"Hessians","text":""},{"location":"Hessians-and-Vibrational-Frequencies.html#overview","title":"Overview","text":"This section relates to the computation of analytic hessians which are available for open and closed shell SCF, except ROHF and for closed shell and unrestricted open shell DFT [1]. Analytic hessians are not currently available for SCF or DFT calculations relativistic all-electron methodologies or for charge fitting with DFT. The current algorithm is fully in-core and does not use symmetry.
There is no required input for the Hessian module. This module only impacts the hessian calculation. For options for calculating the frequencies, please see the Vibrational module.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#hessian-module-input","title":"Hessian Module Input","text":"All input for the Hessian Module is optional since the default definitions are usually correct for most purposes. The generic module input begins with hessian and has the form:
hessian \n thresh <real tol default 1d-6>\n print ... \n profile \n end\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#defining-the-wavefunction-threshold","title":"Defining the wavefunction threshold","text":"You may modify the default threshold for the wavefunction. This keyword is identical to THRESH in the SCF, and the CONVERGENCE gradient in the DFT. The usual defaults for the convergence of the wavefunction for single point and gradient calculations is generally not tight enough for analytic hessians. Therefore, the hessian, by default, tightens these up to 1d-6 and runs an additional energy point if needed. If, during an analytic hessian calculation, you encounter an error:
cphf_solve:the available MOs do not satisfy the SCF equations\n
the convergence criteria of the wavefunction generally needs to be tightened.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#profile","title":"Profile","text":"The PROFILE keyword provides additional information concerning the computation times of different sections of the hessian code. Summary information is given about the maximum, minimum and average times that a particular section of the code took to complete. This is normally only useful for developers.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#print-control","title":"Print Control","text":"Known controllable print options are shown in the table below:
Name Print Level Description \u201chess_follow\u201d high more information about where the calculation is \u201ccphf_cont\u201d debug detailed CPHF information \u201cnucdd_cont\u201d debug detailed nuclear contribution information \u201conedd_cont\u201d debug detailed one electron contribution information \u201ctwodd_cont\u201d debug detailed two electron contribution information \u201cfock_xc\u201d debug detailed XC information during the fock builds
Hessian Print Control Specifications
"},{"location":"Hessians-and-Vibrational-Frequencies.html#vibrational-frequencies","title":"Vibrational frequencies","text":"The nuclear hessian which is used to compute the vibrational frequencies can be computed by finite difference for any ab initio wave-function that has analytic gradients or by analytic methods for SCF and DFT (see Hessians for details). The appropriate nuclear hessian generation algorithm is chosen based on the user input when TASK frequencies is the task directive.
The vibrational package was integrated from the Utah Messkit and can use any nuclear hessian generated from the driver routines, finite difference routines or any analytic hessian modules. There is no required input for the \u201cVIB\u201d package. VIB computes the Infra Red frequencies and intensities for the computed nuclear hessian and the \u201cprojected\u201d nuclear hessian. The VIB module projects out the translations and rotations of the nuclear hessian using the standard Eckart projection algorithm. It also computes the zero point energy for the molecular system based on the frequencies obtained from the projected hessian.
The default mass of each atom is used unless an alternative mass is provided via the geometry input or redefined using the vibrational module input. The default mass is the mass of the most abundant isotope of each element. If the abundance was roughly equal, the mass of the isotope with the longest half life was used.
In addition, the vibrational analysis is given at the default standard temperature of 298.15 degrees.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#vibrational-module-input","title":"Vibrational Module Input","text":"All input for the Vibrational Module is optional since the default definitions will compute the frequencies and IR intensities. The generic module input can begin with vib, freq, frequency and has the form:
{freq || vib || frequency}` \n [reuse [<string hessian_filename>]] \n [mass <integer lexical_index> <real new_mass>] \n [mass <string tag_identifier> <real new_mass>] \n [{temp || temperature} <integer number_of_temperatures>\\ \n <real temperature1 temperature2 ...>] \n [animate [<real step_size_for_animation>]] \n [fd_delta [<real step_size_for_fd_hessian>]] \n [filename <string file_set_name> [overwrite]] \n end\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#hessian-file-reuse","title":"Hessian File Reuse","text":"By default the task frequencies directive will recompute the hessian. To reuse the previously computed hessian you need only specify reuse in the module input block. If you have stored the hessian in an alternate place you may redirect the reuse directive to that file by specifying the path to that file.
reuse /path_to_hessian_file\n
This will reuse your saved Hessian data but one caveat is that the geometry specification at the point where the hessian is computed must be the default \u201cgeometry\u201d on the current run-time-data-base for the projection to work properly.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#redefining-masses-of-elements","title":"Redefining Masses of Elements","text":"You may also modify the mass of a specific center or a group of centers via the input.
To modify the mass of a specific center you can simply use:
mass 3 4.00260324\n
which will set the mass of center 3 to 4.00260324 AMUs. The lexical index of centers is determined by the geometry object.
To modify all Hydrogen atoms in a molecule you may use the tag based mechanism:
mass hydrogen 2.014101779\n
The mass redefinitions always start with the default masses and change the masses in the order given in the input. Care must be taken to change the masses properly. For example, if you want all hydrogens to have the mass of Deuterium and the third hydrogen (which is the 6th atomic center) to have the mass of Tritium you must set the Deuterium masses first with the tag based mechanism and then set the 6th center\u2019s mass to that of Tritium using the lexical center index mechanism.
The mass redefinitions are not fully persistent on the run-time-data-base. Each input block that redefines masses will invalidate the mass definitions of the previous input block. For example,
freq\n reuse\n mass hydrogen 2.014101779\nend\ntask scf frequencies\nfreq\n reuse\n mass oxygen 17.9991603\nend\ntask scf frequencies\n
will use the new mass for all hydrogens in the first frequency analysis. The mass of the oxygen atoms will be redefined in the second frequency analysis but the hydrogen atoms will use the default mass. To get a modified oxygen and hydrogen analysis you would have to use:
freq\n reuse\n mass hydrogen 2.014101779\nend\ntask scf frequencies\nfreq\n reuse\n mass hydrogen 2.014101779\n mass oxygen 17.9991603\nend\ntask scf frequencies\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#temp-or-temperature","title":"Temp or Temperature","text":"The \u201cVIB\u201d module can generate the vibrational analysis at various temperatures other than at standard room temperature. Either temp or temperature can be used to initiate this command.
To modify the temperature of the computation you can simply use:
temp 4 298.15 300.0 350.0 400.0\n
At this point, the temperatures are persistant and so the user must \u201creset\u201d the temperature if the standard behavior is required after setting the temperatures in a previous \u201cVIB\u201d command, i.e.
temp 1 298.15\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#animation","title":"Animation","text":"The \u201cVIB\u201d module also can generate mode animation input files in the standard xyz file format for graphics packages like RasMol or XMol There are scripts to automate this for RasMol in $NWCHEM_TOP/contrib/rasmolmovie. Each mode will have 20 xyz files generated that cycle from the equilibrium geometry to 5 steps in the positive direction of the mode vector, back to 5 steps in the negative direction of the mode vector, and finally back to the equilibrium geometry. By default these files are not generated. To activate this mechanism simply use the following input directive
animate\n
anywhere in the frequency/vib input block.
Given an ordered list of files containing molecular coordinates in XYZ format, the rasmolmovie shell script generates an animated gif for each of the six possible views down a Cartesian axis.
It uses the free utilities
- rasmol https://www.umass.edu/microbio/rasmol/ to manipulate the molecule and generate the individual frames
- convert from ImageMagick https://www.imagemagick.org to combine the frames into an animated gif
It should be easy to modify the script to other file formats or animation tools.
"},{"location":"Hessians-and-Vibrational-Frequencies.html#controlling-the-step-size-along-the-mode-vector","title":"Controlling the Step Size Along the Mode Vector","text":"By default, the step size used is 0.15 a.u. which will give reliable animations for most systems. This can be changed via the animate input directive, e.g.
vib\n animate 0.20\nend\n
where is the real number that is the magnitude of each step along the eigenvector of each nuclear hessian mode in atomic units."},{"location":"Hessians-and-Vibrational-Frequencies.html#specifying-filenames-for-animated-normal-modes","title":"Specifying filenames for animated normal modes","text":"
By default, normal modes will be stored in files that start with \u201cfreq.m-\u201c. This is inconvenient if more than vibrational analysis is run in a single input file. To specify different filename for a particular vibrational analysis use the directive
filename <file_set_name> [overwrite]\n
where is the name that will be prepended to the usual filenames. In addition the code by default requires all files to be new files. When the option \u201coverwrite\u201d is provided any pre-existing files will simply be overwritten."},{"location":"Hessians-and-Vibrational-Frequencies.html#controlling-the-step-size-of-the-finite-difference-hessian","title":"Controlling the Step Size of the Finite difference Hessian","text":"
By default, the step size used for calculating the finite difference Hessian is 0.010 a.u. for DFT and NWPW modules, and 0.001 a.u. otherwise This can be changed via the fd_delta input directive, e.g.
vib\n fd_delta 0.005\nend\n
where is the real number that is the magnitude of each displacement in atomic units for the calculation of the finite difference Hessian. For older versions of NWChem without the fd_delta option just set the \u201cstpr_gen:delta\u201d value on the runtime database, e.g.
set stpr_gen:delta 0.005\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#an-example-input-deck","title":"An Example Input Deck","text":"This example input deck will optimize the geometry for the given basis set, compute the frequencies for H2O, H2O at different temperatures, D2O, HDO, and TDO.
start h2o\ntitle Water \ngeometry units au autosym\n O 0.00000000 0.00000000 0.00000000\n H 0.00000000 1.93042809 -1.10715266\n H 0.00000000 -1.93042809 -1.10715266\nend\nbasis noprint\n H library sto-3g \n O library sto-3g\nend\nscf; thresh 1e-6; end\ndriver; tight; end\ntask scf optimize\n\nscf; thresh 1e-8; print none; end\ntask scf freq \n\nfreq\n reuse; temp 4 298.15 300.0 350.0 400.0\nend\ntask scf freq\n\nfreq \n reuse; mass H 2.014101779\n temp 1 298.15\nend\ntask scf freq\n\nfreq\n reuse; mass 2 2.014101779\nend\ntask scf freq\n\nfreq\n reuse; mass 2 2.014101779 ; mass 3 3.01604927\nend\ntask scf freq\n
"},{"location":"Hessians-and-Vibrational-Frequencies.html#references","title":"References","text":" - Johnson, B.G. and Frisch, M.J. (1994) \u201cAn implementation of analytic second derivatives of the gradient-corrected density functional energy\u201d, Journal of Chemical Physics 100 7429-7442, DOI:10.1063/1.466887
"},{"location":"Home.html","title":"NWChem User Documentation","text":""},{"location":"Home.html#nwchem-user-documentation","title":"NWChem User Documentation","text":""},{"location":"Home.html#overview","title":"Overview","text":""},{"location":"Home.html#system-description","title":"System Description","text":""},{"location":"Home.html#quantum-mechanical-methods","title":"Quantum Mechanical Methods","text":""},{"location":"Home.html#quantum-molecular-dynamics","title":"Quantum Molecular Dynamics","text":""},{"location":"Home.html#molecular-mechanics","title":"Molecular Mechanics","text":""},{"location":"Home.html#hybrid-approaches","title":"Hybrid Approaches","text":""},{"location":"Home.html#potential-energy-surface-analysis","title":"Potential Energy Surface Analysis","text":""},{"location":"Home.html#electronic-structure-analysis","title":"Electronic Structure Analysis","text":""},{"location":"Home.html#other-capabilities","title":"Other Capabilities","text":""},{"location":"Home.html#examples","title":"Examples","text":" - Supplementary Information
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0a00.0\u00a00.5\n\n=\u00a0operator\u00a031\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a032\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a033\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a034\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a035\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a036\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a037\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a038\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a039\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a040\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a041\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a042\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a043\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a044\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a045\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a046\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a047\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a048\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5 \n
"},{"location":"I4Sm.html","title":"I4Sm","text":" group number = 87\n group name = I4/m\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x+1/2,+y+1/2,+z+1/2\n -x+1/2,-y+1/2,+z+1/2\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y+1/2,-x+1/2,-z+1/2\n -y+1/2,+x+1/2,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 10 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 11 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 12 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 13 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 14 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 15 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 16 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n
"},{"location":"I4Smcm.html","title":"I4Smcm","text":" group number = 140\n group name = I4/mcm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 32\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z+1/2\n +x,-y,-z+1/2\n +y,+x,-z+1/2\n -y,-x,-z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z+1/2\n -x,+y,+z+1/2\n -y,-x,+z+1/2\n +y,+x,+z+1/2\n +x+1/2,+y+1/2,+z+1/2\n -x+1/2,-y+1/2,+z+1/2\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,+y+1/2,-z+1\n +x+1/2,-y+1/2,-z+1\n +y+1/2,+x+1/2,-z+1\n -y+1/2,-x+1/2,-z+1\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y+1/2,-x+1/2,-z+1/2\n -y+1/2,+x+1/2,-z+1/2\n +x+1/2,-y+1/2,+z+1\n -x+1/2,+y+1/2,+z+1\n -y+1/2,-x+1/2,+z+1\n +y+1/2,+x+1/2,+z+1\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 17 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 18 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 19 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 20 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 21 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 1.0\n\n = operator 22 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 1.0\n\n = operator 23 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 1.0\n\n = operator 24 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 1.0\n\n = operator 25 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 26 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 27 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 28 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 29 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 1.0\n\n = operator 30 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 1.0\n\n = operator 31 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 1.0\n\n = operator 32 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 1.0\n
"},{"location":"I4Smmm.html","title":"I4Smmm","text":" group number = 139\n group name = I4/mmm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 32\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z\n +x,-y,-z\n +y,+x,-z\n -y,-x,-z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z\n -x,+y,+z\n -y,-x,+z\n +y,+x,+z\n +x+1/2,+y+1/2,+z+1/2\n -x+1/2,-y+1/2,+z+1/2\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,+y+1/2,-z+1/2\n +x+1/2,-y+1/2,-z+1/2\n +y+1/2,+x+1/2,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y+1/2,-x+1/2,-z+1/2\n -y+1/2,+x+1/2,-z+1/2\n +x+1/2,-y+1/2,+z+1/2\n -x+1/2,+y+1/2,+z+1/2\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 17 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 18 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 19 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 20 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 21 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 22 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 23 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 24 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 25 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 26 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 27 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 28 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 29 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 30 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 31 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 32 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n
"},{"location":"I4_1.html","title":"I4 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a080\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0I4_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z+1/2\n-y,+x+1/2,+z+1/4\n+y+1/2,-x,+z+3/4\n+x+1/2,+y+1/2,+z+1/2\n-x+1,-y+1,+z+1\n-y+1/2,+x+1,+z+3/4\n+y+1,-x+1/2,+z+5/4\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25 \n
"},{"location":"I4_122.html","title":"I4 122","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a098\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0I4_122\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a016\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z+1/2\n-y,+x+1/2,+z+1/4\n+y+1/2,-x,+z+3/4\n-x+1/2,+y,-z+3/4\n+x,-y+1/2,-z+1/4\n+y+1/2,+x+1/2,-z+1/2\n-y,-x,-z\n+x+1/2,+y+1/2,+z+1/2\n-x+1,-y+1,+z+1\n-y+1/2,+x+1,+z+3/4\n+y+1,-x+1/2,+z+5/4\n-x+1,+y+1/2,-z+5/4\n+x+1/2,-y+1,-z+3/4\n+y+1,+x+1,-z+1\n-y+1/2,-x+1/2,-z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\n=\u00a0operator\u00a013\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.25\n\n=\u00a0operator\u00a014\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.0\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5 \n
"},{"location":"I4_132.html","title":"I4 132","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0214\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0I4_132\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a048\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a013\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\u00a01.0\u00a00.0\u00a00.0\u00a00.25\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25\n\n=\u00a0operator\u00a014\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.25\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.25\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.25\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a017\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.25\n\n=\u00a0operator\u00a018\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.25\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\u00a00.0\u00a01.0\u00a00.0\u00a00.25\n\n=\u00a0operator\u00a019\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a020\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.25\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a021\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\u00a00.0\u00a01.0\u00a00.0\u00a00.25\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.25\n\n=\u00a0operator\u00a022\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.25\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a023\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\u00a01.0\u00a00.0\u00a00.0\u00a00.25\n\n=\u00a0operator\u00a024\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a025\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a026\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a027\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.0\n\n=\u00a0operator\u00a028\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a029\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a030\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a031\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\n=\u00a0operator\u00a032\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\n=\u00a0operator\u00a033\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a034\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\n=\u00a0operator\u00a035\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a036\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\n=\u00a0operator\u00a037\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.25\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a038\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.25\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.25\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.25\n\n=\u00a0operator\u00a039\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\n=\u00a0operator\u00a040\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\u00a01.0\u00a00.0\u00a00.0\u00a01.25\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a041\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a01.25\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a042\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a043\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.25\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.25\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.25\n\n=\u00a0operator\u00a044\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\u00a00.0\u00a01.0\u00a00.0\u00a01.25\n\n=\u00a0operator\u00a045\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\u00a00.0\u00a01.0\u00a00.0\u00a00.75\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a046\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.75\n\u00a01.0\u00a00.0\u00a00.0\u00a01.25\n\n=\u00a0operator\u00a047\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\u00a00.0\u00a01.0\u00a00.0\u00a01.25\n\u00a01.0\u00a00.0\u00a00.0\u00a00.75\n\n=\u00a0operator\u00a048\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a01.25\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.25\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.25 \n
"},{"location":"I4_1Sa.html","title":"I4 1Sa","text":" group number = 88\n group name = I4_1/a\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z+1/2\n -y,+x+1/2,+z+1/4\n +y+1/2,-x,+z+3/4\n -x,-y+1/2,-z+1/4\n +x+1/2,+y,-z+3/4\n +y,-x,-z\n -y+1/2,+x+1/2,-z+1/2\n +x+1/2,+y+1/2,+z+1/2\n -x+1,-y+1,+z+1\n -y+1/2,+x+1,+z+3/4\n +y+1,-x+1/2,+z+5/4\n -x+1/2,-y+1,-z+3/4\n +x+1,+y+1/2,-z+5/4\n +y+1/2,-x+1/2,-z+1/2\n -y+1,+x+1,-z+1\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.25\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.75\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.25\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.75\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 10 =\n -1.0 0.0 0.0 1.0\n 0.0 -1.0 0.0 1.0\n 0.0 0.0 1.0 1.0\n\n = operator 11 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 1.0\n 0.0 0.0 1.0 0.75\n\n = operator 12 =\n 0.0 1.0 0.0 1.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 1.25\n\n = operator 13 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 1.0\n 0.0 0.0 -1.0 0.75\n\n = operator 14 =\n 1.0 0.0 0.0 1.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 1.25\n\n = operator 15 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 16 =\n 0.0 -1.0 0.0 1.0\n 1.0 0.0 0.0 1.0\n 0.0 0.0 -1.0 1.0\n\n group number = 88\n group name = I4_1/a\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y,+z+1/2\n -y+3/4,+x+1/4,+z+1/4\n +y+3/4,-x+3/4,+z+3/4\n -x,-y,-z\n +x+1/2,+y,-z+1/2\n +y+1/4,-x+3/4,-z+3/4\n -y+1/4,+x+1/4,-z+1/4\n +x+1/2,+y+1/2,+z+1/2\n -x+1,-y+1/2,+z+1\n -y+5/4,+x+3/4,+z+3/4\n +y+5/4,-x+5/4,+z+5/4\n -x+1/2,-y+1/2,-z+1/2\n +x+1,+y+1/2,-z+1\n +y+3/4,-x+5/4,-z+5/4\n -y+3/4,+x+3/4,-z+3/4\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 3 =\n 0.0 -1.0 0.0 0.75\n 1.0 0.0 0.0 0.25\n 0.0 0.0 1.0 0.25\n\n = operator 4 =\n 0.0 1.0 0.0 0.75\n -1.0 0.0 0.0 0.75\n 0.0 0.0 1.0 0.75\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.25\n -1.0 0.0 0.0 0.75\n 0.0 0.0 -1.0 0.75\n\n = operator 8 =\n 0.0 -1.0 0.0 0.25\n 1.0 0.0 0.0 0.25\n 0.0 0.0 -1.0 0.25\n\n = operator 9 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 10 =\n -1.0 0.0 0.0 1.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 1.0\n\n = operator 11 =\n 0.0 -1.0 0.0 1.25\n 1.0 0.0 0.0 0.75\n 0.0 0.0 1.0 0.75\n\n = operator 12 =\n 0.0 1.0 0.0 1.25\n -1.0 0.0 0.0 1.25\n 0.0 0.0 1.0 1.25\n\n = operator 13 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 14 =\n 1.0 0.0 0.0 1.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 1.0\n\n = operator 15 =\n 0.0 1.0 0.0 0.75\n -1.0 0.0 0.0 1.25\n 0.0 0.0 -1.0 1.25\n\n = operator 16 =\n 0.0 -1.0 0.0 0.75\n 1.0 0.0 0.0 0.75\n 0.0 0.0 -1.0 0.75\n
"},{"location":"I4_1Sacd.html","title":"I4 1Sacd","text":"group number = 142 group name = I4_1/acd crystal system = Tetragonal setting number = 1 number of symmetry operators = 32
+x,+y,+z -x+1/2,-y+1/2,+z+1/2 -y,+x+1/2,+z+1/4 +y+1/2,-x,+z+3/4 -x+1/2,+y,-z+1/4 +x,-y+1/2,-z+3/4 +y+1/2,+x+1/2,-z -y,-x,-z+1/2 -x,-y+1/2,-z+1/4 +x+1/2,+y,-z+3/4 +y,-x,-z -y+1/2,+x+1/2,-z+1/2 +x+1/2,-y+1/2,+z -x,+y,+z+1/2 -y+1/2,-x,+z+1/4 +y,+x+1/2,+z+3/4 +x+1/2,+y+1/2,+z+1/2 -x+1,-y+1,+z+1 -y+1/2,+x+1,+z+3/4 +y+1,-x+1/2,+z+5/4 -x+1,+y+1/2,-z+3/4 +x+1/2,-y+1,-z+5/4 +y+1,+x+1,-z+1/2 -y+1/2,-x+1/2,-z+1 -x+1/2,-y+1,-z+3/4 +x+1,+y+1/2,-z+5/4 +y+1/2,-x+1/2,-z+1/2 -y+1,+x+1,-z+1 +x+1,-y+1,+z+1/2 -x+1/2,+y+1/2,+z+1 -y+1,-x+1/2,+z+3/4 +y+1/2,+x+1,+z+5/4
= operator 1 = 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.0
= operator 2 = -1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.5 0.0 0.0 1.0 0.5
= operator 3 = 0.0 -1.0 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 1.0 0.25
= operator 4 = 0.0 1.0 0.0 0.5 -1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.75
= operator 5 = -1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.0 0.0 0.0 -1.0 0.25
= operator 6 = 1.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.5 0.0 0.0 -1.0 0.75
= operator 7 = 0.0 1.0 0.0 0.5 1.0 0.0 0.0 0.5 0.0 0.0 -1.0 0.0
= operator 8 = 0.0 -1.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.5
= operator 9 = -1.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.5 0.0 0.0 -1.0 0.25
= operator 10 = 1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.0 0.0 0.0 -1.0 0.75
= operator 11 = 0.0 1.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0
= operator 12 = 0.0 -1.0 0.0 0.5 1.0 0.0 0.0 0.5 0.0 0.0 -1.0 0.5
= operator 13 = 1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.5 0.0 0.0 1.0 0.0
= operator 14 = -1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.5
= operator 15 = 0.0 -1.0 0.0 0.5 -1.0 0.0 0.0 0.0 0.0 0.0 1.0 0.25
= operator 16 = 0.0 1.0 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 1.0 0.75
= operator 17 = 1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.5 0.0 0.0 1.0 0.5
= operator 18 = -1.0 0.0 0.0 1.0 0.0 -1.0 0.0 1.0 0.0 0.0 1.0 1.0
= operator 19 = 0.0 -1.0 0.0 0.5 1.0 0.0 0.0 1.0 0.0 0.0 1.0 0.75
= operator 20 = 0.0 1.0 0.0 1.0 -1.0 0.0 0.0 0.5 0.0 0.0 1.0 1.25
= operator 21 = -1.0 0.0 0.0 1.0 0.0 1.0 0.0 0.5 0.0 0.0 -1.0 0.75
= operator 22 = 1.0 0.0 0.0 0.5 0.0 -1.0 0.0 1.0 0.0 0.0 -1.0 1.25
= operator 23 = 0.0 1.0 0.0 1.0 1.0 0.0 0.0 1.0 0.0 0.0 -1.0 0.5
= operator 24 = 0.0 -1.0 0.0 0.5 -1.0 0.0 0.0 0.5 0.0 0.0 -1.0 1.0
= operator 25 = -1.0 0.0 0.0 0.5 0.0 -1.0 0.0 1.0 0.0 0.0 -1.0 0.75
= operator 26 = 1.0 0.0 0.0 1.0 0.0 1.0 0.0 0.5 0.0 0.0 -1.0 1.25
= operator 27 = 0.0 1.0 0.0 0.5 -1.0 0.0 0.0 0.5 0.0 0.0 -1.0 0.5
= operator 28 = 0.0 -1.0 0.0 1.0 1.0 0.0 0.0 1.0 0.0 0.0 -1.0 1.0
= operator 29 = 1.0 0.0 0.0 1.0 0.0 -1.0 0.0 1.0 0.0 0.0 1.0 0.5
= operator 30 = -1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.5 0.0 0.0 1.0 1.0
= operator 31 = 0.0 -1.0 0.0 1.0 -1.0 0.0 0.0 0.5 0.0 0.0 1.0 0.75
= operator 32 = 0.0 1.0 0.0 0.5 1.0 0.0 0.0 1.0 0.0 0.0 1.0 1.25
group number = 142 group name = I4_1/acd crystal system = Tetragonal setting number = 2 number of symmetry operators = 32
+x,+y,+z -x+1/2,-y,+z+1/2 -y+1/4,+x+3/4,+z+1/4 +y+1/4,-x+1/4,+z+3/4 -x+1/2,+y,-z +x,-y,-z+1/2 +y+1/4,+x+3/4,-z+3/4 -y+1/4,-x+1/4,-z+1/4 -x,-y,-z +x+1/2,+y,-z+1/2 +y+3/4,-x+1/4,-z+3/4 -y+3/4,+x+3/4,-z+1/4 +x+1/2,-y,+z -x,+y,+z+1/2 -y+3/4,-x+1/4,+z+1/4 +y+3/4,+x+3/4,+z+3/4 +x+1/2,+y+1/2,+z+1/2 -x+1,-y+1/2,+z+1 -y+3/4,+x+5/4,+z+3/4 +y+3/4,-x+3/4,+z+5/4 -x+1,+y+1/2,-z+1/2 +x+1/2,-y+1/2,-z+1 +y+3/4,+x+5/4,-z+5/4 -y+3/4,-x+3/4,-z+3/4 -x+1/2,-y+1/2,-z+1/2 +x+1,+y+1/2,-z+1 +y+5/4,-x+3/4,-z+5/4 -y+5/4,+x+5/4,-z+3/4 +x+1,-y+1/2,+z+1/2 -x+1/2,+y+1/2,+z+1 -y+5/4,-x+3/4,+z+3/4 +y+5/4,+x+5/4,+z+5/4
= operator 1 = 1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.0
= operator 2 = -1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.0 0.0 0.0 1.0 0.5
= operator 3 = 0.0 -1.0 0.0 0.25 1.0 0.0 0.0 0.75 0.0 0.0 1.0 0.25
= operator 4 = 0.0 1.0 0.0 0.25 -1.0 0.0 0.0 0.25 0.0 0.0 1.0 0.75
= operator 5 = -1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.0 0.0 0.0 -1.0 0.0
= operator 6 = 1.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 -1.0 0.5
= operator 7 = 0.0 1.0 0.0 0.25 1.0 0.0 0.0 0.75 0.0 0.0 -1.0 0.75
= operator 8 = 0.0 -1.0 0.0 0.25 -1.0 0.0 0.0 0.25 0.0 0.0 -1.0 0.25
= operator 9 = -1.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 0.0 0.0 -1.0 0.0
= operator 10 = 1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.0 0.0 0.0 -1.0 0.5
= operator 11 = 0.0 1.0 0.0 0.75 -1.0 0.0 0.0 0.25 0.0 0.0 -1.0 0.75
= operator 12 = 0.0 -1.0 0.0 0.75 1.0 0.0 0.0 0.75 0.0 0.0 -1.0 0.25
= operator 13 = 1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.0 0.0 0.0 1.0 0.0
= operator 14 = -1.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 0.5
= operator 15 = 0.0 -1.0 0.0 0.75 -1.0 0.0 0.0 0.25 0.0 0.0 1.0 0.25
= operator 16 = 0.0 1.0 0.0 0.75 1.0 0.0 0.0 0.75 0.0 0.0 1.0 0.75
= operator 17 = 1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.5 0.0 0.0 1.0 0.5
= operator 18 = -1.0 0.0 0.0 1.0 0.0 -1.0 0.0 0.5 0.0 0.0 1.0 1.0
= operator 19 = 0.0 -1.0 0.0 0.75 1.0 0.0 0.0 1.25 0.0 0.0 1.0 0.75
= operator 20 = 0.0 1.0 0.0 0.75 -1.0 0.0 0.0 0.75 0.0 0.0 1.0 1.25
= operator 21 = -1.0 0.0 0.0 1.0 0.0 1.0 0.0 0.5 0.0 0.0 -1.0 0.5
= operator 22 = 1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.5 0.0 0.0 -1.0 1.0
= operator 23 = 0.0 1.0 0.0 0.75 1.0 0.0 0.0 1.25 0.0 0.0 -1.0 1.25
= operator 24 = 0.0 -1.0 0.0 0.75 -1.0 0.0 0.0 0.75 0.0 0.0 -1.0 0.75
= operator 25 = -1.0 0.0 0.0 0.5 0.0 -1.0 0.0 0.5 0.0 0.0 -1.0 0.5
= operator 26 = 1.0 0.0 0.0 1.0 0.0 1.0 0.0 0.5 0.0 0.0 -1.0 1.0
= operator 27 = 0.0 1.0 0.0 1.25 -1.0 0.0 0.0 0.75 0.0 0.0 -1.0 1.25
= operator 28 = 0.0 -1.0 0.0 1.25 1.0 0.0 0.0 1.25 0.0 0.0 -1.0 0.75
= operator 29 = 1.0 0.0 0.0 1.0 0.0 -1.0 0.0 0.5 0.0 0.0 1.0 0.5
= operator 30 = -1.0 0.0 0.0 0.5 0.0 1.0 0.0 0.5 0.0 0.0 1.0 1.0
= operator 31 = 0.0 -1.0 0.0 1.25 -1.0 0.0 0.0 0.75 0.0 0.0 1.0 0.75
= operator 32 = 0.0 1.0 0.0 1.25 1.0 0.0 0.0 1.25 0.0 0.0 1.0 1.25 ```
"},{"location":"I4_1cd.html","title":"I4 1cd","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0110\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0I4_1cd\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a016\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z+1/2\n-y,+x+1/2,+z+1/4\n+y+1/2,-x,+z+3/4\n+x,-y,+z+1/2\n-x+1/2,+y+1/2,+z\n-y,-x+1/2,+z+3/4\n+y+1/2,+x,+z+1/4\n+x+1/2,+y+1/2,+z+1/2\n-x+1,-y+1,+z+1\n-y+1/2,+x+1,+z+3/4\n+y+1,-x+1/2,+z+5/4\n+x+1/2,-y+1/2,+z+1\n-x+1,+y+1,+z+1/2\n-y+1/2,-x+1,+z+5/4\n+y+1,+x+1/2,+z+3/4\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\n=\u00a0operator\u00a013\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a014\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75 \n
"},{"location":"I4_1md.html","title":"I4 1md","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0109\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0I4_1md\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a016\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z+1/2\n-y,+x+1/2,+z+1/4\n+y+1/2,-x,+z+3/4\n+x,-y,+z\n-x+1/2,+y+1/2,+z+1/2\n-y,-x+1/2,+z+1/4\n+y+1/2,+x,+z+3/4\n+x+1/2,+y+1/2,+z+1/2\n-x+1,-y+1,+z+1\n-y+1/2,+x+1,+z+3/4\n+y+1,-x+1/2,+z+5/4\n+x+1/2,-y+1/2,+z+1/2\n-x+1,+y+1,+z+1\n-y+1/2,-x+1,+z+3/4\n+y+1,+x+1/2,+z+5/4\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25\n\n=\u00a0operator\u00a013\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a014\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a01.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a01.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.25 \n
"},{"location":"I4cm.html","title":"I4cm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0108\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0I4cm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a016\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z\n+y,-x,+z\n+x,-y,+z+1/2\n-x,+y,+z+1/2\n-y,-x,+z+1/2\n+y,+x,+z+1/2\n+x+1/2,+y+1/2,+z+1/2\n-x+1/2,-y+1/2,+z+1/2\n-y+1/2,+x+1/2,+z+1/2\n+y+1/2,-x+1/2,+z+1/2\n+x+1/2,-y+1/2,+z+1\n-x+1/2,+y+1/2,+z+1\n-y+1/2,-x+1/2,+z+1\n+y+1/2,+x+1/2,+z+1\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a013\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a014\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a01.0 \n
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3m","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0229\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Im-3m\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a096\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z\n+x,-y,-z\n+z,+x,+y\n+z,-x,-y\n-z,-x,+y\n-z,+x,-y\n+y,+z,+x\n-y,+z,-x\n+y,-z,-x\n-y,-z,+x\n+y,+x,-z\n-y,-x,-z\n+y,-x,+z\n-y,+x,+z\n+x,+z,-y\n-x,+z,+y\n-x,-z,-y\n+x,-z,+y\n+z,+y,-x\n+z,-y,+x\n-z,+y,+x\n-z,-y,-x\n-x,-y,-z\n+x,+y,-z\n+x,-y,+z\n-x,+y,+z\n-z,-x,-y\n-z,+x,+y\n+z,+x,-y\n+z,-x,+y\n-y,-z,-x\n+y,-z,+x\n-y,+z,+x\n+y,+z,-x\n-y,-x,+z\n+y,+x,+z\n-y,+x,-z\n+y,-x,-z\n-x,-z,+y\n+x,-z,-y\n+x,+z,+y\n-x,+z,-y\n-z,-y,+x\n-z,+y,-x\n+z,-y,-x\n+z,+y,+x\n+x+1/2,+y+1/2,+z+1/2\n-x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,-z+1/2\n+z+1/2,+x+1/2,+y+1/2\n+z+1/2,-x+1/2,-y+1/2\n-z+1/2,-x+1/2,+y+1/2\n-z+1/2,+x+1/2,-y+1/2\n+y+1/2,+z+1/2,+x+1/2\n-y+1/2,+z+1/2,-x+1/2\n+y+1/2,-z+1/2,-x+1/2\n-y+1/2,-z+1/2,+x+1/2\n+y+1/2,+x+1/2,-z+1/2\n-y+1/2,-x+1/2,-z+1/2\n+y+1/2,-x+1/2,+z+1/2\n-y+1/2,+x+1/2,+z+1/2\n+x+1/2,+z+1/2,-y+1/2\n-x+1/2,+z+1/2,+y+1/2\n-x+1/2,-z+1/2,-y+1/2\n+x+1/2,-z+1/2,+y+1/2\n+z+1/2,+y+1/2,-x+1/2\n+z+1/2,-y+1/2,+x+1/2\n-z+1/2,+y+1/2,+x+1/2\n-z+1/2,-y+1/2,-x+1/2\n-x+1/2,-y+1/2,-z+1/2\n+x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,+z+1/2\n-z+1/2,-x+1/2,-y+1/2\n-z+1/2,+x+1/2,+y+1/2\n+z+1/2,+x+1/2,-y+1/2\n+z+1/2,-x+1/2,+y+1/2\n-y+1/2,-z+1/2,-x+1/2\n+y+1/2,-z+1/2,+x+1/2\n-y+1/2,+z+1/2,+x+1/2\n+y+1/2,+z+1/2,-x+1/2\n-y+1/2,-x+1/2,+z+1/2\n+y+1/2,+x+1/2,+z+1/2\n-y+1/2,+x+1/2,-z+1/2\n+y+1/2,-x+1/2,-z+1/2\n-x+1/2,-z+1/2,+y+1/2\n+x+1/2,-z+1/2,-y+1/2\n+x+1/2,+z+1/2,+y+1/2\n-x+1/2,+z+1/2,-y+1/2\n-z+1/2,-y+1/2,+x+1/2\n-z+1/2,+y+1/2,-x+1/2\n+z+1/2,-y+1/2,-x+1/2\n+z+1/2,+y+1/2,+x+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a013\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a014\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a017\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a018\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a019\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a020\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a021\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a022\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a023\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a024\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a025\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a026\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a027\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a028\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a029\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a030\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a031\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a032\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a033\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a034\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a035\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a036\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a037\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a038\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a039\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a040\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a041\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a042\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a043\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a044\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a045\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a046\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a047\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a048\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a049\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a050\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a051\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a052\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a053\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a054\u00a0=\n\u00a00.0\u00a00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"},{"location":"Immm.html","title":"Immm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a071\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Immm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a016\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z\n+x,-y,-z\n-x,-y,-z\n+x,+y,-z\n+x,-y,+z\n-x,+y,+z\n+x+1/2,+y+1/2,+z+1/2\n-x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,-z+1/2\n-x+1/2,-y+1/2,-z+1/2\n+x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a013\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a014\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a015\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a016\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Interface.html","title":"Interfaces to Other Programs","text":"NWChem has interfaces to several different packages which are listed below. In general, the NWChem authors work with the authors of the other packages to make sure that the interface works. However, any problems with the interface should be reported through the github issue page https://github.com/nwchemgit/nwchem/issues
"},{"location":"Interface.html#dirdyvtst-direct-dynamics-for-variational-transition-state-theory","title":"DIRDYVTST \u2013 DIRect Dynamics for Variational Transition State Theory","text":"by Bruce C. Garrett, Environmental Molecular Sciences Laboratory, Pacific Northwest Laboratory, Richland, Washington
Yao-Yuan Chuang and Donald G. Truhlar, Department of Chemistry and Super Computer Institute, University of Minnesota, MN 55455-0431
and interfaced to NWChem by
Ricky A. Kendall, Scalable Computing Laboratory, Ames Laboratory and Iowa State University, Ames, IA 50011
Theresa L. Windus, Environmental Molecular Sciences Laboratory, Pacific Northwest Laboratory, Richland, Washington
If you use the DIRDYVTST portion of NWChem, please use following citation in addition to the usual NWChem citation:
DIRDYVTST, Yao-Yuan Chuang and Donald G. Truhlar, Department of Chemistry and Super Computer Institute, \n University of Minnesota; Ricky A. Kendall,Scalable Computing Laboratory, Ames Laboratory and Iowa State \n University; Bruce C. Garrett and Theresa L. Windus, Environmental Molecular Sciences Laboratory, \n Pacific Northwest Laboratory. `\n
"},{"location":"Interface.html#introduction","title":"Introduction","text":"By using DIRDYVTST, a user can carry out electronic structure calculations with NWChem and use the resulting energies, gradients, and Hessians for direct dynamics calculations with POLYRATE. This program prepares the file30 input for POLYRATE from NWChem electronic structure calculations of energies, gradients and Hessians at the reactant, product, and saddle point geometries and along the minimum energy path. Cartesian geometries for the reactants, products, and saddle points need to be input to this program; optimization of geometries is not performed in this program. Note that DIRDYVTST is based on the DIRDYGAUSS program and is similar to two other programs: DDUTILITIES and GAUSSRATE. Users of this module are encouraged to read the POLYRATE manual since they will need to create the file fu5 input to run calculations with POLYRATE.
Notes about the code:
Input. The code has been written to parallel, as much as possible, the POLYRATE code.
Output. There is one default output file for each DIRDYVTST run - .file30.
Integrators for following the reaction path. Currently the Euler and three Page-McIver (PM) methods are implemented. The PM methods are the local quadratic approximation (LQA), the corrected LQA (CLQA), and the cubic (CUBE) algorithm. The PM methods are implemented so that the Hessian can be reused at intermediate steps at which only the gradient is updated.
"},{"location":"Interface.html#files","title":"Files","text":"Test runs are located in directories in $NWCHEM_TOP/QA/tests. Test runs are available for two systems: H + H2 and OH + H2.
The H + H2 test uses the Euler integration method at the SCF/3-21G level of theory to calculate points along the reaction path. This test is located in the $NWCHEM_TOP/QA/tests/h3tr1 directory.
The OH + H2 test uses the Page-McIver CUBE algorithm to calculate points on the SCF/3-21G surface and does additional single point calculations at the SCF/6-31G* level of theory. This test is located in the $NWCHEM_TOP/QA/tests/oh3tr3 directory.
Note: These tests are set up with SCF, however, other levels of theory can be used. The initial hessian calculations at the reactants, products and saddle point can cause some problems when numerical hessians are required (especially when there is symmetry breaking in the wavefunction).
"},{"location":"Interface.html#detailed-description-of-the-input","title":"Detailed description of the input","text":"The input consists of keywords for NWChem and keywords related to POLYRATE input. The first set of inputs are for NWChem with the general input block of the form:
DIRDYVTST [autosym [real tol default 1d-2] | noautosym] \n [THEORY <string theory> [basis <string basis default \"ao basis\">] \\ \n [ecp <string ecp>] [input <string input>]] \n [SPTHEORY <string theory> [basis <string basis default \"ao basis\">] \n [ecp <string ecp>] [input <string input>`]] \n ...\n END\n
"},{"location":"Interface.html#use-of-symmetry","title":"Use of symmetry","text":"The use of symmetry in the calculation is controlled by the keyword autosym | noautosym which is used as described in the geometry directive. Autosym is on by default. A couple words of warning here. The tolerance related to autosym can cause problems when taking the initial step off of the transition state. If the tolerance is too large and the initial step relatively small, the resulting geometry will be close to a higher symmetry than is really wanted and the molecule will be symmetrized into the higher symmetry. To check this, the code prints out the symmetry at each geometry along the path. It is up to the user to check the symmetry and make sure that it is the required one. In perverse cases, the user may need to turn autosym off (noautosym) if changing the tolerance doesn\u2019t produce the desired results. In the case that autosym is used, the user does not need to worry about the different alignment of the molecule between NWChem and POLYRATE, this is taken care of internally in the DIRDYVTST module.
"},{"location":"Interface.html#basis-specification","title":"Basis specification","text":"The basis name on the theory or sptheory directive is that specified on a basis set directive and not the name of a standard basis in the library. If not specified, the basis set for the sptheory defaults to the theory basis which defaults to \u201cao basis\u201d.
"},{"location":"Interface.html#effective-core-potentials","title":"Effective core potentials","text":"If an effective core potential is specified in the usual fashion outside of the DIRDYVTST input then this will be used in all calculations. If an alternative ECP name (the name specified on the ECP directive in the same manner as done for basis sets) is specified on one of the theory directives, then this ECP will be used in preference for that level of theory.
"},{"location":"Interface.html#general-input-strings","title":"General input strings","text":"For many purposes, the ability to specify the theory, basis and effective core potential is adequate. All of the options for each theory are determined from their independent input blocks. However, if the same theory (e.g., DFT) is to be used with different options for theory and sptheory, then the general input strings must be used. These strings are processed as NWChem input each time the theoretical calculation is invoked. The strings may contain any NWChem input, except for options pertaining to DIRDYVTST and the task directive. The intent is that the strings be used just to control the options pertaining to the theory being used.
A word of caution. Be sure to check that the options are producing the desired results. Since the NWChem database is persistent, the input strings should fully define the calculation you wish to have happen.
For instance, if the theory model is DFT/LDA/3-21g and the sptheory model is DFT/B3LYP/6-311g**, the DIRDYVTST input might look like this
dirdyvtst \n theory dft basis 3-21g input \"dft\\; xc\\; end\" \n sptheory dft basis 6-311g** input \"dft\\; xc b3lyp\\; end\" \n .... \n end\n
The empty XC directive restores the default LDA exchange-correlation functional. Note that semi-colons and other quotation marks inside the input string must be preceded by a backslash to avoid special interpretation.
"},{"location":"Interface.html#polyrate-related-options","title":"POLYRATE related options","text":"These keyword options are simlar to the POLYRATE input format, except there are no ENERGETICS, OPTIMIZATION, SECOND, TUNNELING, and RATE sections.
"},{"location":"Interface.html#general-section","title":"GENERAL section","text":"The GENERAL section has the following format:
* GENERAL\n\n [TITLE <string title>] \n ATOMS \n <integer num> <string tag> [<real mass>] \n ... \n END \n [SINGLEPOINT] \n [SAVEFILE (vecs || hess || spc)\n
Descriptions
TITLE is a keyword that allows the user to input a description of the calculation. In this version, the user can only have a single-line description.
For example:
TITLE Calculation of D + HCl reaction
ATOMS is a list keyword that is used to input a list of the atoms. It is similar to POLYRATE in that the order of the atom and the atomic symbol are required in a single line. If isotope of the element is considered then the atomic mass is required in units of amu.
For example:
ATOMS \n 1 H 2.014 \n 2 H \n 3 Cl \n END`\n
SINGLEPOINT is a keyword that specifies that a single point calculation is to be performed at the reactants, products and saddle point geometries. The type of single point calculation is specified in the sptheory line.
SAVEFILE is a keyword that specifies that NWChem files are to be saved. Allowed values of variable input to SAVEFILE are vecs, hess, and spc for saving the files base theory movecs, base theory hessian and singlepoint calculation movecs.
"},{"location":"Interface.html#react1-react2-prod1-prod2-and-start-sections","title":"REACT1, REACT2, PROD1, PROD2, and START sections","text":"These sections have the following format:
*(REACT1 || REACT2 || PROD1 || PROD2 || START) \n GEOM \n <integer num> <real x y z> \n ... \n END \n SPECIES (ATOMIC || LINRP || NONLINRP || LINTS || NONLINTS default NONLINRP)\n
REACT1 and REACT2 are input for each of the reactants and PROD1 and PROD2 are input for each of the products. REACT1 and PROD1 are required. START is the input for the transition state if one exists, or starting point to follow downhill the MEP.
Descriptions
GEOM is a list keyword that indicates the geometry of the molecule in Cartesian coordinates with atomic unit.
For example:
GEOM \n 1 0.0 0.0 0.0 \n 2 0.0 0.0 1.5 \n END\n
SPECIES is a variable keyword that indicates the type of the molecule. Options are: ATOMIC (atomic reactant or product), LINRP (linear reactant or product), NONLINRP (nonlinear reactant or product), LINTS (linear transition state), and NONLINTS (nonlinear transition state).
For example:
SPECIES atomic
"},{"location":"Interface.html#path-section","title":"PATH section","text":"The Path section has the format:
*PATH \n [SCALEMASS <real scalemass default 1.0>] \n [SSTEP <real sstep default 0.01>] \n [SSAVE <real ssave default 0.1>] \n [SHESS <real shess default SSAVE>] \n [SLP <real slp default 1.0>] \n [SLM <real slm default -1.0>] \n [SIGN (REACTANT || PRODUCT default REACTANT)] \n [INTEGRA (EULER || LQA || CLQA || CUBE default EULER)] \n [PRINTFREQ (on || off default off)]\n
Descriptions
SCALEMASS is a variable keyword that indicates the arbitrary mass (in amu) used for mass-scaled Cartesian coordinates. This is the variable called mu in published papers. Normally, this is taken as either 1.0 amu or, for bimolecular reactions, as the reduced mass of relative translation of the reactants.
SSTEP is a variable keyword that indicates the numerical step size (in bohrs) for the gradient grid. This is the step size for following the minimum energy path.
SSAVE is a variable keyword that indicates the numerical step size (in bohrs) for saving the Hessian grid. At each save point the potential and its first and second derivatives are recalculated and written to the .file30 file. For example, if SSTEP=0.01 and SSAVE=0.1, then the potential information is written to .file30 every 10 steps along the gradient grid.
SHESS is a variable keyword that indicates the numerical step size (in bohrs) for recomputing the Hessian when using a Page-McIver integrator (e.g., LQA, CLQA, or CUBE). For Euler integration SHESS = SSAVE. For intermediate points along the gradient grid, the Hessian matrix from the last Hessian calculation is reused. For example, if SSTEP=0.01 and SHESS=0.05, then the Hessian matrix is recomputed every 5 steps along the gradient grid.
SLP is a variable keyword that indicates the positive limit of the reaction coordinate (in bohrs).
SLM is a variable keyword that indicates the negative limit of the reaction coordinate (in bohrs).
SIGN is a variable keyword used to ensure the conventional definition of the sign of s, s \\< 0 for the reactant side and s > 0 for the product side, is followed. PRODUCT should be used if the eigenvector at the saddle point points toward the product side and REACTANT if the eigenvector points toward the reactant side.
INTEGRA is a variable keyword that indicates the integration method used to follow the reaction path. Options are: EULER, LQA, CLQA, and CUBE.
PRINTFREQ is a variable keyword that indicates that projected frequencies and eigenvectors will be printed along the MEP.
"},{"location":"Interface.html#restart","title":"Restart","text":"DIRDYVTST calculations should be restarted through the normal NWChem mechanism. The user needs to change the start directive to a restart directive and get rid of any information that will overwrite important information in the RTDB. The file.db and file.file30 need to be available for the calculation to restart properly.
"},{"location":"Interface.html#example","title":"Example","text":"This is an example that creates the file30 file for POLYRATE for H + H2. Note that the multiplicity is that of the entire supermolecule, a doublet. In this example, the initial energies, gradients, and Hessians are calculated at the UHF/3-21G level of theory and the singlepoint calculations are calculated at the MP2/cc-pVDZ level of theory with a tighter convergence threshold than the first SCF.
start h3test \n\nbasis \n h library 3-21G \nend \n\nbasis singlepoint \n h library cc-pVDZ \nend \n\nscf \n uhf \n doublet \n thresh 1.0e-6 \nend \n\ndirdyvtst autosym 0.001 \n theory scf input \"scf\\; uhf\\; doublet\\; thresh 1.0e-06\\; end\" \n sptheory mp2 basis singlepoint input \\ \n \"scf\\; uhf\\; doublet\\; thresh 1.0e-07\\; end\" \n*GENERAL \n TITLE \n Test run: H+H2 reaction, Page-McIver CLQA algorithm, no restart \n\n ATOMS \n 1 H \n 2 H \n 3 H \n END \n\n SINGLEPOINT \n\n*REACT1 \n GEOM \n 1 0.0 0.0 0.0 \n 2 0.0 0.0 1.3886144 \n END \n\n SPECIES LINRP \n\n*REACT2 \n GEOM \n 3 0.0 0.0 190.3612132 \n END \n\n SPECIES ATOMIC \n\n*PROD2 \n GEOM \n 1 0.0 0.0 190.3612132 \n END \n\n SPECIES ATOMIC \n\n*PROD1 \n\n GEOM \n 2 0.0 0.0 1.3886144 \n 3 0.0 0.0 0.0 \n END \n\n SPECIES LINRP \n\n*START \n\n GEOM \n 1 0.0 0.0 -1.76531973 \n 2 0.0 0.0 0.0 \n 3 0.0 0.0 1.76531973 \n END \n\n SPECIES LINTS \n\n*PATH \n SSTEP 0.05 \n SSAVE 0.05 \n SLP 0.50 \n SLM -0.50 \n SCALEMASS 0.6718993 \n INTEGRA CLQA \nend \n\ntask dirdyvtst\n
"},{"location":"Interfaces-with-External-Software.html","title":"Interfaces with External Software","text":""},{"location":"Interfaces-with-External-Software.html#overview","title":"Overview","text":"NWChem can be interfaced with external software packages by following the instructions below.
The interface can be set either using a pre-exisiting software package or by downloading and compiling the software from the NWChem makefile infrastructure.
"},{"location":"Interfaces-with-External-Software.html#simint-integrals-library","title":"Simint integrals library","text":"To generate the Simint library and enable the NWChem interface (only for energy and first derivative code), you need to define the following environment variables at compile time:
USE_SIMINT=y (mandatory)SIMINT_MAXAM=\u201cMaximum angular momentum\u201d (optional, default is 3, therefore up to f orbitals)
The following set directives are required in the input file to trigger use of Simint
set int:cando_txs f\nset int:cando_nw f\n
"},{"location":"Interfaces-with-External-Software.html#openblas","title":"OpenBLAS","text":"To build NWChem with the optimized BLAS and Lapack OpenBLAS library, you need to define the following environment variables at compile time:
BUILD_OPENBLAS=1\nBLAS_SIZE=8\n
This procedure requires an internet connection to dowload the OpenBLAS source. Instead, to use a pre-compiled OpenBLAS library, the BLASOPT, LAPACK_LIB and BLAS_SIZE environment variable need to be set.
"},{"location":"Interfaces-with-External-Software.html#scalapack","title":"ScaLAPACK","text":"To build NWChem with the ScaLAPACK library, you need to define the following environment variables at compile time:
BUILD_SCALAPACK=1\nSCALAPACK_SIZE=8\n
This procedure requires an internet connection to dowload the OpenBLAS source. Instead, to use a pre-compiled ScaLAPACK library, the SCALAPACK_LIB and SCALAPACK_SIZE environment variable need to be set.
"},{"location":"Interfaces-with-External-Software.html#elpa","title":"ELPA","text":"To build NWChem with the ELPA eigensolver library, you need first to set the ScaLAPACK settings as described in the previous section and then you need to define the following environment variables at compile time:
BUILD_ELPA=1\n
This procedure requires an internet connection to dowload the OpenBLAS source. Instead, to use a pre-compiled ELPA library, the ELPA and ELPA_SIZE environment variable need to be set.
"},{"location":"Interfaces-with-External-Software.html#plumed","title":"Plumed","text":"The BUILD_PLUMED environment variable installs Plumed and interfaces it with the qmd module. This procedure requires an internet connection to dowload the Plumed source.
Instead, if you wish to use an existing Plumed installation, the following environment variables must be set (after having unset BUILD_PLUMED):
USE_PLUMED=1\n
Requirements: * The environment variable PATH should to point to the location of the plumed command and LD_LIBRARY_PATH should point to the location of the plumed libraries. * BLAS_SIZE and SCALAPACK_SIZE must be equal to 4 (this is not a requirement when using BUILD_PLUMED)
"},{"location":"Interfaces-with-External-Software.html#libxc","title":"Libxc","text":"Building NWChem with the libxc DFT library requires setting the environment variable USE_LIBXC=1.
This procedure requires an internet connection to dowload the Libxc source.
Instead, if you wish to use an existing libxc library, the following environment variables must be set, after having unset USE_LIBXC:
LIBXC_INCLUDE location of the libxc C header filesLIBXC_MODDIR location of the libxc fortran90 module filesLIBXC_LIB location of the libxc libraries files
For example, for Debian/Ubuntu systems, the following is needed after having installed the libxc-dev package
unset USE_LIBXC\n export LIBXC_LIB=/usr/lib/x86_64-linux-gnu\n export LIBXC_INCLUDE=/usr/include\n
For example, for Fedora systems, the following is needed after having installed the libxc-devel package
unset USE_LIBXC\n export LIBXC_LIB=/usr/lib64\n export LIBXC_INCLUDE=/usr/include \n export LIBXC_MODDIR=/usr/lib64/gfortran/modules\n
"},{"location":"Interfaces-with-External-Software.html#xtb","title":"XTB","text":"Building NWChem with the Light-weight tight-binding framework tblite requires
- setting theenvironment variable
USE_TBLITE=1 - adding
xtb to list of NWCHEM_MODULES
Example:
make nwchem_config NWCHEM_MODULES='tinyqmpw xtb'\nexport USE_TBLITE=1\nmake\n
"},{"location":"Introduction.html","title":"NWChem Introduction","text":""},{"location":"Introduction.html#getting-started","title":"Getting Started","text":""},{"location":"Introduction.html#nwchem-architecture","title":"NWChem Architecture","text":""},{"location":"Keywords-on-the-GEOMETRY-directive.html","title":"Keywords on the GEOMETRY directive","text":""},{"location":"Keywords-on-the-GEOMETRY-directive.html#keywords-on-the-geometry-directive","title":"Keywords on the GEOMETRY directive","text":"This section presents the options that can be specified using the keywords and optional input on the main line of the GEOMETRY directive. As described above, the first line of the directive has the general form,
GEOMETRY [<string name default geometry>] \\ \n [units <string units default angstroms>] \\ \n [bqbq] \\ \n [print [xyz] || noprint] \\ \n [center || nocenter] \\\n [autosym [real tol default 1d-2] || noautosym] \n [autoz || noautoz] \\ \n [adjust] \\ \n [(nuc || nucl || nucleus) <string nucmodel>]\n
All of the keywords and input on this line are optional. The following list describes all options and their defaults.
<name> - user-supplied name for the geometry; the default name is geometry, and all NWChem modules look for a geometry with this name. However, multiple geometries may be specified by using a different name for each. Subsequently, the user can direct a module to a named geometry by using the SET directive (see the example in the SET Section) to associate the default name of geometry with the alternate name.units - keyword specifying that a value will be entered by the user for the string variable . The default units for the geometry input are Angstr\u00f8ms (Note: atomic units or Bohr are used within the code, regardless of the option specified for the input units. The default conversion factor used in the code to convert from Angstr\u00f8ms to Bohr is 1.8897265 which may be overidden with the angstrom_to_au keyword described below.). The code recognizes the following possible values for the string variable : angstroms or an \u2013 Angstroms , the default (converts to A.U. using the Angstrom to A.U. conversion factor)au or atomic or bohr \u2013 Atomic units (A.U.)nm or nanometers \u2013 nanometers (converts to A.U. using a conversion factor computed as 10.0 times the Angstrom to A.U. conversion factor)pm or picometers \u2013 picometers (converts to A.U. using a conversion factor computed as 0.01 times the Angstrom to A.U. conversion factor)
angstrom_to_au - may also be specified as ang2au. This enables the user to modify the conversion factors used to convert between Angstrom and A.U.. The default value is 1.8897265.bqbq - keyword to specify the treatment of interactions between dummy centers. The default in NWChem is to ignore such interactions when computing energies or energy derivatives. These interactions will be included if the keyword bqbq is specified.print and noprint - complementary keyword pair to enable or disable printing of the geometry. The default is to print the output associated with the geometry. In addition, the keyword print may be qualified by the additional keyword xyz, which specifies that the coordinates should be printed in the XYZ format of molecular graphics program XMolcenter and nocenter - complementary keyword pair to enable or disable translation of the center of nuclear charge to the origin. With the origin at this position, all three components of the nuclear dipole are zero. The default is to move the center of nuclear charge to the origin.autosym and noautosym - keyword to specify that the symmetry of the geometric system should be automatically determined. This option is on by default, but can be turned off with noautosym. Only groups up to and including Oh are recognized. Occasionally NWChem will be unable to determine the full symmetry of a molecular system, but will find a proper subgroup of the full symmetry. The default tolerance is set to work for most cases, but may need to be decreased to find the full symmetry of a geometry. Note that autosym will be turned off if the SYMMETRY group input is given (See Symmetry Group Input). Also note that if symmetry equivalent atoms have different tags in the geometry they will not be detected as symmetry equivalent by the autosym capability. The reason for this is that atoms with different tags might be assigned different basis sets, for example, after which they are no longer symmetry equivalent. Therefore autosym chooses to make the save choice.noautoz - by default NWChem (release 3.3 and later) will generate redundant internal coordinates from user input Cartesian coordinates. The internal coordinates will be used in geometry optimizations. The noautoz keyword disables use of internal coordinates. The autoz keyword is provided only for backward compatibility. See Forcing internal coordinates for a more detailed description of redundant internal coordinates, including how to force the definition of specific internal variables in combination with automatically generated variables.adjust - This indicates that an existing geometry is to be adjusted. Only new input for the redundant internal coordinates may be provided (ZCOORD: Forcing internal coordinates). It is not possible to define new centers or to modify the point group using this keyword. See Forcing internal coordinates for an example of its usage.nucleus - keyword to specify the default model for the nuclear charge distribution. The following values are recognized: NOTE: If you specify a finite nuclear size, you should ensure that the basis set you use is contracted for a finite nuclear size.
The following examples illustrate some of the various options that the user can specify on the first input line of the GEOMETRY directive, using the keywords and input options described above.
The following directives all specify the same geometry for H2 (a bond length of 0.732556 \u00c5):
geometry geometry units nm \n h 0 0 0 h 0 0 0 \n h 0 0 0.732556 h 0 0 0.0732556 \n end end \n\n geometry units pm geometry units atomic \n h 0 0 0 h 0 0 0 \n h 0 0 73.2556 h 0 0 1.3843305 \n end end\n
"},{"location":"Known-Bugs.html","title":"Known Bugs","text":""},{"location":"Known-Bugs.html#how-to-report-bugs","title":"How to report bugs","text":"Use our Github issue tracker to report new bugs.
Also check there for other issues that may not have made it into these lists.
See the FAQ page for solutions to common issues.
"},{"location":"Known-Bugs.html#bugs-present-in-nwchem-binary-packages","title":"Bugs present in NWChem binary packages","text":" - The packages shipped with Ubuntu Bionic 18.04 are buggy. Calculations stop with the error
spcart_bra2etran: nbf_xj.ne.nbf_sj (xj-sj) = 5\n
https://groups.google.com/g/nwchem-forum/c/RA0tYxdfvaw https://nwchemgit.github.io/Special_AWCforum/st/id3386/Ubuntu_18.html https://bugs.launchpad.net/ubuntu/+source/nwchem/+bug/1675817
Please use commands to install an updated version (as described at the NWChem 7.0.0 release page)
sudo apt -y install curl python3-dev gfortran mpi-default-bin mpi-default-dev libopenblas-dev ssh\n\ncurl -LJO https://github.com/nwchemgit/nwchem/releases/download/v7.0.0-release/nwchem-data_7.0.0-3_all.ubuntu_bionic.deb\ncurl -LJO https://github.com/nwchemgit/nwchem/releases/download/v7.0.0-release/nwchem_7.0.0-3_amd64.ubuntu_bionic.deb\n\nsudo dpkg -i nwchem-data_7.0.0-3*_bionic.deb nwchem_7.0.0-3*_bionic.deb\n
"},{"location":"Known-Bugs.html#known-bugs-for-nwchem-68","title":"Known bugs for NWChem 6.8","text":" - AR comppilation failure on Mac OSX https://github.com/nwchemgit/nwchem/issues/5 Temporary fix: set the env. variable USE_ARUR=n, e.g.
make USE_ARUR=n\n
Fix available in the branches master and hotfix/release-6-8
- Moldenfile property bug when symmetry and linear dependencies are present https://github.com/nwchemgit/nwchem/issues/7 Workaround described in the issue entry
"},{"location":"MD.html","title":"Molecular dynamics","text":""},{"location":"MD.html#introduction","title":"Introduction","text":""},{"location":"MD.html#spacial-decomposition","title":"Spacial decomposition","text":"The molecular dynamics module of NWChem uses a distribution of data based on a spacial decomposition of the molecular system, offering an efficient parallel implementation in terms of both memory requirements and communication costs, especially for simulations of large molecular systems.
Inter-processor communication using the global array tools and the design of a data structure allowing distribution based on spacial decomposition are the key elements in taking advantage of the distribution of memory requirements and computational work with minimal communication.
In the spacial decomposition approach, the physical simulation volume is divided into rectangular cells, each of which is assigned to a processor. Depending on the conditions of the calculation and the number of available processors, each processor contains one or more of these spacially grouped cells. The most important aspects of this decomposition are the dependence of the cell sizes and communication cost on the number of processors and the shape of the cells, the frequent reassignment of atoms to cells leading to a fluctuating number of atoms per cell, and the locality of communication which is the main reason for the efficiency of this approach for very large molecular systems.
To improve efficiency, molecular systems are broken up into separately treated solvent and solute parts. Solvent molecules are assigned to the domains according to their center of geometry and are always owned by a one node. This avoids solvent-solvent bonded interactions crossing node boundaries. Solute molecules are broken up into segments, with each segment assigned to a processor based on its center of geometry. This limits the number of solute bonded interactions that cross node boundaries. The processor to which a particular cell is assigned is responsible for the calculation of all interactions between atoms within that cell. For the calculation of forces and energies in which atoms in cells assigned to different processors are involved, data are exchanged between processors. The number of neighboring cells is determined by the size and shape of the cells and the range of interaction. The data exchange that takes place every simulation time step represents the main communication requirements. Consequently, one of the main efforts is to design algorithms and data structures to minimize the cost of this communication. However, for very large molecular systems, memory requirements also need to be taken into account.
To compromise between these requirements exchange of data is performed in successive point to point communications rather than using the shift algorithm which reduces the number of communication calls for the same amount of communicated data.
For inhomogeneous systems, the computational load of evaluating atomic interactions will generally differ between cell pairs. This will lead to load imbalance between processors. Two algorithms have been implemented that allow for dynamically balancing the workload of each processor. One method is the dynamic resizing of cells such that cells gradually become smaller on the busiest node, thereby reducing the computational load of that node. Disadvantages of this method are that the efficiency depends on the solute distribution in the simulation volume and the redistribution of work depends on the number of nodes which could lead to results that depend on the number of nodes used. The second method is based on the dynamic redistribution of intra-node cell-cell interactions. This method represents a more coarse load balancing scheme, but does not have the disadvantages of the cell resizing algorithm. For most molecular systems the cell pair redistribution is the more efficient and preferred method.
The description of a molecular system consists of static and dynamic information. The static information does not change during a simulation and includes items such as connectivity, excluded and third neighbor lists, equilibrium values and force constants for all bonded and non-bonded interactions. The static information is called the topology of the molecular system, and is kept on a separate topology file. The dynamic information includes coordinates and velocities for all atoms in the molecular system, and is kept in a so-called restart file.
"},{"location":"MD.html#topology","title":"Topology","text":"The static information about a molecular system that is needed for a molecular simulation is provided to the simulation module in a topology file. Items in this file include, among many other things, a list of atoms, their non-bonded parameters for van der Waals and electrostatic interactions, and the complete connectivity in terms of bonds, angles and dihedrals.
In molecular systems, a distinction is made between solvent and solute, which are treated separately. A solvent molecule is defined only once in the topology file, even though many solvent molecules usually are included in the actual molecular system. In the current implementation only one solvent can be defined. Everything that is not solvent in the molecular system is solute. Each solute atom in the system must be explicitly defined in the topology.
Molecules are defined in terms of one or more segments. Typically, repetitive parts of a molecule are each defined as a single segment, such as the amino acid residues in a protein. Segments can be quite complicated to define and are, therefore, collected in a set of database files. The definition of a molecular system in terms of segments is a sequence.
Topology files are created using the prepare module.
"},{"location":"MD.html#files","title":"Files","text":"File names used have the form system_calc.ext, with exception of the topology file, which is named system.top. Anything that refers to the definition of the chemical system can be used for system, as long as no periods or underlines are used. The identifier calc can be anything that refers to the type of calculation to be performed for the system with the topology defined. This file naming convention allows for the creation of a single topology file system.top that can be used for a number of different calculations, each identified with a different calc. For example, if crown.top is the name of the topology file for a crown ether, crown_em, crown_md, crown_ti could be used with appropriate extensions for the filenames for energy minimization, molecular dynamics simulation and multi-configuration thermodynamic integration, respectively. All of these calculations would use the same topology file crown.top.
The extensions <ext> identify the kind of information on a file, and are pre-determined.
dbg debug file frg fragment file gib free energy data file mri free energy multiple run input file mro free energy multiple run output file nw NWChem input file nwout NWChem output file out molecular dynamics output file pdb PDB formatted coordinate file prp property file qrs quenched restart file, resulting from an energy minimization rst restart file, used to start or restart a simulation seq sequence file, describing the system in segments sgm segment file, describing segments syn synchronization time file tst test file tim timing analysis file top topology file, contains the static description of a system trj trajectory file"},{"location":"MD.html#databases","title":"Databases","text":"Database file supplied with NWChem and used by the prepare module are found in directories with name ffield_level, where ffield is any of the supported force fields. The source of the data is identified by level, and can be
level Description s original published data x additional published data q contributed data u user preferred data t user defined temporary data The user is can replace these directories or add additional database files by specifying them in the .nwchemrc file. or in the prepare input file.
The extension 1-9 defines the priority of database file.
frg fragments par parameters seq sequences sgm segments"},{"location":"MD.html#force-fields","title":"Force fields","text":"Force fields recognized are
Keyword Force field Status amber AMBER99 AMBER95,GLYCAM also available charmm CHARMM"},{"location":"MD.html#format-of-fragment-files","title":"Format of fragment files","text":"Fragment files contain the basic information needed to specify all interactions that need to be considered in a molecular simulation. Normally these files are created by the prepare module. Manual editing is needed when, for example, the prepare module could not complete atom typing, or when modified charges are required.
The formats of files used in NWChem are listed here.
"},{"location":"MD.html#creating-segment-files","title":"Creating segment files","text":"The prepare module is used to generate segment files from corresponding fragment files. A segment file contains all information for the calculation of bonded and non-bonded interactions for a given chemical system using a specific force field.
Which atoms form a fragment is specified in the coordinate file, currently only in PDB format. The segment entries define three sets of parameters for each interaction.
Free energy perturbations can be performed using set 1 for the generation of the ensemble while using sets 2 and/or 3 as perturbations. Free energy multiconfiguration thermodynamic integration and multistep thermodynamic perturbation calculations are performed by gradually changing the interactions in the system from parameter set 2 to parameter set 3. These modifications can be edited into the segment files manually, or introduced directly into the topology file using the modify commands in the input for the prepare module.
"},{"location":"MD.html#creating-sequence-files","title":"Creating sequence files","text":"A sequence file describes a molecular system in terms of segments. This file is generated by the prepare module for the molecular system provided on a PDB-formatted coordinate file
"},{"location":"MD.html#creating-topology-files","title":"Creating topology files","text":"The topology describes all static information that describes a molecular system. This includes the connectivity in terms of bond-stretching, angle-bending and torsional interactions, as well as the non-bonded van der Waals and Coulombic interactions.
The topology of a molecular system is generated by the prepare module from the sequence in terms of segments as specified on the PDB file. For each unique segment specified in this file the segment database directories are searched for the segment definition. For segments not found in one of the database directories a segment definition is generated in the temporary directory if a fragment file was found. If a fragment file could not be found, it is generated by the prepare module base on what is found on the PDB file.
When all segments are found or created, the parameter substitutions are performed, using force field parameters taken from the parameter databases. After all lists have been generated the topology is written to a local topology file <system>.top.
"},{"location":"MD.html#creating-restart-files","title":"Creating restart files","text":"Restart files contain all dynamical information about a molecular system and are created by the prepare module if a topology file is available. The prepare module will automatically generate coordinates for hydrogen atoms and monatomic counter ions not found on the PDB formatted coordinate file, if no fragment or segment files were generated using that PDB file.
The prepare module has a number of other optional input command, including solvation.
"},{"location":"MD.html#molecular-simulations","title":"Molecular simulations","text":"The type of molecular dynamics simulation is specified by the NWChem task directive.
task md [ energy | optimize | dynamics | thermodynamics ]\n
where the theory keyword md specifies use of the molecular dynamics module, and the operation keyword is one of
- energy for single configuration energy evaluation
- optimize for energy minimization
- dynamics for molecular dynamics simulations and single step thermodynamic perturbation free energy molecular dynamics simulations
- thermodynamics for combined multi-configuration thermodynamic integration and multiple step thermodynamic perturbation free energy molecular dynamics simulations.
"},{"location":"MD.html#system-specification","title":"System specification","text":"The chemical system for a calculation is specified in the topology and restart files. These files should be created using the utilities nwtop and nwrst before a simulation can be performed. The names of these files are determined from the required system directive.
system <string systemid>_<string calcid>\n
where the strings systemid and calcid are user defined names for the chemical system and the type of calculation to ber performed, respectively. These names are used to derive the filenames used for the calculation. The topoly file used will be systemid.top, while all other files are named systemid_calcid.ext.
"},{"location":"MD.html#restarting-and-continuing-simulations","title":"Restarting and continuing simulations","text":" finish\n
Specifies that the current job will finish a previous, incomplete simulation, using the input data that have been recorded by that previous run in the restart file. Most of the input in the current md input block will be ignored.
resume\n
Specifies that the current job will be an extension of a previous simulation, using most of the input data that have been recorded by that previous run in the restart file. Typically the input in the current md input block defines a larger number of steps than the previous job.
"},{"location":"MD.html#parameter-set","title":"Parameter set","text":"set <integer iset>\n
Specifies the use of parameter set <iset> for the molecular dynamics simulation. The topology file contains three separate parameters sets that can be used. The default for <iset> is 1.
lambda <integer ilambda> <integer ilambda>\n
Specifies the use of parameter set for the ilambda-th of mlambda steps.
pset <integer isetp1> [<integer isetp2>]\n
Specifies the parameter sets to be used as perturbation potentials in single step thermodynamic perturbation free energy evaluations, where <isetp1> specifies the first perturbation parameter set and <isetp2> specifies the second perturbation parameter set. Legal values for <isetp1> are 2 and 3. Legal value for <isetp2> is 3, in which case <isetp1> can only be 2. If specified, <iset> is automatically set to 1.
pmf [ equilharm <integer npmfc> | scale <real facpmf>]\n
Specifies that any potential of mean force functions defined in the topology files are to be used. If equilharm is specified, the first npmfc dynamics steps will use a harmonic potential in stead of any pmf constraint. If scale is specified, all pmf force constants are scaled by a factor facpmf.
distar [draver [<integer ndaver default 1>]] \n [scale <real drsscl>]\n [after <integer nfdrss>]\n
Specifies that any distance restraint functions defined in the topology files are to be used.
qhop [<integer nfhop default 10>] \n [<real rhop default 0.35>]\n [<real thop default 0.02>]\n
Specifies that a Q-HOP simulation is to be carried out with attempted proton hops every nfhop steps, a cutoff for the donor-acceptor pair distance of rhop nm, and a minimum time before back hopping can occur of thop ps.
"},{"location":"MD.html#energy-minimization-algorithms","title":"Energy minimization algorithms","text":"The energy minimization of the system as found in the restart file is performed with the following directives. If both are specified, steepest descent energy minimization precedes conjugate gradient minimization.
sd <integer msdit> [init <real dx0sd>] [min <real dxsdmx>] \\\n [max <real dxmsd>]\n
Specifies the variables for steepest descent energy minimizations, where <msdit> is the maximum number of steepest descent steps taken, for which the default is 100, <dx0sd> is the initial step size in nm for which the default is 0.001, <dxsdmx> is the threshold for the step size in nm for which the default is 0.0001, and <dxmsd> is the maximum allowed step size in nm for which the default is 0.05.
cg <integer mcgit> [init <real dx0cg>] [min <real dxcgmx>] \\\n [cy <integer ncgcy>]\n
Specifies the variables for conjugate gradient energy minimizations, where <mcgit> is the maximum number of conjugate gradient steps taken, for which the default is 100, <dx0cg> is the initial search interval size in nm for which the default is 0.001, <dxcgmx> is the threshold for the step size in nm for which the default is 0.0001, and <ncgcy> is the number of conjugate gradient steps after which the gradient history is discarded for which the default is 10. If conjugate gradient energy minimization is preceded by steepest descent energy minimization, the search interval is set to twice the final step of the steepest descent energy minimization.
"},{"location":"MD.html#multi-configuration-thermodynamic-integration","title":"Multi-configuration thermodynamic integration","text":"The following keywords control free energy difference simulations. Multi-configuration thermodynamic integrations are always combined with multiple step thermodynamic perturbations.
(forward | reverse) [[<integer mrun> of] <integer maxlam>]\n
Specifies the direction and number of integration steps in free energy evaluations, with forward being the default direction. <mrun> is the number of ensembles that will be generated in this calculation, and <maxlam> is the total number of ensembles to complete the thermodynamic integration. The default value for <maxlam> is 21. The default value of <mrun> is the value of <maxlam>.
error <real edacq>\n
Specifies the maximum allowed statistical error in each generated ensemble, where <edacq> is the maximum error allowed in the ensemble average derivative of the Hamiltonian with respect to \u03bb with a default of 5.0 kJ mol-1.
drift <real ddacq>\n
Specifies the maximum allowed drift in the free energy result, where is the maximum drift allowed in the ensemble average derivative of the Hamiltonian with respect to \u03bb with a default of 5.0 kJ mol-1 ps-1.
factor <real fdacq>\n
Specifies the maximum allowed change in ensemble size where <fdacq> is the minimum size of an ensemble relative to the previous ensemble in the calculation with a default value of 0.75.
decomp\n
Specifies that a free energy decomposition is to be carried out. Since free energy contributions are path dependent, results from a decomposition analysis can no be unambiguously interpreted, and the default is not to perform this decomposition.
sss [delta <real delta>]\n
Specifies that atomic non-bonded interactions describe a dummy atom in either the initial or final state of the thermodynamic calculation will be calculated using separation-shifted scaling, where <delta> is the separation-shifted scaling factor with a default of 0.075 nm2. This scaling method prevents problems associated with singularities in the interaction potentials.
new | renew | extend\n
Specifies the initial conditions for thermodynamic calculations. new indicates that this is an initial mcti calculation, which is the default. renew instructs to obtain the initial conditions for each \u03bb from the mro-file from a previous mcti calculation, which has to be renamed to an mri-file. The keyword extend will extend a previous mcti calculation from the data read from an mri-file.
"},{"location":"MD.html#time-and-integration-algorithm-directives","title":"Time and integration algorithm directives","text":"Following directives control the integration of the equations of motion.
leapfrog | leapfrog_bc\n
Specifies the integration algorithm, where leapfrog specifies the default leap frog integration, and leapfrog_bc specifies the Brown-Clarke leap frog integrator.
guided [<real fguide default 0.2> [<real tguide default 0.2>]]\n
Specifies the use of the guided molecular dynamics simulation technique. Variable fguide defines the fraction of the averaged forces g to be added to the forces ff evaluated using the force field functions to obtain the forces f used to advance the coordinates.
Variable tguide defines the length of the averaging relative to the timestep \u0394 t.
The current implementation is still under development.
equil <integer mequi>\n
Specifies the number of equilibration steps <mequi>, with a default of 100.
data <integer mdacq> [over <integer ldacq>]]\n
Specifies the number of data gathering steps <mdacq> with a default of 500. In multi-configuration thermodynamic integrations <mequi> and <mdacq> are for each of the ensembles, and variable <ldacq> specifies the minimum number of data gathering steps in each ensemble. In regular molecular dynamics simulations <ldacq> is not used. The default value for <ldacq> is the value of <mdacq>.
time <real stime>\n
Specifies the initial time <stime> of a molecular simulation in ps, with a default of 0.0.
step <real tstep>\n
Specifies the time step <tstep> in ps, with 0.001 as the default value.
"},{"location":"MD.html#ensemble-selection","title":"Ensemble selection","text":"Following directives control the ensemble type.
isotherm [<real tmpext> [<real tmpext2>]] [trelax <real tmprlx> [<real tmsrlx>]] \\\n [anneal [<real tann1>] <real tann2>]\n
Specifies a constant temperature ensemble using Berendsen\u2019s thermostat, where <tmpext> is the external temperature with a default of 298.15 K, and <tmprlx> and <tmsrlx> are temperature relaxation times in ps with a default of 0.1. If only <tmprlx> is given the complete system is coupled to the heat bath with relaxation time <tmprlx>. If both relaxation times are supplied, solvent and solute are independently coupled to the heat bath with relaxation times <tmprlx> and <tmsrlx>, respectively. If keyword anneal is specified, the external temperature will change from tmpext to tempext2 between simulation time tann1 and tann2
isobar [<real prsext>] [trelax <real prsrlx> ] \\\n [compress <real compr>] [anisotropic] [xy | z | xy-z]\n
Specifies a constant pressure ensemble using Berendsen\u2019s piston, where <prsext> is the external pressure with a default of 1.025 105 Pa, <prsrlx> is the pressure relaxation time in ps with a default of 0.5, and <compr> is the system compressibility in with a default of 4.53E-10. Optional keywords xy, z and xy-z may be used to specify that pressure scaling is to be applied in the x and y dimension only, the z dimension only, or, in all three dimensions with identical scaling in the x and y dimension. The last option requires that anisotropic is also specified.
"},{"location":"MD.html#velocity-reassignments","title":"Velocity reassignments","text":"Velocities can be periodically reassigned to reflect a certain temperature.
vreass <integer nfgaus> <real tgauss>\n [fraction [<real frgaus default 0.5]]\n [once]\n [(first | initial)] [(last | final)]\n
Specifies that velocities will be reassigned every <nfgaus> molecular dynamics steps, reflecting a temperature of <tgauss> K. The default is not to reassign velocities, i.e. <nfgaus> is 0. Keyword fraction allows the specification of the fraction of the new velocities are random. Keyword once specifies that velocity reassignment only should be done in the first step. Keywords first or initial and last or final specify that velocity reassigment should only be applied in the first and last window of multiple run simulations.
"},{"location":"MD.html#cutoff-radii","title":"Cutoff radii","text":"Cutoff radii can be specified for short range and long range interactions.
cutoff [short] <real rshort> [long <real rlong>] \\\n [qmmm <real rqmmm>]\n
Specifies the short range cutoff radius <rshort>, and the long range cutoff radius <rlong> in nm. If the long range cutoff radius is larger than the short range cutoff radius the twin range method will be used, in which short range forces and energies are evaluated every molecular dynamics step, and long range forces and energies with a frequency of <nflong> molecular dynamics steps. Keyword qmmm specifies the radius of the zone around quantum atoms defining the QM/MM bare charges. The default value for <rshort>, <rlong> and <rqmmm> is 0.9 nm.
"},{"location":"MD.html#polarization","title":"Polarization","text":"First order and self consistent electronic polarization models have been implemented.
polar (first | scf [[<integer mpolit>] <real ptol>])\n
Specifies the use of polarization potentials, where the keyword first specifies the first order polarization model, and scf specifies the self consistent polarization field model, iteratively determined with a maximum of <mpolit> iterations to within a tolerance of <ptol> D in the generated induced dipoles. The default is not to use polarization models.
"},{"location":"MD.html#external-electrostatic-field","title":"External electrostatic field","text":" field <real xfield> [freq <real xffreq>] [vector <real xfvect(1:3)>]\n
Specifies an external electrostatic field, where <xfield> is the field strength, <xffreq> is the frequency in MHz and <xfvect> is the external field vector.
"},{"location":"MD.html#constraints","title":"Constraints","text":"Constraints are satisfied using the SHAKE coordinate resetting procedure.
shake [<integer mshitw> [<integer mshits>]] \\\n [<real tlwsha> [<real tlssha>]]\n
Specifies the use of SHAKE constraints, where <mshitw> is the maximum number of solvent SHAKE iterations, and <mshits> is the maximum number of solute SHAKE iterations. If only <mshitw> is specified, the value will also be used for <mshits>. The default maximum number of iterations is 100 for both. <tlwsha> is the solvent SHAKE tolerance in nm, and <tlssha> is the solute SHAKE tolerance in nm. If only <tlwsha> is specified, the value given will also be used for <tlssha>. The default tolerance is 0.001 nm for both.
noshake (solvent | solute)\n
Disables SHAKE and treats the bonded interaction according to the force field.
"},{"location":"MD.html#long-range-interaction-corrections","title":"Long range interaction corrections","text":"Long range electrostatic interactions are implemented using the smooth particle mesh Ewald technique, for neutral periodic cubic systems in the constant volume ensemble, using pair interaction potentials. Particle-mesh Ewald long range interactions can only be used in molecular dynamics simulations using effective pair potentials, and not in free energy simulations, QMD or QM/MM simulations.
pme [grid <integer ng>] [alpha <real ealpha>] \\\n [order <integer morder>] [fft <integer imfft>]\\\n [procs <integer nprocs>] [solvent]\n
Specifies the use of smooth particle-mesh Ewald long range interaction treatment, where ng is the number of grid points per dimension, ealpha is the Ewald coefficient in , with a default that leads to a tolerance of at the short range cutoff radius, and morder is order of the Cardinal B-spline interpolation which must be an even number and at least 4 (default value). A platform specific 3D fast Fourier transform is used, if available, when imfft is set to 2. nprocs can be used to define a subset of processors to be used to do the FFT calculations. If solvent is specified, the charge grid will be calculated from the solvent charges only.
react [<real dielec default 80.0>]\n
Specifies that a simple reaction field correction is used with a dielectric constant dielec. This is an experimental option that has not been well tested.
"},{"location":"MD.html#fixing-coordinates","title":"Fixing coordinates","text":"Solvent or solute may be fixed using the following keywords.
( fix | free ) \n solvent ( [<integer idfirst> [<integer idlast>]] | \n ( within | beyond) <real rfix> <string atomname> ) | \\\n solute ( [<integer idfirst> [<integer idlast>]] [ heavy | {<string atomname>}] |\n ( within | beyond) <real rfix> <string atomname> )\n [permanent]\n
For solvent the molecule numbers idfirst and idlastmay be specified to be the first and last molecule to which the directive applies. If omitted, the directive applies to all molecules. For solute, the segment numbers idfirst and idlastmay be specified to be the first and last segment to which the directive applies. If omitted, the directive applies to all segments. In addition, the keyword heavy may be specified to apply to all non hydrogen atoms in the solute, or a set of atom names may be specified in which a wildcard character ? may be used. Keyword permanent is used to keep the specification on the restart file for subsequent simulations.
"},{"location":"MD.html#special-options","title":"Special options","text":" import [<integer impfr default 1> [<integer impto default impfr> \\\n [<integer nftri default 1>]]]\n
Specifies the import of frames impfr to impto with frequency nftri from a trajectory file with extension tri for which energies and forces are to be recalculated. This option only applied to task md energy.
detail\n
Specifies that moments of inertia and radii of gyration will be part of the recorded properties.
profile\n
Specifies that execution time profiling data will be part of the recorded properties.
scale <real scaleq>\n
Specifies that all charges will be scaled by the factro scaleq.
collapse [<real fcoll default 10.0> [ segment | z | xy ]\n
Specifies that additional forces directed to the origin of the simulation cell with strength fcoll will be applied to all solute molecules. If z or xy is specified, these forces will only apply in the specified dimension(s).
include fixed\n
Specifies that energies will be evaluated between fixed atoms. Normally these interactions are excluded from the pairlists.
eqm <real eqm>\n
Specifies the zero point of energy in QMD simulations.
atomlist\n
Specifies that pairlists will be atom based. Normally pairlist are charge group based.
"},{"location":"MD.html#autocorrelation-function","title":"Autocorrelation function","text":"For the evaluation of the statistical error of multi-configuration thermodynamic integration free energy results a correlated data analysis is carried out, involving the calculation of the autocorrelation function of the derivative of the Hamiltonian with respect to the control variable \u03bb.
auto <integer lacf> [fit <integer nfit>] [weight <real weight>]\n
Controls the calculation of the autocorrelation, where <lacf> is the length of the autocorrelation function, with a default of 1000, <nfit> is the number of functions used in the fit of the autocorrelation function, with a default of 15, and <weight> is the weight factor for the autocorrelation function, with a default value of 0.0.
"},{"location":"MD.html#print-options","title":"Print options","text":"Keywords that control print to the output file, with extension out. Print directives may be combined to a single directive.
print [topol [nonbond] [solvent] [solute]] \\\n [step <integer nfoutp> [extra] [energy]] \\\n [stat <integer nfstat>] \\\n [energies [<integer nfener>]] \\\n [forces [<integer nfforce>]] \\\n [matrix] \\\n [expect <integer npxpct>] \\\n [timing] \\\n [pmf [<integer iprpmf>]] \\\n [out6] \\\n [dayout]\n
- Keyword topol specifies printing the topology information, where nonbond refers to the non-bonded interaction parameters, solvent to the solvent bonded parameters, and solute to the solute bonded parameters. If only topol is specified, all topology information will be printed to the output file.
- Keyword step specifies the frequency nfoutp of printing molecular dynamics step information to the output file. If the keyword extra is specified additional energetic data are printed for solvent and solute separately. If the keyword energy is specified, information is printed for all bonded solute interactions. The default for nfoutp is 0. For molecular dynamics simulations this frequency is in time steps, and for multi-configuration thermodynamic integration in \u03bb-steps.
- Keyword stat specifies the frequency
<nfstat> of printing statistical information of properties that are calculated during the simulation. For molecular dynamics simulation this frequency is in time steps, for multi-configuration thermodynamic integration in \u03bb-steps.
- Keyword energies specifies the frequency nfener of printing solute bonded energies the output file for energy/import calculations. The default for nfener is 0.
- Keyword forces specifies the frequency nfforc of printing solute forces the output file for energy/import calculations. The default for nfforc is 0.
- Keyword matrix specifies that a solute distance matrix is to be printed.
- Keyword expect is obsolete.
- Keyword timing specifies that timing data is printed.
- Keyword pmf specifies that pmf data is printed every iprpmf steps. Keyword out6 specifies that output is written to standard out in stead of the output file with extension out.
- Keyword dayout is obsolete.
"},{"location":"MD.html#periodic-updates","title":"Periodic updates","text":"Following keywords control periodic events during a molecular dynamics or thermodynamic integration simulation. Update directives may be combined to a single directive.
update [pairs <integer nfpair default 1>] \\\n\n [long <integer nflong default 1>] \\\n\n [center <integer nfcntr default 0> [zonly | xyonly] \\\n\n [fraction <integer idscb(1:5)>] \\\n\n [motion <integer nfslow default 0>] \\\n\n [analysis <integer nfanal default 0>] \\\n\n [rdf <integer nfrdf default 0> \\\n\n [range <real rrdf>] [bins <integer ngl>] \\\n
- Keyword pairs specifies the frequency
<nfpair> in molecular dynamics steps of updating the pair lists. The default for the frequency is 1. In addition, pair lists are also updated after each step in which recording of the restart or trajectory files is performed. Updating the pair lists includes the redistribution of atoms that changed domain and load balancing, if specified.
- Keyword long specifies the frequency
<nflong> in molecular dynamics steps of updating the long range forces. The default frequency is 1. The distinction of short range and long range forces is only made if the long range cutoff radius was specified to be larger than the short range cutoff radius. Updating the long range forces is also done in every molecular dynamics step in which the pair lists are regenerated.
- Keywrod center specifies the frequency
<nfcntr> in molecular dynamics steps in which the center of geometry of the solute(s) is translated to the center of the simulation volume. Optional keyword zonly or xyonly can be used to specify that centering will take place in the z-direction or in the xy-plane only. The solute fractions determining the solutes that will be centered are specified by the keyword fraction and the vector <idscb>, with a maximum of 5 entries. This translation is implemented such that it has no effect on any aspect of the simulation. The default is not to center, i.e. nfcntr is 0. The default fraction used to center solute is 1.
- Keyword motion specifies the frequency
<nfslow> in molecular dynamics steps of removing the overall rotational and center of mass translational motion.
- Keyword analysis specifies the frequency
<nfanal> in molecular dynamics steps of invoking the analysis module. This option is obsolete.
- Keyword rdf specifies the frequency
<nfrdf> in molecular dynamics steps of calculating contributions to the radial distribution functions. The default is 0. The range of the radial distribution functions is given by <rrdf> in nm, with a default of the short range cutoff radius. Note that radial distribution functions are not evaluated beyond the short range cutoff radius. The number of bins in each radial distribution function is given by <ngl>, with a default of 1000. This option is no longer supported. If radial distribution function are to be calculated, a rdi files needs to be available in which the contributions are specified as follows.
Card Format Description I-1 i Type, 1=solvent-solvent, 2=solvent-solute, 3-solute-solute I-2 i Number of the rdf for this contribution I-3 i First atom number I-4 i Second atom number"},{"location":"MD.html#recording","title":"Recording","text":"The following keywords control recording data to file. Record directives may be combined to a single directive.
record [rest <integer nfrest> [keep]] \\\n\n [coord <integer nfcoor default 0>] \\\n\n [wcoor <integer nfwcoo default 0>] \\\n\n [scoor <integer nfscoo default 0>] \\\n\n [veloc <integer nfvelo default 0>] \\\n\n [wvelo <integer nfwvel default 0>] \\\n\n [svelo <integer nfsvel default 0>] \\\n\n [force <integer nfvelo default 0>] \\\n\n [wforc <integer nfwvel default 0>] \\\n\n [sforc <integer nfsvel default 0>] \\\n\n [(prop | prop_average) <integer nfprop default 0>] \\\n\n [free <integer nffree default 1>] \\\n\n [sync <integer nfsync default 0>] \\\n\n [times <integer nftime default 0>] \\\n\n [acf] [cnv] [fet]\n\n [binary] [ascii] [ecce] [argos]\n
- Keyword rest specifies the frequency
<nfrest> in molecular dynamics steps of rewriting the restart file, with extension rst. For multi-configuration thermodynamic integration simulations the frequency is in steps in \u03bb. The default is not to record. The restart file is used to start or restart simulations. The keyword keep causes all restart files written to be kept on disk, rather than to be overwritten.
- Keyword coord specifies the frequency
<nfcoor> in molecular dynamics steps of writing coordinates to the trajectory file. This directive redefines previous coord, wcoor and scoor directives. The default is not to record.
- Keyword wcoor specifies the frequency
<nfcoor> in molecular dynamics steps of writing solvent coordinates to the trajectory file. This keyword takes precedent over coord. This directive redefines previous coord, wcoor and scoor directives. The default is not to record.
- Keyword scoor specifies the frequency
<nfscoo> in molecular dynamics steps of writing solute coordinates to the trajectory file. This keyword takes precedent over coord. This directive redefines previous coord, wcoor and scoor directives. The default is not to record.
- Keyword veloc specifies the frequency
<nfvelo> in molecular dynamics steps of writing velocities to the trajectory file. This directive redefines previous veloc, wvelo and svelo directives. The default is not to record.
- Keyword wvelo specifies the frequency
<nfvelo> in molecular dynamics steps of writing solvent velocitiesto the trajectory file. This keyword takes precedent over veloc. This directive redefines previous veloc, wvelo and svelo directives. The default is not to record.
- Keyword svelo specifies the frequency
<nfsvel> in molecular dynamics steps of writing solute velocities to the trajectory file. This keyword takes precedent over veloc. This directive redefines previous veloc, wvelo and svelo directives. The default is not to record.
- Keyword force specifies the frequency
<nfvelo> in molecular dynamics steps of writing forces to the trajectory file. This directive redefines previous vforce, wforc and sforc directives. The default is not to record.
- Keyword wforc specifies the frequency
<nfvelo> in molecular dynamics steps of writing solvent forcesto the trajectory file. This keyword takes precedent over force. This directive redefines previous vforce, wforc and sforc directives. The default is not to record.
- Keyword sforc specifies the frequency
<nfsvel> in molecular dynamics steps of writing solute forces to the trajectory file. This keyword takes precedent over force. This directive redefines previous vforce, wforc and sforc directives. The default is not to record.
- Keyword prop specifies the frequency
<nfprop> in molecular dynamics steps of writing information to the property file, with extension prp. The default is not to record.
- Keyword prop_average specifies the frequency
<nfprop> in molecular dynamics steps of writing average information to the property file, with extension prp. The default is not to record.
- Keyword free specifies the frequency
<nffree> in multi-configuration thermodynamic integration steps to record data to the free energy data file, with extension gib. The default is 1, i.e. to record at every \u03bb. This option is obsolete. All data are required to do the final analysis.
- Keyword sync specifies the frequency
<nfsync> in molecular dynamics steps of writing information to the synchronization file, with extension syn. The default is not to record. The information written is the simulation time, the wall clock time of the previous MD step, the wall clock time of the previous force evaluation, the total synchronization time, the largest synchronization time and the node on which the largest synchronization time was found. The recording of synchronization times is part of the load balancing algorithm. Since load balancing is only performed when pair-lists are updated, the frequency <nfsync> is correlated with the frequency of pair-list updates <nfpair>. This directive is only needed for analysis of the load balancing performance. For normal use this directive is not used.
- Keyword times specifies the frequency
<nfsync> in molecular dynamics steps of writing information to the timings file, with extension tim. The default is not to record. The information written is wall clock time used by each of the processors for the different components in the force evaluation. This directive is only needed for analysis of the wall clock time distribution. For normal use this directive is not used.
- Keywords acf, cnv and fet are obsolete.
- Keywords binary, ascii, ecce and argos are obsolete.
"},{"location":"MD.html#program-control-options","title":"Program control options","text":" load [reset] \n ( none | \n size [<real factld>] |\n sizez [<real factld>] | pairs | \n (pairs [<integer ldpair>] size [<real factld>]) )\n [last]\n [minimum]\n [average]\n [combination]\n [iotime]\n [experimental]\n
Determines the type of dynamic load balancing performed, where the default is none. Load balancing option size is resizing cells on a node, and pairs redistributes the cell-cell interactions over nodes. Keyword reset will reset the load balancing read from the restart file. The level of cell resizing can be influenced with factld. The cells on the busiest node are resized with a factor
Where is the accumulated synchronization time of all nodes, is the total number of nodes, is the synchronization time of the busiest node, and is the wall clock time of the molecular dynamics step. For the combined load balancing, ldpair is the number of successive pair redistribution load balancing steps in which the accumulated synchronization time increases, before a resizing load balancing step will be attempted. Load balancing is only performed in molecular dynamics steps in which the pair-list is updated. The default load balancing is equivalent to specifying
load pairs 10 size 0.75\n
Keyword last specifies that the load balancing is based on the synchronization times of the last step. This is the default. Keyword average specifies that the load balancing is based on the average synchronization times since the last load balancing step. Keyword minimum specifies that the load balancing is based on the minimum synchronization times since the last load balancing step. Keywords combination, iotime and experimental are experimental load balancing options that should not be used in production runs.
(pack | nopack)\n
Specifies if data are communicated in packed or unpacked form. The default is pack.
procs <integer npx> <integer npy> <integer npz>\n
Specifies the distribution of the available processors over the three Cartesian dimensions. The default distribution is chosen such that, <npx>*<npy>*<npz>=<np> and <npx> <= <npy> <= <npz>, where <npx>, <npy> and <npz> are the processors in the x, y and z dimension respectively, and <np> is the number of processors allocated for the calculation. Where more than one combination of <npx>, <npy> and <npz> are possible, the combination is chosen with the minimum value of <npx>+<npy>+<npz>. To change the default setting the following optional input option is provided.
cells <integer nbx> <integer nby> <integer nbz>\n
Specifies the distribution of cells, where <nbx>, <nby> and <nbz> are the number of cells in x, y and z direction, respectively. The molecular system is decomposed into cells that form the smallest unit for communication of atomic data between nodes. The size of the cells is per default set to the short-range cutoff radius. If long-range cutoff radii are used the cell size is set to half the long-range cutoff radius if it is larger than the short-range cutoff. If the number of cells in a dimension is less than the number of processors in that dimension, the number of cells is set to the number of processors.
extra <integer madbox>\n
Sets the number of additional cells for which memory is allocated. In rare events the amount of memory set aside per node is insufficient to hold all atomic coordinates assigned to that node. This leads to execution which aborts with the message that mwm or msa is too small. Jobs may be restarted with additional space allocated by where <madbox> is the number of additional cells that are allocated on each node. The default for <madbox> is 6. In some cases <madbox> can be reduced to 4 if memory usage is a concern. Values of 2 or less will almost certainly result in memory shortage.
mwm <integer mwmreq>\n
Sets the maximum number of solvent molecules <mwmreq> per node, allowing increased memory to be allocated for solvent molecules. This option can be used if execution aborted because mwm was too small.
msa <integer msareq>\n
Sets the maximum number of solute atoms <msareq> per node, allowing increased memory to be allocated for solute atoms. This option can be used if execution aborted because msa was too small.
mcells <integer mbbreq>\n
Sets the maximum number of cell pairs <mbbreq> per node, allowing increased memory to be allocated for the cell pair lists. This option can be used if execution aborted because mbbl was too small.
boxmin <real rbox>\n
Sets the minimum size of a cell. This directive is obsolete. The use of mcells is preferred.
segmentsize <real rsgm>\n
Sets the maximum size of a segment. This value is used to determine which segments at the boundary of the cutoff radius should be considered in the generation of the pairlists. This value is also determined by the prepare module and written to the restart file. Use of this directive is not needed for simulations that use the current prepare module to generate the restart file.
memory <integer memlim>\n
Sets a limit <memlim> in kB on the allocated amount of memory used by the molecular dynamics module. Per default all available memory is allocated. Use of this command is required for QM/MM simulations only.
expert\n
Enables the use of certain combinations of features that are considered unsafe. This directive should not be used for production runs.
develop <integer idevel>\n
Enables the use of certain development options specified by the integer idevel. This option is for development purposes only, and should not be used for production runs.
control <integer icntrl>\n
Enables the use of certain development options specified by the integer icntrl. This option is for development purposes only, and should not be used for production runs.
numerical\n
Writes out analytical and finite difference forces for test purposes.
server <string servername> <integer serverport>\n
Allows monitoring over a socket connection to the specified port on the named server of basic data as a simulation is running.
For development purposes debug information can be written to the debug file with extension dbg with
debug <integer idebug>\n
where idebug specifies the type of debug information being written.
For testing purposes test information can be written to the test file with extension tst with
test <integer itest>\n
where itest specifies the number of steps test information is written.
On some platforms prefetching of data can improve the efficiency. This feature can be turned on using
prefetch [<integer nbget>]\n
where nbget is the number of outstanding communication operations.
Application of periodic boundary conditions for the evaluation of forces can be controlled with
pbc ( atom | residue | molecule )\n
This option rarely needs to be used.
Autocorrelation functions for error analysis are controlled using
auto [ fit <integer iapprx> | weight <real weight> ]\n
This option is disabled in the current release.
Membrane system equilibration can be made more efficient using
membrane [ rotations ]\n
Constraining the center of mass of solute molecules in the xy plane is accomplished using
scmxy [<integer icmopt default 1>]\n
where icmopt determines if the constraint is mass weighted (2).
Radius of gyration calculations are enabled using
radius_gyration\n
Calculations of diffusion coefficients is enabled using
diffusion\n
This option is disabled in the current release.
comlim ( on | off )\n
is disabled
To limit the size of recoding files, new files are opened every nfnewf md steps using
batch <integer nfnewf>\n
"},{"location":"MM_Parameters.html","title":"MM Parameters","text":"The molecular mechanics parameters are given in the form of standard MD input block as used by the MD module. At the basic level the molecular mechanics input block specifies the restart and topology file that were generated during QM/MM preparation stage. It also contains information relevant to the calculation of the classical region (e.g. cutoff distances, constraints, optimization and dynamics parameters, etc) in the system. In this input block one can also set fixed atom constraints on classical atoms. Continuing with our prepare example for ethanol molecule here is a simple input block that may be used for this system.
md #\u00a0this\u00a0specifies\u00a0that\u00a0etl_md.rst\u00a0will\u00a0be\u00a0used\u00a0as\u00a0a\u00a0restart\u00a0file #\u00a0\u00a0and\u00a0etl.top\u00a0will\u00a0be\u00a0a\u00a0topology\u00a0file system\u00a0etl_md #\u00a0if\u00a0we\u00a0ever\u00a0wanted\u00a0to\u00a0fix\u00a0C1\u00a0atom fix\u00a0solute\u00a01\u00a0_C1 noshake\u00a0solute end
The noshake solute, shown in the above example is a recommended directive for QM/MM simulations that involve optimizations. Otherwise user has to ensure that the optimization method for classical solute atoms is a steepest descent
"},{"location":"MP2.html","title":"MP2","text":""},{"location":"MP2.html#overview","title":"Overview","text":"There are (at least) three algorithms within NWChem that compute the M\u00f8ller-Plesset (or many-body) perturbation theory second-order correction1 to the Hartree-Fock energy (MP2). They vary in capability, the size of system that can be treated and use of other approximations
- Semi-direct \u2013 this is recommended for most large applications (up to about 2800 basis functions), especially on the IBM SP and other machines with significant disk I/O capability. Partially transformed integrals are stored on disk, multi-passing as necessary. RHF and UHF references may be treated including computation of analytic derivatives. This is selected by specifying mp2 on the task directive, e.g.
TASK\u00a0MP2\n
- Fully-direct2 \u2013 this is of utility if only limited I/O resources are available (up to about 2800 functions). Only RHF references and energies are available. This is selected by specifying
direct_mp2 on the task directive, e.g.
TASK\u00a0DIRECT_MP2\n
- Resolution of the identity (RI) approximation MP2 (RI-MP2)3 \u2013 this uses the RI approximation and is therefore only exact in the limit of a complete fitting basis. However, with some care, high accuracy may be obtained with relatively modest fitting basis sets. An RI-MP2 calculation can cost over 40 times less than the corresponding exact MP2 calculation. RHF and UHF references with only energies are available. This is selected by specifying rimp2 on the task directive, e.g.,
TASK\u00a0RIMP2\n
All three MP2 tasks share the same input block.
MP2 \n [FREEZE [[core] (atomic || <integer nfzc default 0>)] \\ \n [virtual <integer nfzv default 0>]] \n [TIGHT] \n [PRINT] \n [NOPRINT] \n [VECTORS <string filename default scf-output-vectors> \\ \n [swap [(alpha||beta)] <integer pair-list>] ] \n [RIAPPROX <string riapprox default V>] \n [FILE3C <string filename default $file_prefix$.mo3cint> \n [SCRATCHDISK <integer>] \n END\n
"},{"location":"MP2.html#freeze-freezing-orbitals","title":"FREEZE: Freezing orbitals","text":"All MP2 modules support frozen core orbitals, however, only the direct MP2 and RI-MP2 modules support frozen virtual orbitals.
By default, no orbitals are frozen. The atomic keyword causes orbitals to be frozen according to the rules in the table below. Note that no orbitals are frozen on atoms on which the nuclear charge has been modified either by the user or due to the presence of an ECP. The actual input would be
freeze atomic\n
For example, in a calculation on Si(OH)2, by default the lowest seven orbitals would be frozen (the oxygen 1s, and the silicon 1s, 2s and 2p).
Period Elements Core Orbitals Number of Core 0 H - He - 0 1 Li - Ne 1s 1 2 Na - Ar 1s2s2p 5 3 K - Kr 1s2s2p3s3p 9 4 Rb - Xe 1s2s2p3s3p4s3d4p 18 5 Cs - Rn 1s2s2p3s3p4s3d4p5s4d5p 27 6 Fr - Lr 1s2s2p3s3p4s3d4p5s4d5p6s4f5d6p 43 Number of orbitals considered \u201ccore\u201d in the \u201cfreeze by atoms\u201d algorithm
Caution: The rule for freezing orbitals \u201cby atoms\u201d are rather unsophisticated since the number of orbitals to be frozen is computed from the table above by summing the number of core orbitals in each atom present. Therefore, the corresponding number of lowest-energy orbitals are frozen. If for some reason the actual core orbitals are not the lowest lying, then correct results will not be obtained. It is likely that special attention should be paid to systems including third- and higher- period atoms.
The user may also specify the number of orbitals to be frozen by atom. Following the Si(OH)2 example, the user could specify
freeze atomic O 1 Si 3\n
In this case only the lowest four orbitals would be frozen. If the user does not specify the orbitals by atom, the rules default to Table 16.1.
Caution: The system does not check for a valid number of orbitals per atom. If the user specifies to freeze more orbitals then are available for the atom, the system will not catch the error. The user must specify a logical number of orbitals to be frozen for the atom.
The FREEZE directive may also be used to specify the number of core orbitals to freeze. For instance, to freeze the first 10 orbitals
freeze 10\n
or equivalently, using the optional keyword core
freeze core 10\n
Again, note that if the 10 orbitals to be frozen do not correspond to the first 10 orbitals, then the swap keyword of the VECTORS directive must be used to order the input orbitals correctly (MO vectors).
To freeze the highest virtual orbitals, use the virtual keyword. For instance, to freeze the top 5 virtuals
freeze virtual 5\n
Again, note that this only works for the direct-MP2 and RI-MP2 energy codes.
"},{"location":"MP2.html#tight-increased-precision","title":"TIGHT: Increased precision","text":"The TIGHT directive can be used to increase the precision in the MP2 energy and gradients.
By default the MP2 gradient package should compute energies accurate to better than a micro-Hartree, and gradients accurate to about five decimal places (atomic units). However, if there is significant linear dependence in the basis set the precision might not be this good. Also, for computing very accurate geometries or numerical frequencies, greater precision may be desirable.
This option increases the precision to which both the SCF (from 10-6 to 10-8 and CPHF 10-4 to $10-6 are solved, and also tightens thresholds for computation of the AO and MO integrals (from 10-9 to 10-11 within the MP2 code.
"},{"location":"MP2.html#scratchdisk-limiting-io-usage","title":"SCRATCHDISK: Limiting I/O usage","text":"This directive - used only in the semi-direct algorithm - allows to limit the per process disk usage. Mandatory argument for this keyword is the maximum number of MBytes. For example, the following input line
scratchdisk 512\n
puts an upper limit of 512 MBytes to the semi-direct MP2 usage of disk (again, on a per process base).
"},{"location":"MP2.html#print-and-noprint","title":"PRINT and NOPRINT","text":"The standard print control options are recognized. The list of recognized names are given in the table below.
Item Print Level Description RI-MP2 \u201c2/3 ints\u201d debug Partial 3-center integrals \u201c3c ints\u201d debug MO 3-center integrals \u201c4c ints b\u201d debug \u201cB\u201d matrix with approx. 4c integrals \u201c4c ints\u201d debug Approximate 4-center integrals \u201camplitudes\u201d debug \u201cB\u201d matrix with denominators \u201cbasis\u201d high \u201cfit xf\u201d debug Transformation for fitting basis \u201cgeombas\u201d debug Detailed basis map info \u201cgeometry\u201d high \u201cinformation\u201d low General information about calc. \u201cintegral i/o\u201d high File size information \u201cmo ints\u201d debug \u201cpair energies\u201d debug (working only in direct_mp2) \u201cpartial pair energies\u201d debug Pair energy matrix each time it is updated \u201cprogress reports\u201d default Report completion of time-consuming steps \u201creference\u201d high Details about reference wavefunction \u201cwarnings\u201d low Non-fatal warnings
Printable items in the MP2 modules and their default print levels
"},{"location":"MP2.html#vectors-mo-vectors","title":"VECTORS: MO vectors","text":"All of the (supported) MP2 modules require use of converged canonical SCF (RHF or UHF) orbitals for correct results. The vectors are by default obtained from the preceding SCF calculation, but it is possible to specify a different source using the VECTORS directive. For instance, to obtain vectors from the file /tmp/h2o.movecs, use the directive
vectors /tmp/h2o.movecs\n
As noted above (FREEZE) if the SCF orbitals are not in the correct order, it is necessary to permute the input orbitals using the swap keyword of the VECTORS directive. For instance, if it is desired to freeze a total six orbitals corresponding to the SCF orbitals 1-5, and 7, it is necessary to swap orbital 7 into the 6th position. This is accomplished by
vectors swap 6 7\n
The swap capability is examined in more detail in Input/output of MO vectors.
"},{"location":"MP2.html#ri-mp2-fitting-basis","title":"RI-MP2 fitting basis","text":"The RI-MP2 method requires a fitting basis, which must be specified with the name \u201cri-mp2 basis\u201d (see Basis). For instance,
basis \"ri-mp2 basis\"\n O s; 10000.0 1\n O s; 1000.0 1\n O s; 100.0 1\n ...\n end\n
Alternatively, using a standard capability of basis sets (Basis) another named basis may be associated with the fitting basis. For instance, the following input specifies a basis with the name \u201csmall fitting basis\u201d and then defines this to be the \u201cri-mp2 basis\u201d.
basis \"small fitting basis\"\n H s; 10 1\n H s; 3 1\n H s; 1 1\n H s; 0.1 1\n H s; 0.01 1\n end\n
set \"ri-mp2 basis\" \"small fitting basis\"\n
"},{"location":"MP2.html#file3c-ri-mp2-3-center-integral-filename","title":"FILE3C: RI-MP2 3-center integral filename","text":"The default name for the file used to store the transformed 3-center integrals is \u201cfile_prefix.mo3cint\u201d in the scratch directory. This may be overridden using the FILE3C directive. For instance, to specify the file /scratch/h2o.3c, use this directive
file3c /scratch/h2o.3c\n
"},{"location":"MP2.html#riapprox-ri-mp2-approximation","title":"RIAPPROX: RI-MP2 Approximation","text":"The type of RI approximation used in the RI-MP2 calculation is controlled by means of the RIAPPROX directive. The two possible values are V and SVS (case sensitive), which correspond to the approximations with the same names described by Vahtras et al.4. The default is V.
"},{"location":"MP2.html#advanced-options-for-ri-mp2","title":"Advanced options for RI-MP2","text":"These options, which functioned at the time of writing, are not currently supported.
"},{"location":"MP2.html#control-of-linear-dependence","title":"Control of linear dependence","text":"Construction of the RI fit requires the inversion of a matrix of fitting basis integrals which is carried out via diagonalization. If the fitting basis includes near linear dependencies, there will be small eigenvalues which can ultimately lead to non-physical RI-MP2 correlation energies. Eigenvectors of the fitting matrix are discarded if the corresponding eigenvalue is less than min eval which defaults to 10-8. This parameter may be changed by setting the a parameter in the database. For instance, to set it to 10-10
set \"mp2:fit min eval\" 1e-10\n
"},{"location":"MP2.html#reference-spin-mapping-for-ri-mp2-calculations","title":"Reference Spin Mapping for RI-MP2 Calculations","text":"The user has the option of specifying that the RI-MP2 calculations are to be done with variations of the SCF reference wavefunction. This is accomplished with a SET directive of the form,
set \"mp2:reference spin mapping\" <integer array default 0>\n
Each element specified for array is the SCF spin case to be used for the corresponding spin case of the correlated calculation. The number of elements set determines the overall type of correlated calculation to be performed. The default is to use the unadulterated SCF reference wavefunction.
For example, to perform a spin-unrestricted calculation (two elements) using the alpha spin orbitals (spin case 1) from the reference for both of the correlated reference spin cases, the SET directive would be as follows,
set \"mp2:reference spin mapping\" 1 1\n
The SCF calculation to produce the reference wavefunction could be either RHF or UHF in this case.
The SET directive for a similar case, but this time using the beta-spin SCF orbitals for both correlated spin cases, is as follows,
set \"mp2:reference spin mapping\" 2 2\n
The SCF reference calculation must be UHF in this case.
The SET directive for a spin-restricted calculation (one element) from the beta-spin SCF orbitals using this option is as follows,
set \"mp2:reference spin mapping\" 2\n
The SET directive for a spin-unrestricted calculation with the spins flipped from the original SCF reference wavefunction is as follows,
set \"mp2:reference spin mapping\" 2 1\n
"},{"location":"MP2.html#batch-sizes-for-the-ri-mp2-calculation","title":"Batch Sizes for the RI-MP2 Calculation","text":"The user can control the size of each batch in the transformation and energy evaluation in the MP2 calculation, and consequently the memory requirements and number of passes required. This is done using two SET directives of the following form,
set \"mp2:transformation batch size\" <integer size default -1>\n set \"mp2:energy batch size\" <integer isize jsize default -1 -1>\n
The default is for the code to determine the batch size based on the available memory. Should there be problems with the program-determined batch sizes, these variables allow the user to override them. The program will always use the smaller of the user\u2019s value of these entries and the internally computed batch size.
The transformation batch size computed in the code is the number of occupied orbitals in the (occ vir|fit) three-center integrals to be produced at a time. If this entry is less than the number of occupied orbitals in the system, the transformation will require multiple passes through the two-electron integrals. The memory requirements of this stage are two global arrays of dimension batch size x vir x fit with the \u201cfit\u201d dimension distributed across all processors (on shell-block boundaries). The compromise here is memory space versus multiple integral evaluations.
The energy evaluation batch sizes are computed in the code from the number of occupied orbitals in the two sets of three-center integrals to be multiplied together to produce a matrix of approximate four-center integrals. Two blocks of integrals of dimension (batch isize x vir) and (batch jsize x vir) by fit are read in from disk and multiplied together to produce batch isize batch jsize vir^2 approximate integrals. The compromise here is performance of the distributed matrix multiplication (which requires large matrices) versus memory space.
"},{"location":"MP2.html#energy-memory-allocation-mode-ri-mp2-calculation","title":"Energy Memory Allocation Mode: RI-MP2 Calculation","text":"The user must choose a strategy for the memory allocation in the energy evaluation phase of the RI-MP2 calculation, either by minimizing the amount of I/O, or minimizing the amount of computation. This can be accomplished using a SET directive of the form,
set \"mp2:energy mem minimize\" <string mem_opt default I>\n
A value of I entered for the string mem_opt means that a strategy to minimize I/O will be employed. A value of C tells the code to use a strategy that minimizes computation.
When the option to minimize I/O is selected, the block sizes are made as large as possible so that the total number of passes through the integral files is as small as possible. When the option to minimize computation is selected, the blocks are chosen as close to square as possible so that permutational symmetry in the energy evaluation can be used most effectively.
"},{"location":"MP2.html#local-memory-usage-in-three-center-transformation","title":"Local Memory Usage in Three-Center Transformation","text":"For most applications, the code will be able to size the blocks without help from the user. Therefore, it is unlikely that users will have any reason to specify values for these entries except when doing very particular performance measurements.
The size of xf3ci:AO 1 batch size is the most important of the three, in terms of the effect on performance.
Local memory usage in the first two steps of the transformation is controlled in the RI-MP2 calculation using the following SET directives,
set \"xf3ci:AO 1 batch size\" <integer max>\n set \"xf3ci:AO 2 batch size\" <integer max>\n set \"xf3ci:fit batch size\" <integer max>\n
The size of the local arrays determines the sizes of the two matrix multiplications. These entries set limits on the size of blocks to be used in each index. The listing above is in order of importance of the parameters to performance, with xf3ci:AO 1 batch size being most important.
Note that these entries are only upper bounds and that the program will size the blocks according to what it determines as the best usage of the available local memory. The absolute maximum for a block size is the number of functions in the AO basis, or the number of fitting basis functions on a node. The absolute minimum value for block size is the size of the largest shell in the appropriate basis. Batch size entries specified for max that are larger than these limits are automatically reset to an appropriate value.
"},{"location":"MP2.html#one-electron-properties-and-natural-orbitals","title":"One-electron properties and natural orbitals","text":"If an MP2 energy gradient is computed, all contributions are available to form the MP2 linear-response density. This is the density that when contracted with any spin-free, one-electron operator yields the associated property defined as the derivative of the energy. Thus, the reported MP2 dipole moment is the derivative of the energy w.r.t. an external electric field and is not the expectation value of the operator over the wavefunction. It has been shown that evaluating the MP2 density through a derivative provides more accurate results, presumably because this matches the way experiments probe the electron density more closely[raghavachari1981]567.
Only dipole moments are printed by the MP2 gradient code, but natural orbitals are produced and stored in the permanent directory with a file extension of \u201c.mp2nos\u201d. These may be fed into the property package to compute more general properties as in the following example.
start h2o\ngeometry\n O 2.15950 0.88132 0.00000\n H 3.12950 0.88132 0.00000\n H 1.83617 0.89369 -0.91444\nend\n\nbasis spherical\n * library aug-cc-pVDZ\nend\n\nmp2\n freeze atomic\nend\n\ntask mp2 gradient\n\nproperty\n vectors h2o.mp2nos\n mulliken\nend\n\ntask mp2 property\n
Note that the MP2 linear response density matrix is not necessarily positive definite so it is not unusual to see a few small negative natural orbital occupation numbers. Significant negative occupation numbers have been argued to be a sign that the system might be near degenerate8.
"},{"location":"MP2.html#scs-mp2-spin-component-scaled-mp2","title":"SCS-MP2: Spin-Component Scaled MP2","text":"Each MP2 output contains the calculation of the SCS-MP2 correlation energies as suggested by S.Grimme9
The SCS keyword is only required for gradients calculations:
MP2 \n [SCS] \n END\n
Scaling factors for the two components (parallel and opposite spin) can be defined by using the keywords FSS (same spin factor) and FOS (opposite spin factor):
mp2 \n scs \n fss 1.13 \n fos 0.56 \nend\n
Default values are FSS=0.333333333, FOS=1.2 for MP2, and FSS=1.13, FOS=1.27 for CCSD.
"},{"location":"MP2.html#references","title":"References","text":" -
M\u00f8ller, Chr.; Plesset, M. S. Note on an Approximation Treatment for Many-Electron Systems. Physical Review 1934, 46 (7), 618\u2013622. https://doi.org/10.1103/PhysRev.46.618.\u00a0\u21a9
-
Wong, A. T.; Harrison, R. J.; Rendell, A. P. Parallel Direct Four-Index Transformations. Theoretica Chimica Acta 1996, 93 (6), 317\u2013331. https://doi.org/10.1007/BF01129213.\u00a0\u21a9
-
Bernholdt, D. E.; Harrison, R. J. Large-Scale Correlated Electronic Structure Calculations: The RI-MP2 Method on Parallel Computers. Chemical Physics Letters 1996, 250 (5-6), 477\u2013484. https://doi.org/10.1016/0009-2614(96)00054-1.\u00a0\u21a9
-
Vahtras, O.; Alml\u00f6f, J.; Feyereisen, M. W. Integral Approximations for LCAO-SCF Calculations. Chemical Physics Letters 1993, 213 (5-6), 514\u2013518. https://doi.org/10.1016/0009-2614(93)89151-7.\u00a0\u21a9
-
Diercksen, G. H. F.; Roos, B. O.; Sadlej, A. J. Legitimate Calculation of First-Order Molecular Properties in the Case of Limited CI Functions. Dipole Moments. Chemical Physics 1981, 59 (1-2), 29\u201339. https://doi.org/10.1016/0301-0104(81)80082-1.\u00a0\u21a9
-
Rice, J. E.; Amos, R. D. On the Efficient Evaluation of Analytic Energy Gradients. Chemical Physics Letters 1985, 122 (6), 585\u2013590. https://doi.org/10.1016/0009-2614(85)87275-4.\u00a0\u21a9
-
Wiberg, K. B.; Hadad, C. M.; LePage, T. J.; Breneman, C. M.; Frisch, M. J. Analysis of the Effect of Electron Correlation on Charge Density Distributions. The Journal of Physical Chemistry 1992, 96 (2), 671\u2013679. https://doi.org/10.1021/j100181a030.\u00a0\u21a9
-
Gordon, M. S.; Schmidt, M. W.; Chaban, G. M.; Glaesemann, K. R.; Stevens, W. J.; Gonzalez, C. A Natural Orbital Diagnostic for Multiconfigurational Character in Correlated Wave Functions. The Journal of Chemical Physics 1999, 110 (9), 4199\u20134207. https://doi.org/10.1063/1.478301.\u00a0\u21a9
-
Grimme, S. Improved Second-Order M\u00f8ller-Plesset Perturbation Theory by Separate Scaling of Parallel- and Antiparallel-Spin Pair Correlation Energies. The Journal of Chemical Physics 2003, 118 (20), 9095\u20139102. https://doi.org/10.1063/1.1569242.\u00a0\u21a9
"},{"location":"Memory.html","title":"Memory","text":""},{"location":"Memory.html#memory","title":"MEMORY","text":"This is a start-up directive that allows the user to specify the amount of memory PER PROCESSOR CORE that NWChem can use for the job. If this directive is not specified, memory is allocated according to installation-dependent defaults. The defaults should generally suffice for most calculations, since the defaults usually correspond to the total amount of memory available on the machine.
The general form of the directive is as follows:
MEMORY\u00a0[[total]\u00a0<integer total_size>]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\\ \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[stack\u00a0<integer stack_size>]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\\ \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[heap\u00a0<integer heap_size>]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\\ \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[global\u00a0<integer global_size>]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\\\u00a0 \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[units\u00a0<string units default real>]\u00a0\u00a0\\\u00a0 \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[(verify||noverify)]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\\ \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0[(nohardfail||hardfail)]\n
NWChem recognizes the following memory units:
- real and double (synonyms)
- integer
- real and double (synonyms)
- integer
- byte
- kb (kilobytes)
- mb (megabytes)
- mw (megawords, 64-bit word)
In most cases, the user need specify only the total memory limit to adjust the amount of memory used by NWChem. The following specifications all provide for eight megabytes of total memory (assuming 64-bit floating point numbers), which will be distributed according to the default partitioning:
memory\u00a0total\u00a08\u00a0mb\u00a0 \nmemory\u00a0total\u00a01048576\nmemory total 1 gb\n
In NWChem there are three distinct regions of memory: stack, heap, and global. Stack and heap are node-private, while the union of the global region on all processors is used to provide globally-shared memory. The allowed limits on each category are determined from a default partitioning (currently 25% heap, 25% stack, and 50% global). Alternatively, the keywords stack, heap, and global can be used to define specific allocations for each of these categories. If the user sets only one of the stack, heap, or global limits by input, the limits for the other two categories are obtained by partitioning the remainder of the total memory available in proportion to the weight of those two categories in the default memory partitioning. If two of the category limits are given, the third is obtained by subtracting the two given limits from the total limit (which may have been specified or may be a default value). If all three category limits are specified, they determine the total memory allocated. However, if the total memory is also specified, it must be larger than the sum of all three categories. The code will abort if it detects an inconsistent memory specification.
The following memory directives also allocate 8 megabytes, but specify a complete partitioning as well:
memory\u00a0total\u00a08 mb\u00a0stack\u00a02 mb \u00a0heap\u00a02 mb\u00a0global\u00a04\u00a0mb\u00a0 \nmemory\u00a0stack\u00a02\u00a0mb heap\u00a02\u00a0mb global\u00a04\u00a0mb\n
The optional keywords verify and noverify in the directive give the user the option of enabling or disabling automatic detection of corruption of allocated memory. The default is verify, which enables the feature. This incurs some overhead (which can be around 10% increase in walltime on some platforms), which can be eliminated by specifying noverify.
The keywords hardfail and nohardfail give the user the option of forcing (or not forcing) the local memory management routines to generate an internal fatal error if any memory operation fails. The default is nohardfail, which allows the code to continue past any memory operation failure, and perhaps generate a more meaningful error message before terminating the calculation. Forcing a hard-fail can be useful when poorly coded applications do not check the return status of memory management routines.
When assigning the specific memory allocations using the keywords stack, heap, and global in the MEMORY directive, the user should be aware that some of the distinctions among these categories of memory have been blurred in their actual implementation in the code. The memory allocator (MA) allocates both the heap and the stack from a single memory region of size heap+stack, without enforcing the partition. The heap vs. stack partition is meaningful only to applications developers, and can be ignored by most users. Further complicating matters, the global array (GA) toolkit is allocated from within the MA space on distributed memory machines, while on shared-memory machines it is separate. This is because on true shared-memory machines there is no choice but to allocate GAs from within a shared-memory segment, which is managed differently by the operating system.
On distributed memory platforms, the MA region is actually the total size of stack+heap+global. All three types of memory allocation compete for the same pool of memory, with no limits except on the total available memory. This relaxation of the memory category definitions usually benefits the user, since it can allow allocation requests to succeed where a stricter memory model would cause the directive to fail. These implementation characteristics must be kept in mind when reading program output that relates to memory usage.
Standard default for memory is currently 512 MB.
"},{"location":"Multiconfiguration_SCF.html","title":"MCSCF","text":""},{"location":"Multiconfiguration_SCF.html#overview","title":"Overview","text":"The NWChem multiconfiguration SCF (MCSCF) module can currently perform complete active space SCF (CASSCF) calculations with at most 20 active orbitals and about 500 basis functions.
MCSCF \n STATE <string state> \n ACTIVE <integer nactive> \n ACTELEC <integer nactelec> \n MULTIPLICITY <integer multiplicity> \n [SYMMETRY <integer symmetry default 1>] \n [VECTORS [[input] <string input_file default file_prefix.movecs>] \n [swap <integer vec1 vec2> ...] \\ \n [output <string output_file default input_file>] \\ \n [lock] \n [HESSIAN (exact||onel)] \n [MAXITER <integer maxiter default 20>] \n [THRESH <real thresh default 1.0e-4>] \n [TOL2E <real tol2e default 1.0e-9>] \n [LEVEL <real shift default 0.1d0>] \n END\n
Note that the ACTIVE, ACTELEC, and MULTIPLICITY directives are required. The symmetry and multiplicity may alternatively be entered using the STATE directive.
"},{"location":"Multiconfiguration_SCF.html#active-number-of-active-orbitals","title":"ACTIVE: Number of active orbitals","text":"The number of orbitals in the CASSCF active space must be specified using the ACTIVE directive.
E.g.,
active 10\n
The input molecular orbitals (see the vectors directive in MCSCF Vectors and SCF Vectors) must be arranged in order
- doubly occupied orbitals,
- active orbitals, and
- unoccupied orbitals.
"},{"location":"Multiconfiguration_SCF.html#actelec-number-of-active-electrons","title":"ACTELEC: Number of active electrons","text":"The number of electrons in the CASSCF active space must be specified using the ACTELEC directive. An error is reported if the number of active electrons and the multiplicity are inconsistent.
The number of closed shells is determined by subtracting the number of active electrons from the total number of electrons (which in turn is derived from the sum of the nuclear charges minus the total system charge).
"},{"location":"Multiconfiguration_SCF.html#multiplicity","title":"MULTIPLICITY","text":"The spin multiplicity must be specified and is enforced by projection of the determinant wavefunction.
E.g., to obtain a triplet state
multiplicity 3\n
"},{"location":"Multiconfiguration_SCF.html#symmetry-spatial-symmetry-of-the-wavefunction","title":"SYMMETRY: Spatial symmetry of the wavefunction","text":"This species the irreducible representation of the wavefunction as an integer in the range 1\u20138 using the same numbering of representations as output by the SCF program. Note that only Abelian point groups are supported.
E.g., to specify a B1 state when using the C2v group
symmetry 3\n
"},{"location":"Multiconfiguration_SCF.html#state-symmetry-and-multiplicity","title":"STATE: Symmetry and multiplicity","text":"The electronic state (spatial symmetry and multiplicity) may alternatively be specified using the conventional notation for an electronic state, such as 3B2 for a triplet state of B2 symmetry. This would be accomplished with the input
state 3b2\n
which is equivalent to
symmetry 4 \n multiplicity 3\n
"},{"location":"Multiconfiguration_SCF.html#vectors-inputoutput-of-mo-vectors","title":"VECTORS: Input/output of MO vectors","text":"Calculations are best started from RHF/ROHF molecular orbitals (see SCF), and by default vectors are taken from the previous MCSCF or SCF calculation. To specify another input file use the VECTORS directive. Vectors are by default output to the input file, and may be redirected using the output keyword. The swap keyword of the VECTORS directive may be used to reorder orbitals to obtain the correct active space.
The LOCK keyword allows the user to specify that the ordering of orbitals will be locked to that of the initial vectors, insofar as possible. The default is to order by ascending orbital energies within each orbital space. One application where locking might be desirable is a calculation where it is necessary to preserve the ordering of a previous geometry, despite flipping of the orbital energies. For such a case, the LOCK directive can be used to prevent the SCF calculation from changing the ordering, even if the orbital energies change.
Output orbitals of a converged MCSCF calculation are canonicalized as follows:
- Doubly occupied and unoccupied orbitals diagonalize the corresponding blocks of an effective Fock operator. Note that in the case of degenerate orbital energies this does not fully determine the orbtials.
- Active-space orbitals are chosen as natural orbitals by diagonalization of the active space 1-particle density matrix. Note that in the case of degenerate occupations that this does not fully determine the orbitals.
"},{"location":"Multiconfiguration_SCF.html#hessian-select-preconditioner","title":"HESSIAN: Select preconditioner","text":"The MCSCF will use a one-electron approximation to the orbital-orbital Hessian until some degree of convergence is obtained, whereupon it will attempt to use the exact orbital-orbital Hessian which makes the micro iterations more expensive but potentially reduces the total number of macro iterations. Either choice may be forced throughout the calculation by specifying the appropriate keyword on the HESSIAN directive.
E.g., to specify the one-electron approximation throughout
hessian onel\n
"},{"location":"Multiconfiguration_SCF.html#level-level-shift-for-convergence","title":"LEVEL: Level shift for convergence","text":"The Hessian used in the MCSCF optimization is by default level shifted by 0.1 until the orbital gradient norm falls below 0.01, at which point the level shift is reduced to zero. The initial value of 0.1 may be changed using the LEVEL directive. Increasing the level shift may make convergence more stable in some instances.
E.g., to set the initial level shift to 0.5
level 0.5\n
"},{"location":"Multiconfiguration_SCF.html#print-and-noprint","title":"PRINT and NOPRINT","text":"Specific output items can be selectively enabled or disabled using the print control mechanism with the available print options listed in the table below.
MCSCF Print Options Option Class Synopsis ci energy default CI energy eigenvalue fock energy default Energy derived from Fock matrices gradient norm default Gradient norm movecs default Converged occupied MO vectors trace energy high Trace Energy converge info high Convergence data and monitoring precondition high Orbital preconditioner iterations microci high CI iterations in line search canonical high Canonicalization information new movecs debug MO vectors at each macro-iteration ci guess debug Initial guess CI vector density matrix debug One- and Two-particle density matrices
"},{"location":"NWChem-Architecture.html","title":"NWChem Architecture","text":"As described in the Getting Started section, NWChem consists of independent modules that perform the various functions of the code. Examples include the input parser, self-consistent field (SCF) energy, SCF analytic gradient, and density functional theory (DFT) energy modules. The independent NWChem modules can share data only through a disk-resident database, which is similar to the GAMESS-UK dumpfile or the Gaussian checkpoint file. This allows the modules to share data, or to share access to files containing data.
It is not necessary for the user to be intimately familiar with the contents of the database in order to run NWChem. However, a nodding acquaintance with the design of the code will help in clarifying the logic behind the input requirements, especially when restarting jobs or performing multiple tasks within one job.
As detailed in the section describing the (input file structure), all start-up directives are processed at the beginning of the job by the main program, and then the input module is invoked. Each input directive usually results in one or more entries being made in the database. When a TASK directive is encountered, control is passed to the appropriate module, which extracts relevant data from the database and any associated files. Upon completion of the task, the module will store significant results in the database, and may also modify other database entries in order to affect the behavior of subsequent computations.
"},{"location":"NWChem-Architecture.html#database-structure","title":"Database Structure","text":"Data is shared between modules of NWChem by means of the database. Three main types of information are stored in the data base: (1) arrays of data, (2) names of files that contain data, and (3) objects. Arrays are stored directly in the database, and contain the following information:
- the name of the array, which is a string of ASCII characters (e.g., \u201creference energies\u201d)
- the type of the data in the array (i.e., real, integer, logical, or character)
- the number (N) of data items in the array (Note: A scalar is stored as an array of unit length.)
- the N items of data of the specified type
It is possible to enter data directly into the database using the SET directive. For example, to store a (64-bit precision) three-element real array with the name \u201creference energies\u201d in the database, the directive is as follows:
set \"reference energies\" 0.0 1.0 -76.2
NWChem determines the data to be real (based on the type of the first element, 0.0), counts the number of elements in the array, and enters the array into the database.
Much of the data stored in the database is internally managed by NWChem and should not be modified by the user. However, other data, including some NWChem input options, can be freely modified.
Objects are built in the database by storing associated data as multiple entries, using an internally consistent naming convention. This data is managed exclusively by the subroutines (or methods) that are associated with the object. Currently, the code has two main objects: basis sets and geometries. GEOMETRY and BASIS present a complete discussion of the input to describe these objects.
As an illustration of what comprises a geometry object, the following table contains a partial listing of the database contents for a water molecule geometry named \u201ctest geom\u201d. Each entry contains the field test geom, which is the unique name of the object.
Contents of RTDB h2o.db \n----------------------- \nEntry Type[nelem] \n--------------------------- ---------------------- \ngeometry:test geom:efield double[3] \ngeometry:test geom:coords double[9] \ngeometry:test geom:ncenter int[1] \ngeometry:test geom:charges double[3] \ngeometry:test geom:tags char[6] \n...\n
Using this convention, multiple instances of objects may be stored with different names in the same database. For example, if a user needed to do calculations considering alternative geometries for the water molecule, an input file could be constructed containing all the geometries of interest by storing them in the database under different names.
The runtime database contents for the file h2o.db listed above were generated from the user-specified input directive,
geometry \"test geom\" \n O 0.00000000 0.00000000 0.00000000 \n H 0.00000000 1.43042809 -1.10715266 \n H 0.00000000 -1.43042809 -1.10715266 \n end\n
The GEOMETRY directive allows the user to specify the coordinates of the atoms (or centers), and identify the geometry with a unique name.
Unless a specific name is defined for the geometry, (such as the name \"test geom\" shown in the example), the default name of geometry is assigned. This is the geometry name that computational modules will look for when executing a calculation. The SET directive can be used in the input to force NWChem to look for a geometry with a name other than geometry. For example, to specify use of the geometry with the name \"test geom\" in the example above, the SET directive is as follows:
set geometry \"test geom\"\n
NWChem will automatically check for such indirections when loading geometries. Storage of data associated with basis sets, the other database resident object, functions in a similar fashion, using the default name \"ao basis\".
"},{"location":"NWChem-Architecture.html#persistence-of-data-and-restart","title":"Persistence of data and restart","text":"The database is persistent, meaning that all input data and output data (calculation results) that are not destroyed in the course of execution are permanently stored. These data are therefore available to subsequent tasks or jobs. This makes the input for restart jobs very simple, since only new or changed data must be provided. It also makes the behavior of successive restart jobs identical to that of multiple tasks within one job.
Sometimes, however, this persistence is undesirable, and it is necessary to return an NWChem module to its default behavior by restoring the database to its input-free state. In such a case, the UNSET directive can be used to delete all database entries associated with a given module (including both inputs and outputs).
"},{"location":"Names-of-3-dimensional-space-groups.html","title":"Names of 3 dimensional space groups","text":""},{"location":"Names-of-3-dimensional-space-groups.html#names-of-3-dimensional-space-groups","title":"Names of 3-dimensional space groups","text":"Web resources:
- \u201cA Hypertext Book of Crystallographic Space Group Diagrams and Tables\u201d Birkbeck College, University of London http://img.chem.ucl.ac.uk/sgp/mainmenu.htm
- NRL Crystal Lattice Structures 2
- Three-Dimensional Space Groups from Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay https://stevedutch.net/symmetry/3dspacegrps/3dspgrp.htm
- REPRES, Space Group Irreducible Representations http://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-repres
For many of the space groups there are multiple choices of symmetry transformations. They are denoted as settings for each of the groups. By default, the code will use the first setting. By defining setting <integer setting> on the symmetry input line (see Symmetry Group Input paragraph), you can tell the code to choose a different setting/symmetry transformation.
"},{"location":"Names-of-3-dimensional-space-groups.html#triclinic-space-groups-group-numbers-1-2","title":"Triclinic space groups (group numbers: 1-2)","text":"P1P-1
"},{"location":"Names-of-3-dimensional-space-groups.html#monoclinic-space-groups-group-numbers-3-15","title":"Monoclinic space groups (group numbers: 3-15)","text":"P2P2_1C2PmPcCmCcP2/mP2_1/mC2/mP2/cP2_1/cC2/c
"},{"location":"Names-of-3-dimensional-space-groups.html#orthorhombic-space-groups-group-numbers-16-74","title":"Orthorhombic space groups (group numbers: 16-74)","text":"P222P222_1P2_12_12P2_12_12_1C222_1 C222F222I222I2_12_12_1Pmm2 Pmc2_1Pcc2Pma2Pca2_1Pnc2 Pmn2_1Pba2Pna2_1Pnn2Cmm2 Cmc2_1Ccc2Amm2Abm2Ama2 Aba2Fmm2Fdd2Imm2Iba2 Ima2PmmmPnnnPccmPban PmmaPnnaPmnaPccaPbam PccnPbcmPnnmPmmnPbcn PbcaPnmaCmcmCmcaCmmm CccmCmmaCccaFmmmFddd ImmmIbamIbcaImma
"},{"location":"Names-of-3-dimensional-space-groups.html#tetragonal-space-groups-group-numbers-75-142","title":"Tetragonal space groups (group numbers: 75-142)","text":"P4 P4_1P4_2P4_3I4I4_1 P-4I-4P4/mP4_2/mP4/n P4_2/nI4/mI4_1/aP422P42_12 P4_122P4_12_12P4_222P4_22_12P4_322 P4_32_12I422I4_122P4mmP4bm P4_2cmP4_2nmP4ccP4ncP4_2mc P4_2bcI4mmI4cmI4_1mdI4_1cd P-42mP-42cP-42_1mP-42_1cP-4m2 P-4c2P-4b2P-4n2I-4m2I-4c2 I-42mI-42dP4/mmmP4/mccP4/nbm P4/nncP4/mbmP4/mncP4/nmmP4/ncc P4_2/mmcP4_2/mcmP4_2/nbcP4_2/nnmP4_2/mbc P4_2/mnmP4_2/nmcP4_2/ncmI4/mmmI4/mcm I4_1/amdI4_1/acd
"},{"location":"Names-of-3-dimensional-space-groups.html#trigonal-space-groups-group-numbers-143-167","title":"Trigonal space groups (group numbers: 143-167)","text":"P3P3_1P3_2 R3P-3R-3P312P321 P3_112P3_121P3_212P3_221R32 P3m1P31mP3c1P31cR3m R3cP-31mP-31cP-3m1P-3c1 R-3mR-3c
"},{"location":"Names-of-3-dimensional-space-groups.html#hexagonal-space-groups-group-numbers-168-194","title":"Hexagonal space groups (group numbers: 168-194)","text":"P6P6_1P6_5 P6_2P6_4P6_3P-6P6/m P6_3/mP622P6_122P6_522P6_222 P6_422P6_322P6mmP6ccP6_3cm P6_3mcP-6m2P-6c2P-62mP-62c P6/mmmP6/mccP6_3/mcmP6_3/mmc
"},{"location":"Names-of-3-dimensional-space-groups.html#cubic-space-groups-group-numbers-195-230","title":"Cubic space groups (group numbers: 195-230)","text":"P23 F23I23P2_13I2_13Pm-3 Pn-3Fm-3Fd-3Im-3Pa-3 Ia-3P432P4_232F432F4_132 I432P4_332P4_132I4_132P-43m F-43mI-43mP-43nF-43cI-43d Pm-3mPn-3nPm-3nPn-3mFm-3m Fm-3cFd-3mFd-3cIm-3mIa-3d
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html","title":"Nudged Elastic Band (NEB) method","text":"The NEB module is an implementation of the nudged elastic band (NEB) method of Jonsson et al., and it is one of two drivers in NWChem that can be used to perform minimum energy path optimizations. NEB can be used at all levels of theory, including SCF, HF, DFT, PSPW, BAND, MP2, RIMP2, CCSD, TCE.
Input to the NEB modules is contained with the NEB block
NEB \n ... \n END\n
To run a NEB calculation the following the following task directives is used
TASK <theory> NEB \nTASK <theory> NEB ignore\n
where <theory> is SCF, HF, DFT, PSPW, BAND, MP2, CCSD, TCE, etc.. The Task directive with the ignore option is recommended, otherwise NWChem will crash if the path is not optimized in the allowed maximum number of iterations.
Optional input for this module is specified within the compound directive,
NEB \n NBEADS <integer nbeads default 5> \n KBEADS <float kbeads default 0.1> \n MAXITER <integer maxiter default 5> \n\n STEPSIZE <integer stepsize default 1.0> \n NHIST <integer nhist default 5> \n ALGORITHM <integer algorithm default 0> \n\n [loose | default | tight] \n GMAX <float gmax default 0.00045> \n GRMS <float grms default 0.00030> \n XMAX <float xmax default 0.00018> \n XMRS <float xmrs default 0.00012> \n\n [IMPOSE] \n [HASMIDDLE] \n [XYZ_PATH <string xyzfilename>] \n [RESET] \n [PRINT_SHIFT <integer print_shift default 0>] \n END\n
The following list describes the input for the NEB block
- nbeads - number of beads (or images) used to represent the path
- kbeads - value for the NEB spring constant
- maxiter - maximum number of NEB path optimizations to be performed
- stepsize - value for the stepsize used in the optimization. Typically less than 1.
- nhist - number of histories to use for quasi-Newton optimization (algorithm =0)
- LOOSE|DEFAULT|TIGHT - options specifying thresholds for convergence
- gmax - value for the maximum gradient used to determine convergence
- grms - value for the root mean square gradient used to determine convergence
- xmax - value for the maximum cartesian step used to determine convergence
- xrmx - value for the root mean square cartesian step used to determine convergence
- algorithm - 0: quasi-Newton Fixed Point optimization, 1: dampled Verlet optimization, 2: refining conjugate gradient optimization
- IMPOSE - if specified causes the initial geometries used to specify the path to be aligned with one another
- HASMIDDLE - if specified causes the initial path to use the the \u201cmidgeom\u201d geometry to be used as the midpoint, i.e. the initial path is defined as a linear morphing from \u201cgeometry\u201d \u2013> \u201cmidgeom\u201d \u2013> \u201cendgeom\u201d
- XYZ_PATH - if specified the initial path is defined from the sequence of geometries contained in xyzfilename
- RESET - if specified causes the NEB optimization and path to be started from scratch
- print_shift - setting the
PRINT_SHIFT directive causes the path energies and geometries to be outputed every <print_shift> steps. The current path energies are appended to the file jobname.neb_epath and the current geometries are appended to the file jobname.nebpath_\"current iteration\".xyz.
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#setting-up-initial-path","title":"Setting up initial path","text":"There are three different ways to define the initial path for NEB optimization.
- Linear interpolation between two geometries
The geometries in the path are defined by
where the starting geometry is entered in the geometry block labeled geometry, e.g.
geometry nocenter noautosym noautoz \nO 0.00000000 -0.02293938 0.00000000 \nH 0.00000000 0.55046969 0.75406534 \nH 0.00000000 0.55046969 -0.75406534 \nend\n
and the last geometry in the path is entered in the geometry block label endgeom, e.g.
geometry endgeom nocenter noautosym noautoz \nO 0.00000000 0.02293938 0.00000000 \nH 0.00000000 -0.55046969 0.75406534 \nH 0.00000000 -0.55046969 -0.75406534 \nend\n
- Linear interpolation between three geometries
The geometries for this path are defined by
and
where the starting , middle and last geometries are entered in the geometry blocks geometry, midgeom and endgeom respectively, e.g.
geometry nocenter noautosym noautoz \nO 0.00000000 -0.02293938 0.00000000 \nH 0.00000000 0.55046969 0.75406534 \nH 0.00000000 0.55046969 -0.75406534 \nend\n\ngeometry midgeom nocenter noautosym noautoz \nO 0.00000000 0.00000000 0.00000000 \nH 0.00000000 0.00000000 1.00000000 \nH 0.00000000 0.00000000 -1.00000000 \nend\n\ngeometry endgeom nocenter noautosym noautoz \nO 0.00000000 0.02293938 0.00000000 \nH 0.00000000 -0.55046969 0.75406534 \nH 0.00000000 -0.55046969 -0.75406534 \nend\n
- Using
xyz_path to explicitly input a path of geometries
The xyz_path option can also be used to define the initial path.
... \nNEB \n ... \n XYZ_PATH path.xyz\nEND \n...\n
where path.xyz contains a list of geometries in xyz format, e.g.
--------------- path.xyz ------------------ \n 3 \nenergy= -17.107207699285738 \nO 0.000000 -0.022939 0.000000 \nH 0.000000 0.550469 0.754065 \nH 0.000000 0.550469 -0.754065 \n 3 \nenergy= -17.094903833074170 \nO -0.000003 -0.110080 -0.000000 \nH -0.000000 0.273180 0.847029 \nH -0.000000 0.273180 -0.847029 \n 3 \nenergy= -17.063823686395292 \nO -0.000000 -0.000080 -0.000000 \nH 0.000000 -0.000002 0.941236 \nH 0.000000 -0.000002 -0.941236 \n 3 \nenergy= -17.094944036147005 \nO -0.000000 0.110472 -0.000000 \nH -0.000000 -0.273172 0.846957 \nH -0.000000 -0.273172 -0.846957 \n 3 \nenergy= -17.107208157343706 \nO 0.000000 0.022939 0.000000 \nH 0.000000 -0.550469 0.754065 \nH 0.000000 -0.550469 -0.754065 \n--------------- path.xyz ------------------\n
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#convergence-criteria","title":"Convergence criteria","text":"The defaults may be used, or the directives LOOSE, DEFAULT, or TIGHT specified to use standard sets of values, or the individual criteria adjusted. All criteria are in atomic units. GMAX and GRMS control the maximum and root mean square gradient in the coordinates. XMAX and XRMS control the maximum and root mean square of the Cartesian step.
LOOSE DEFAULT TIGHT GMAX 0.0045d0 0.00045 0.000015 GRMS 0.0030d0 0.00030 0.00001 XMAX 0.0054d0 0.00180 0.00006 XRMS 0.0036d0 0.00120 0.00004"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#neb-tutorial-1-h2o-inversion","title":"NEB Tutorial 1: H2O Inversion","text":"(input:h2o-neb.nw, output:h2o-neb.nwout, datafiles: h2o-neb.neb_epath.dat h2o-neb.neb_final_epath.dat )
(xyzfiles: h2o-neb.nebpath_000001.xyz h2o-neb.nebpath_000005.xyz h2o-neb.nebpath_000010.xyz h2o-neb.nebpath_000020.xyz h2o-neb.nebpath_final.xyz )
Title \"H2O inversion calculation\"\necho\nstart h2o-neb\n\ngeometry nocenter noautosym noautoz \nO 0.00000000 -0.02293938 0.00000000 \nH 0.00000000 0.55046969 0.75406534 \nH 0.00000000 0.55046969 -0.75406534 \nend \n\ngeometry endgeom nocenter noautosym noautoz \nO 0.00000000 0.02293938 0.00000000 \nH 0.00000000 -0.55046969 0.75406534 \nH 0.00000000 -0.55046969 -0.75406534 \nend \n#### Gaussian DFT #### \nbasis \n* library 3-21G \nend \n\ndft \n xc b3lyp \n maxiter 5001 \n cgmin \nend \n\nneb \n nbeads 10 \n kbeads 1.0 \n maxiter 10 \n stepsize 0.10 \n print_shift 1 \nend \ntask dft neb ignore\nneb \n # increase the number of images \n nbeads 20 \n kbeads 1.0 \n stepsize 1.0 \n maxiter 30 \n loose \nend \ntask dft neb ignore\n
After each optimization step the path energies are outputed as follows
neb: Path Energy # 9 \nneb: 1 -75.970000166349976 \nneb: 2 -75.973958450556779 \nneb: 3 -75.973964391052448 \nneb: 4 -75.973965560274110 \nneb: 5 -75.973961077512683 \nneb: 6 -75.973087554095144 \nneb: 7 -75.965847261117744 \nneb: 8 -75.950292780255126 \nneb: 9 -75.932932759963109 \nneb: 10 -75.921912278179292 \nneb: 11 -75.921834552460439 \nneb: 12 -75.932680002200939 \nneb: 13 -75.949868818688529 \nneb: 14 -75.965372754426866 \nneb: 15 -75.972788885848303 \nneb: 16 -75.973958649400714 \nneb: 17 -75.973965255113598 \nneb: 18 -75.973964962774133 \nneb: 19 -75.973959526041568 \nneb: 20 -75.970000163960066 \n
Another way to keep track of the optimization process is to run the following grep command on the output file.
[WE24397:NWChem/NEB/Example2] bylaska% grep @ h2o-neb.nwout \n@neb \n@neb NEB Method \n@neb algorithm = 0 \n@neb maxiter = 10 \n@neb nbeads = 10 \n@neb nhist = 5 \n@neb natoms = 3 \n@neb stepsize = 0.100E+01 \n@neb trust = 0.100E+00 \n@neb kbeads = 0.100E+00 \n@neb Gmax tolerance = 0.450E-03 \n@neb Grms tolerance = 0.300E-03 \n@neb Xmax tolerance = 0.180E-03 \n@neb Xrms tolerance = 0.120E-03 \n@neb \n@neb Step Intrinsic E Mid-Point E Minimum E Maximum E Gmax Grms Xrms Xmax Walltime \n@neb ---- -------------- -------------- -------------- -------------- -------- -------- -------- -------- -------- \n@neb 1 -75.951572 -75.921109 -75.970632 -75.921109 0.55875 0.01606 0.14221 1.54029 454.9 \n@neb 2 -75.953755 -75.923180 -75.972590 -75.923177 0.38930 0.01116 0.01588 0.45644 624.4 \n@neb 3 -75.956726 -75.924391 -75.972861 -75.924387 0.25587 0.00961 0.03673 0.83118 805.2 \n@neb 4 -75.957861 -75.924279 -75.973059 -75.924275 0.23572 0.00894 0.01793 0.24399 971.8 \n@neb 5 -75.959613 -75.925045 -75.973869 -75.925036 0.10257 0.00464 0.03197 0.20350 1152.8 \n@neb 6 -75.959964 -75.925503 -75.973957 -75.925486 0.04762 0.00196 0.00905 0.10433 1316.4 \n@neb 7 -75.960068 -75.925822 -75.973956 -75.925791 0.03897 0.00141 0.00308 0.04432 1519.9 \n@neb 8 -75.960091 -75.925914 -75.973959 -75.925877 0.03707 0.00127 0.00070 0.01691 2055.8 \n@neb 9 -75.960129 -75.926078 -75.973962 -75.926028 0.03353 0.00108 0.00127 0.03707 2297.2 \n@neb 10 -75.960142 -75.926142 -75.973963 -75.926085 0.03199 0.00101 0.00054 0.00420 2756.6 \n@neb NEB calculation not converged \n@neb \n@neb NEB Method \n@neb algorithm = 0 \n@neb maxiter = 30 \n@neb nbeads = 20 \n@neb nhist = 5 \n@neb natoms = 3 \n@neb stepsize = 0.100E+01 \n@neb trust = 0.100E+00 \n@neb kbeads = 0.100E+01 \n@neb Gmax tolerance = 0.450E-02 \n@neb Grms tolerance = 0.300E-02 \n@neb Xmax tolerance = 0.540E-02 \n@neb Xrms tolerance = 0.360E-02 \n@neb \n@neb Step Intrinsic E Mid-Point E Minimum E Maximum E Gmax Grms Xrms Xmax Walltime \n@neb ---- -------------- -------------- -------------- -------------- -------- -------- -------- -------- -------- \n@neb 1 -75.960225 -75.921704 -75.973965 -75.921669 0.24799 0.00398 0.00272 0.08741 3966.5 \n@neb 2 -75.960339 -75.921782 -75.973965 -75.921745 0.24794 0.00328 0.00199 0.12148 5023.2 \n@neb 3 -75.960424 -75.921742 -75.973965 -75.921701 0.19390 0.00286 0.00164 0.08342 5741.4 \n@neb 4 -75.960494 -75.921849 -75.973965 -75.921804 0.19681 0.00266 0.00143 0.09030 6079.7 \n@neb 5 -75.960646 -75.921874 -75.973965 -75.921820 0.17459 0.00240 0.00241 0.22047 6751.5 \n@neb 6 -75.960674 -75.921856 -75.973965 -75.921797 0.14246 0.00165 0.00060 0.00256 7572.3 \n@neb 7 -75.960724 -75.921884 -75.973966 -75.921817 0.13004 0.00153 0.00082 0.05401 7893.3 \n@neb 8 -75.960747 -75.921892 -75.973966 -75.921822 0.12809 0.00149 0.00038 0.00237 8631.2 \n@neb 9 -75.960792 -75.921912 -75.973966 -75.921835 0.12267 0.00142 0.00075 0.05081 9222.0 \n@neb 10 -75.960813 -75.921923 -75.973966 -75.921841 0.11902 0.00138 0.00035 0.00212 10163.2 \n@neb 11 -75.960834 -75.921934 -75.973966 -75.921846 0.11569 0.00135 0.00035 0.00203 10478.3 \n@neb 12 -75.961060 -75.922060 -75.973966 -75.921889 0.07709 0.00104 0.00365 0.30944 10863.8 \n@neb 13 -75.961255 -75.922186 -75.973966 -75.921919 0.04600 0.00087 0.00309 0.19999 11357.0 \n@neb 14 -75.961405 -75.922286 -75.973966 -75.921927 0.03549 0.00079 0.00244 0.03857 11860.0 \n@neb NEB calculation converged\n
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#zero-temperature-string-method","title":"Zero Temperature String Method","text":"The STRING module is an implementation of the zero temperature string method of vanden Eijden et al., and it is one of two drivers in NWChem that can be used to perform minimum energy path optimizations. STRING can be used at all levels of theory, including SCF, HF, DFT, PSPW, BAND, MP2, RIMP2, CCSD, TCE.
Input to the STRING module is contained with the STRING block
STRING\n ...\n END\n
To run a STRING calculation the following the following task directives is used
TASK <theory> STRING\nTASK <theory> STRING ignore\n
where <theory> is SCF, HF, DFT, PSPW, BAND, MP2, CCSD, TCE, etc.. The Task directive with the ignore option is recommended, otherwise NWChem will crash if the path is not optimized in the allowed maximum number of iterations.
Optional input for this module is specified within the compound directive,
STRING \n NBEADS <integer nbeads default 5> \n MAXITER <integer maxiter default 5> \n\n STEPSIZE <integer stepsize default 1.0> \n NHIST <integer nhist default 5> \n INTERPOL <integer algorithm default 1> \n\n FREEZE1 <logical freeze1 default .false.> \n FREEZEN <logical freezen default .false.> \n\n TOL <float tol default 0.00045> \n\n [IMPOSE] \n [HASMIDDLE] \n [XYZ_PATH <string xyzfilename>] \n [RESET] \n PRINT_SHIFT <integer print_shift default 0> \n END\n
The following list describes the input for the STRING block
- nbeads - number of beads (or images) used to represent the path
- maxiter - maximum number of NEB path optimizations to be performed
- stepsize - value for the stepsize used in the optimization. Typically less than 1.
- nhist - number of histories to use for quasi-Newton optimization (algorithm =0)
- tol - value for the maximum gradient used to determine convergence
- freeze1 -
.true.: first bead of simulation frozen, .false.:first bead of simulation not frozen. - freezeN -
.true.:last bead of simulation frozen, .false.:last bead of simulation not frozen - interpol - 1: linear, 2: spline, 3: Akima spline
- IMPOSE - if specified causes the initial geometries used to specify the path to be aligned with one another
- HASMIDDLE - if specified causes the initial path to use the the \u201cmidgeom\u201d geometry to be used as the midpoint, i.e. the initial path is defined as a linear morphing from \u201cgeometry\u201d \u2013> \u201cmidgeom\u201d \u2013> \u201cendgeom\u201d
- XYZ_PATH - if specified the initial path is defined from the sequence of geometries contained in xyzfilename
- RESET - if specified causes the NEB optimization and path to be started from scratch
- print_shift - setting the PRINT_SHIFT directive causes the path energies and geometries to be outputed every
<print_shift> steps. The current path energies are appended to the file jobname.neb_epath and the current geometries are appended to the file jobname.nebpath _\"current iteration\".xyz
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#setting-up-the-initial-path","title":"Setting up the initial path","text":"There are three different ways to define the initial path for NEB optimization.
- Linear interpolation between two geometries
The geometries in the path are defined by
where the starting geometry is entered in the geometry block labeled geometry, e.g.
geometry nocenter noautosym noautoz \nO 0.00000000 -0.02293938 0.00000000 \nH 0.00000000 0.55046969 0.75406534 \nH 0.00000000 0.55046969 -0.75406534 \nend\n
and the last geometry in the path is entered in the geometry block label endgeom, e.g.
geometry endgeom nocenter noautosym noautoz \nO 0.00000000 0.02293938 0.00000000 \nH 0.00000000 -0.55046969 0.75406534 \nH 0.00000000 -0.55046969 -0.75406534 \nend\n
- Linear interpolation between three geometries
The geometries for this path are defined by
and
where the starting , middle and last \u201d geometries are entered in the geometry blocks geometry, midgeom and endgeom respectively, e.g.
geometry nocenter noautosym noautoz \nO 0.00000000 -0.02293938 0.00000000 \nH 0.00000000 0.55046969 0.75406534 \nH 0.00000000 0.55046969 -0.75406534 \nend\n\ngeometry midgeom nocenter noautosym noautoz \nO 0.00000000 0.00000000 0.00000000 \nH 0.00000000 0.00000000 1.00000000 \nH 0.00000000 0.00000000 -1.00000000 \nend\n\ngeometry endgeom nocenter noautosym noautoz \nO 0.00000000 0.02293938 0.00000000 \nH 0.00000000 -0.55046969 0.75406534 \nH 0.00000000 -0.55046969 -0.75406534 \nend\n
- Using
xyz_path to explicitly input a path of geometries
The xyz_path option can also be used to define the initial path, e.g.
...\nSTRING\n ...\n XYZ_PATH path.xyz\nEND\n...\n
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#string-tutorial-1hcn-hnc-path-optimization","title":"String Tutorial 1:HCN \u2013> HNC path optimization","text":"(input:HCN-string1.nw, output:HCN-string1.nwout, datafiles: HCN-string1.string_epath.dat HCN-string1.string_final_epath.dat )
(xyzfiles: HCN-string1.stringpath_000001.xyz HCN-string1.stringpath_000005.xyz HCN-string1.stringpath_000010.xyz HCN-string1.stringpath_000020.xyz HCN-string1.stringpath_000030.xyz HCN-string1.stringpath_final.xyz )
In this example, the path energy for the reaction HCN \u2013> HNC is calculated.
# \n# The initial path has the Carbon moving through the Nitrogen. \n# So for this simulation to work that atom avoidance code needs to work. \n# Because the initial path is so stiff the wavefunction optimizer needs to requires \n# lots of iterations during the early stages of the path optimization. \n# \n# \nTitle \"HCN --> HNC Zero-Temperature String Simulation\" \necho \nstart hcn-hnc-dft \n\ngeometry noautoz noautosym \nC 0.00000000 0.00000000 -0.49484657 \nN 0.00000000 0.00000000 0.64616359 \nH 0.00000000 0.00000000 -1.56151539 \nend \n\ngeometry endgeom noautoz noautosym \nC 0.00000000 0.00000000 0.73225318 \nN 0.00000000 0.00000000 -0.42552059 \nH 0.00000000 0.00000000 -1.42351006 \nend \n\n#### Gaussian DFT #### \nbasis \n* library 3-21G \nend \n\ndft \n xc b3lyp \n maxiter 501 \nend \n\nstring \n nhist 10 \n nbeads 10 \n maxiter 10 \n stepsize 0.10 \n print_shift 1 \n\n # don't allow the end points of the path to move \n freeze1 .true. \n freezeN .true. \nend \ntask dft string ignore\n\nstring \n # increase the number of images \n nbeads 20 \n maxiter 20 \n\n # allow the end points of the path to move \n freeze1 .false. \n freezeN .false. \nend \ntask dft string ignore\n
After each optimization step the path energies are outputed as follows
string: Path Energy # 2 \n string: 1 -92.906682492969779 \n string: 2 -92.743446565848473 \n string: 3 -92.751945829987775 \n string: 4 -92.756507971834026 \n string: 5 -92.726984154346979 \n string: 6 -92.701651474021503 \n string: 7 -92.672613497521183 \n string: 8 -92.825096796032099 \n string: 9 -92.716422030970662 \n string: 10 -92.881713271394148\n
Another way to keep track of the optimization process is to run the following grep command on the output file.
[WE24397:NWChem/NEB/Example2] bylaska% grep @ HCN-dft.out \n@zts \n@zts String method. \n@zts Temperature = 0.00000 \n@zts Covergence Tolerance = 0.00010 \n@zts Step Size = 0.10000 \n@zts Maximum Time Steps = 10 \n@zts Number of replicas = 10 \n@zts Number of histories = 10 \n@zts String Interpolator = 1 \n@zts First Replica = frozen \n@zts Last Replica = frozen \n@zts \n@zts Step xrms xmax E start E middle E end E max E average \n@zts 1 0.460700 2.602234 -92.9066825 -83.4767173 -92.8817133 -83.4767173 -91.6169775 \n@zts 2 0.862226 5.405612 -92.9066825 -92.3028437 -92.8817133 -92.3028437 -92.6631831 \n@zts 3 0.105285 0.530157 -92.9066825 -92.3289676 -92.8817133 -92.3289676 -92.6702949 \n@zts 4 0.134687 0.740991 -92.9066825 -92.3512584 -92.8817133 -92.3512584 -92.6821949 \n@zts 5 0.117113 0.916210 -92.9066825 -92.3767826 -92.8817133 -92.3767826 -92.6899234 \n@zts 6 0.124464 0.844439 -92.9066825 -92.4195957 -92.8817133 -92.4195957 -92.7045117 \n@zts 7 0.092105 0.731434 -92.9066825 -92.4510785 -92.8817133 -92.4510785 -92.7156403 \n@zts 8 0.049227 0.330651 -92.9066825 -92.4690983 -92.8817133 -92.4690983 -92.7288274 \n@zts 9 0.032819 0.177356 -92.9066825 -92.4827444 -92.8817133 -92.4827444 -92.7344806 \n@zts 10 0.076249 0.444246 -92.9066825 -92.4930430 -92.8817133 -92.4930430 -92.7381477 \n@zts The string calculation failed to converge \n@zts Bead number 1 Potential Energy = -92.906682487840 \n@zts Bead number 2 Potential Energy = -92.850640135623 \n@zts Bead number 3 Potential Energy = -92.819370566454 \n@zts Bead number 4 Potential Energy = -92.680821335407 \n@zts Bead number 5 Potential Energy = -92.505231918657 \n@zts Bead number 6 Potential Energy = -92.493042984646 \n@zts Bead number 7 Potential Energy = -92.637367419044 \n@zts Bead number 8 Potential Energy = -92.775376312982 \n@zts Bead number 9 Potential Energy = -92.831230727986 \n@zts Bead number 10 Potential Energy = -92.881713271394 \n@zts \n@zts String method. \n@zts Temperature = 0.00000 \n@zts Covergence Tolerance = 0.00010 \n@zts Step Size = 0.10000 \n@zts Maximum Time Steps = 20 \n@zts Number of replicas = 20 \n@zts Number of histories = 10 \n@zts String Interpolator = 1 \n@zts First Replica = moves \n@zts Last Replica = moves \n@zts \n@zts Step xrms xmax E start E middle E end E max E average \n@zts 1 1.039809 5.039486 -92.9071472 -92.4998400 -92.8820628 -92.4998400 -92.7500136 \n@zts 2 0.192562 0.999019 -92.9073958 -92.5259828 -92.8821500 -92.5259828 -92.7624061 \n@zts 3 0.244943 1.236459 -92.9075306 -92.5735140 -92.8821223 -92.5735140 -92.7816692 \n@zts 4 0.207031 1.093667 -92.9075888 -92.6229190 -92.8821177 -92.6154678 -92.7979112 \n@zts 5 0.056648 0.293829 -92.9075975 -92.6672565 -92.8821033 -92.6507897 -92.8101666 \n@zts 6 0.078950 0.555245 -92.9076044 -92.7245122 -92.8822536 -92.7014407 -92.8241914 \n@zts 7 0.065564 0.521110 -92.9076101 -92.7539982 -92.8822915 -92.7376310 -92.8326007 \n@zts 8 0.050188 0.319477 -92.9076113 -92.7695725 -92.8824219 -92.7612604 -92.8378464 \n@zts 9 0.055301 0.322130 -92.9076168 -92.7754581 -92.8825732 -92.7740099 -92.8408900 \n@zts 10 0.038769 0.195102 -92.9076177 -92.7775695 -92.8826652 -92.7775695 -92.8425440 \n@zts 11 0.064900 0.273480 -92.9076215 -92.7800330 -92.8827175 -92.7800330 -92.8443574 \n@zts 12 0.062593 0.266337 -92.9076224 -92.7823972 -92.8826993 -92.7823972 -92.8458976 \n@zts 13 0.205437 0.948190 -92.9076243 -92.7842034 -92.8826408 -92.7842034 -92.8469810 \n@zts 14 0.015025 0.068924 -92.9076247 -92.7844362 -92.8826536 -92.7844362 -92.8472227 \n@zts 15 0.129208 0.602636 -92.9076254 -92.7849856 -92.8826676 -92.7849856 -92.8477169 \n@zts 16 0.013479 0.056561 -92.9076260 -92.7855201 -92.8826783 -92.7855201 -92.8481626 \n@zts 17 0.472858 2.220715 -92.9076271 -92.7878088 -92.8826913 -92.7878088 -92.8497919 \n@zts 18 0.162617 0.766201 -92.9076273 -92.7879912 -92.8826934 -92.7879912 -92.8499197 \n@zts 19 0.013204 0.060562 -92.9076276 -92.7885097 -92.8826994 -92.7885097 -92.8502675 \n@zts 20 0.718205 3.423813 -92.9076278 -92.7905066 -92.8827009 -92.7895258 -92.8514863 \n@zts The string calculation failed to converge \n@zts Bead number 1 Potential Energy = -92.907627751439 \n@zts Bead number 2 Potential Energy = -92.905047596626 \n@zts Bead number 3 Potential Energy = -92.897944354806 \n@zts Bead number 4 Potential Energy = -92.887494117302 \n@zts Bead number 5 Potential Energy = -92.874059841858 \n@zts Bead number 6 Potential Energy = -92.857382758537 \n@zts Bead number 7 Potential Energy = -92.837207959079 \n@zts Bead number 8 Potential Energy = -92.815902497386 \n@zts Bead number 9 Potential Energy = -92.798474907121 \n@zts Bead number 10 Potential Energy = -92.789525765222 \n@zts Bead number 11 Potential Energy = -92.790506632257 \n@zts Bead number 12 Potential Energy = -92.799861168980 \n@zts Bead number 13 Potential Energy = -92.814252430183 \n@zts Bead number 14 Potential Energy = -92.830704548760 \n@zts Bead number 15 Potential Energy = -92.847248091296 \n@zts Bead number 16 Potential Energy = -92.861557132126 \n@zts Bead number 17 Potential Energy = -92.871838446832 \n@zts Bead number 18 Potential Energy = -92.878543965696 \n@zts Bead number 19 Potential Energy = -92.881844751735 \n@zts Bead number 20 Potential Energy = -92.882700859222\n
A plotting program (e.g. gnuplot, xmgrace) can be used to look at final path as well as the the convergence of the path i.e.,
[WE24397:NEB/Example2/perm] bylaska% gnuplot \n\n G N U P L O T \n Version 4.6 patchlevel 0 last modified 2012-03-04 \n Build System: Darwin x86_64 \n\n Copyright (C) 1986-1993, 1998, 2004, 2007-2012 \n Thomas Williams, Colin Kelley and many others \n\n gnuplot home: <http://www.gnuplot.info> \n faq, bugs, etc: type \"help FAQ\" \n immediate help: type \"help\" (plot window: hit 'h') \n\nTerminal type set to 'aqua' \ngnuplot> set xlabel \"Reaction Coordinate\" \ngnuplot> set ylabel \"Energy (kcal/mol)\" \ngnuplot> set yrange [0:100] \ngnuplot> set grid \ngnuplot> set style data linespoints \ngnuplot> plot \"hcn-hnc-dft.string_epath\" using 1:($2+92.908)*27.2116*23.06,\"hcn-hnc-dft.string_final_epath\" using 1:($2+92.908)*27.2116*23.06 \ngnuplot> \n
400px
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#string-tutorial-2","title":"String Tutorial 2:","text":"Title \"2SiO4H4 --> H3O3Si-O-SiO3H3 + H2O\" \necho \nstart sio4h4-dimer \n\ngeometry noautoz noautosym \nSi -3.90592 -0.11789 0.03791 \nO -2.32450 -0.24327 -0.05259 \nO -4.45956 -1.13247 1.13159 \nO -4.53584 -0.45118 -1.38472 \nO -4.28179 1.37363 0.44838 \nSi 1.27960 0.06912 0.14555 \nO 2.85122 0.23514 0.32761 \nO 0.54278 0.38513 1.52092 \nO 0.94484 -1.42248 -0.29913 \nO 0.75605 1.07390 -0.97272 \nH -1.66762 -0.74425 -0.29362 \nH -4.05734 2.06481 0.90983 \nH -4.30983 -1.85807 1.57116 \nH -4.43621 -0.88060 -2.12508 \nH 3.59374 -0.16315 0.50572 \nH 0.36896 0.10990 2.31839 \nH 0.53993 -2.15495 -0.09488 \nH 0.43207 1.85525 -1.13531 \nend \n\ngeometry endgeom noautoz noautosym \nSi -3.07373 0.18232 -0.24945 \nO -1.50797 0.23823 -0.53062 \nO -3.36758 -0.93058 0.85023 \nO -3.83958 -0.20093 -1.59101 \nO -3.57993 1.59735 0.27471 \nSi -0.05186 0.25441 0.11277 \nO 0.94679 -0.58168 -0.80206 \nO -0.10091 -0.40972 1.55838 \nO 1.41035 -3.75872 1.22931 \nO 0.47135 1.75206 0.24209 \nH 1.03624 -4.62405 0.92620 \nH -3.81554 2.06192 0.96069 \nH -3.97094 -1.38510 1.26383 \nH -4.39754 -0.73964 -1.96563 \nH 1.45990 -0.57144 -1.49361 \nH -0.44444 -0.37536 2.34765 \nH 2.15751 -4.00850 1.82933 \nH 0.77180 2.44229 -0.17616 \nend \n\nnwpw \n simulation_cell \n SC 18.0 \n end \n cutoff 30.0 \n lmbfgs \nend \n\nstring \n nhist 10 \n nbeads 10 \n maxiter 10 \n stepsize 0.10 \n print_shift 1 \n\n # don't allow the end points of the path to move \n freeze1 .true. \n freezeN .true. \nend \ntask pspw string ignore\n\nstring \n # increase the number of images \n nbeads 20 \n maxiter 20 \n\n # allow the end points of the path to move \n freeze1 .false. \n freezeN .false. \nend \ntask pspw string ignore\n
"},{"location":"Nudged-Elastic-Band-and-Zero-Temperature-String-Methods.html#string-tutorial-3-combining-neb-and-string-path-optimizations","title":"String Tutorial 3: Combining NEB and String path optimizations","text":""},{"location":"ONIOM.html","title":"Hybrid Calculations with ONIOM","text":""},{"location":"ONIOM.html#overview","title":"Overview","text":"ONIOM is the hybrid method of Morokuma and co-workers that enables different levels of theory to be applied to different parts of a molecule/system and combined to produce a consistent energy expression. The objective is to perform a high-level calculation on just a small part of the system and to include the effects of the remainder at lower levels of theory, with the end result being of similar accuracy to a high-level calculation on the full system.
- M. Svensson, S. Humbel, R.D.J. Froese, T. Mastubara, S. Sieber, and K. Morokuma, J. Phys. Chem., 100, 19357 (1996).
- S. Dapprich, I. Komaromi, K.S. Byun, K. Morokuma, and M.J. Frisch, J. Mol. Struct. (Theochem), 461-462, 1 (1999).
- R.D.J. Froese and K. Morokuma in \u201cEncylopedia of Computational Chemistry\u201d, volume 2, pp.1244-1257, (ed. P. von Rague Schleyer, John Wiley and Sons, Chichester, Sussex, 1998).
The NWChem ONIOM module implements two- and three-layer ONIOM models for use in energy, gradient, geometry optimization, and vibrational frequency calculations with any of the pure quantum mechanical methods within NWChem. At the present time, it is not possible to perform ONIOM calculations with either solvation models or classical force fields. Nor is it yet possible to compute properties except as derivatives of the total energy.
Using the terminology of Morokuma et al., the full molecular geometry including all atoms is referred to as the \u201creal\u201d geometry and it is treated using a \u201clow\u201d-level of theory. A subset of these atoms (referred to as the \u201cmodel\u201d geometry) are treated using both the \u201clow\u201d-level and a \u201chigh\u201d-level of theory. A three-layer model also introduces an \u201cintermediate\u201d model geometry and a \u201cmedium\u201d level of theory.
The two-layer model requires a high and low level of theory and a real and model molecular geometry. The energy at the high-level of theory for the real geometry is estimated as
E(High,Real) = E(Low,Real) + [E(High,Model) - E(Low,Model)].\n
The three-layer model requires high, medium and low levels of theory, and real, intermediate and model geometries and the corresponding energy estimate is
E(High,Real) = E(Low,Real) + [E(High,Model) - E(Medium,Model)]\n + [E(Medium,Inter) - E(Low,Inter)].\n
When does ONIOM work well? The approximation for a two-layer model will be good if
- the model system includes the interactions that dominate the energy difference being computed and the high-level of theory describes these to the required precision, and
- the interactions between the model and the rest of the real system (substitution effects) are described to sufficient accuracy at the lower level of theory.
ONIOM is used to compute energy differences and the absolute energies are not all that meaningful even though they are well defined. Due to cancellation of errors, ONIOM actually works better than you might expect, but a poorly designed calculation can yield very bad results. Please read and heed the caution at the end of the article by Dapprich et al.
The input options are as follows
ONIOM \n HIGH <string theory> [basis <string basis default \"ao basis\">] \\ \n [ecp <string ecp>] [input <string input>] \n [MEDIUM <string theory> [basis <string basis default \"ao basis\">] \\ \n [ecp <string ecp>] [input <string input>]] \n LOW <string theory> [basis <string basis default \"ao basis\">] \\ \n [ecp <string ecp>] [input <string input>] \n MODEL <integer natoms> [charge <double charge>] \\ \n [<integer i1 j1> <real g1> [<string tag1>] ...] \n [INTER <integer natoms> [charge <double charge>] \\ \n [<integer i1 j1> <real g1> [<string tag1>] ...]] \n [VECTORS [low-real <string mofile>] [low-model <string mofile>] \\ \n [high-model <string mofile>] [medium-model <string mofile]\\ \n [medium-inter <string mofile>] [low-inter <string mofile>]] \n [PRINT ...] \n [NOPRINT ...] \nEND\n
which are described in detail below.
For better validation of user input, the HIGH, LOW and MODEL directives must always be specified. If the one of the MEDIUM or INTER directives are specified, then so must the other.
"},{"location":"ONIOM.html#real-model-and-intermediate-geometries","title":"Real, model and intermediate geometries","text":"The geometry and total charge of the full or real system should be specified as normal using the geometry directive. If of the atoms are to be included in the model system, then these should be specified first in the geometry. Similarly, in a three-layer calculation, if there are atoms to be included in the intermediate system, then these should also be arranged together at the beginning of the geometry. The implict assumption is that the model system is a subset of the intermediate system which is a subset of the real system. The number of atoms to be included in the model and intemediate systems are specified using the MODEL and INTER directives. Optionally, the total charge of the model and intermediate systems may be adjusted. The default is that all three systems have the same total charge.
Example 1. A two-layer calculation on taking the potassium ion as the model system. Note that no bonds are broken so no link atoms are introduced. The real geometry would be specified with potassium (the model) first.
geometry autosym \n K 0 0.00 1.37 \n O 0 0.00 -1.07 \n H 0 -0.76 -1.68 \n H 0 0.76 -1.68 \n end\n
and the following directive in the ONIOM input block indicates that one atom (implicitly the first in the geometry) is in the model system
model 1\n
"},{"location":"ONIOM.html#link-atoms","title":"Link atoms","text":"Link atoms for bonds spanning two regions are automatically generated from the bond information. The additional parameters on the MODEL and INTER directives describe the broken bonds including scale factors for placement of the link atom and, optionally, the type of link atom. The type of link atom defaults to hydrogen, but any type may be specified (actually here you are specifying a geometry tag which is used to associate a geometrical center with an atom type and basis sets, etc. For each broken bond specify the numbers of the two atoms (i and j), the scale factor (g) and optionally the tag of the link atom. Link atoms are placed along the vector connecting the the first to the second atom of the bond according to the equation
where g is the scale factor. If the scale factor is one, then the link atom is placed where the second atom was. More usually, the scale factor is less than one, in which case the link atom is placed between the original two atoms. The scale factor should be chosen so that the link atom (usually hydrogen) is placed near its equilibrium bond length from the model atom. E.g., when breaking a single carbon-carbon bond (typical length 1.528 Angstr\u00f8ms) using a hydrogen link atom we will want a carbon-hydrogen bond length of about 1.084 Angstr\u00f8ms, so the scale factor should be chosen as 1.084/1.528 ~ 0.709.
Example 2. A calculation on acetaldehyde (H3C-CHO) using aldehyde (H-CHO) as the model system. The covalent bond between the two carbon atoms is broken and a link atom must be introduced to replace the methyl group. The link atom is automatically generated \u2013 all you need to do is specify the atoms in the model system that are also in the real system (here CHO) and the broken bonds. Here is the geometry of acetaldehyde with the CHO of aldehyde first
geometry \n C -0.383 0.288 0.021 \n H -1.425 0.381 0.376 \n O 0.259 1.263 -0.321 \n\n H 0.115 -1.570 1.007 \n H -0.465 -1.768 -0.642 \n H 1.176 -1.171 -0.352 \n C 0.152 -1.150 0.005 \n end\n
There are three atoms (the first three) of the real geometry included in the model geometry, and we are breaking the bond between atoms 1 and 7, replacing atom 7 with a hydrogen link atom. This is all accomplished by the directive
model 3 1 7 0.709 H\n
Since the default link atom is hydrogen there is actually no need to specify the \u201cH\u201d.
See also the ONIOM three layer example for a more complex example.
"},{"location":"ONIOM.html#numbering-of-the-link-atoms","title":"Numbering of the link atoms","text":"The link atoms are appended to the atoms of the model or intermediate systems in the order that the broken bonds are specified in the input. This is of importance only if manually constructing an initial guess.
"},{"location":"ONIOM.html#high-medium-and-low-theories","title":"High, medium and low theories","text":"The two-layer model requires both the high-level and low-level theories be specified. The three-layer model also requires the medium-level theory. Each of these includes a theory (such as SCF, MP2, DFT, CCSD, CCSD(T), etc.), an optional basis set, an optional ECP, and an optional string containing general NWChem input.
"},{"location":"ONIOM.html#basis-specification","title":"Basis specification","text":"The basis name on the theory directive (high, medium, or low) is that specified on a basis set directive (see Section 7) and not the name of a standard basis in the library. If not specified, the basis set for the high-level theory defaults to the standard \u201cao basis\u201d. That for the medium level defaults to the high-level basis, and the low-level basis defaults to the medium-level basis. Other wavefunction parameters are obtained from the standard wavefunction input blocks. See Effective core potentials for an example.
"},{"location":"ONIOM.html#effective-core-potentials","title":"Effective core potentials","text":"If an effective core potential is specified in the usual fashion outside of the ONIOM input then this will be used in all calculations. If an alternative ECP name (the name specified on the ECP directive in the same manner as done for basis sets) is specified on one of the theory directives, then this ECP will be used in preference for that level of theory. See the ONIOM three layer example for sample input.
"},{"location":"ONIOM.html#general-input-strings","title":"General input strings","text":"For many purposes, the ability to specify the theory, basis and effective core potential is adequate. All of the options for each theory are determined from their independent input blocks. However, if the same theory (e.g., DFT) is to be used with different options for the ONIOM theoretical models, then the general input strings must be used. These strings are processed as NWChem input each time the theoretical model is invoked. The strings may contain any NWChem input, except for options pertaining to ONIOM and the task directive. The intent that the strings be used just to control the options pertaining to the theory being used.
A word of caution. Be sure to check that the options are producing the desired results. Since the NWChem database is persistent and the ONIOM calculations happen in an undefined order, the input strings should fully define the calculation you wish to have happen.
For instance, if the high model is DFT/B3LYP/6-311g** and the low model is DFT/LDA/3-21g, the ONIOM input might look like this
oniom \n model 3 \n low dft basis 3-21g input \"dft; xc; end\" \n high dft basis 6-311g** input \"dft; xc b3lyp; end\" \n end\n
The empty XC directive restores the default LDA exchange-correlation option (see Section 11.3). Note that semi-colons and other quotation marks inside the input string must be preceded by a backslash to avoid special interpretation.
See |DFT with and without charge fitting for another example.
"},{"location":"ONIOM.html#use-of-symmetry","title":"Use of symmetry","text":"Symmetry should work just fine as long as the model and intermediate regions respect the symmetry \u2013 i.e., symmetry equivalent atoms need to be treated equivalently. If symmetry equivalent atoms must be treated in separate regions then the symmetry must be lowered (or completely switched off).
"},{"location":"ONIOM.html#molecular-orbital-files","title":"Molecular orbital files","text":"The VECTORS directive in the ONIOM block is different to that elsewhere in NWChem. For each of the necessary combinations of theory and geometry you can specify a different file for the molecular orbitals. By default each combination will store the MO vectors in the permanent directory using a file name created by appending to the name of the calculation the following string
- low-real \u2013 \u201c.lrmos\u201d
- low-inter \u2013 \u201c.limos\u201d
- low-model \u2013 \u201c.lmmos\u201d
- medium-inter \u2013 \u201c.mimos\u201d
- medium-model \u2013 \u201c.mmmos\u201d
- high-model \u2013 \u201c.hmmos\u201d
Each calculation will utilize the appropriate vectors which is more efficient during geometry optimizations and frequency calculations, and is also useful for the initial calculation. In the absence of existing MO vectors files, the default atomic guess is used (see |Input/output of MO vectors).
If special measures must be taken to converge the initial SCF, DFT or MCSCF calculation for one or more of the systems, then initial vectors may be saved in a file with the default name, or another name may be specified using the VECTORS directive. Note that subsequent vectors (e.g., from a geometry optimization) will be written back to this file, so take a copy if you wish to preserve it. To generate the initial guess for the model or intermediate systems it is necessary to generate the geometries which is most readily done, if there are link atoms, by just running NWChem on the input for the ONIOM calculation on your workstation. It will print these geometries before starting any calculations which you can then terminate.
E.g., in a calculation on Fe(III) surrounded by some ligands, it is hard to converge the full (real) system from the atomic guess so as to obtain a configuration for the iron atom since the d orbitals are often nominally lower in energy than some of the ligand orbitals. The most effective mechanism is to converge the isolated Fe(III) and then to use the fragment guess as a starting guess for the real system. The resulting converged molecular orbitals can be saved either with the default name (as described above in this section), in which case no additional input is necessary. If an alternative name is desired, then the VECTORS directive may be used as follows
vectors low-real /u/rjh/jobs/fe_ether_water.mos\n
"},{"location":"ONIOM.html#restarting","title":"Restarting","text":"Restart of ONIOM calculations does not currently work as smoothly as we would like. For geometry optimizations that terminated gracefully by running out of iterations, the restart will work as normal. Otherwise, specify in the input of the restart job the last geometry of the optimization. The Hessian information will be reused and the calculation should proceed losing at most the cost of one ONIOM gradient evaluation. For energy or frequency calculations, restart may not currently be possible.
"},{"location":"ONIOM.html#examples","title":"Examples","text":""},{"location":"ONIOM.html#hydrocarbon-bond-energy","title":"Hydrocarbon bond energy","text":"A simple two-layer model changing just the wavefunction with one link atom.
This reproduces the two-layer ONIOM (MP2:HF) result from Dapprich et al. for the reaction with using as the model. The geometries of and are optimized at the DFT-B3LYP/6-311++G** level of theory, and then ONIOM is used to compute the binding energy using UMP2 for the model system and HF for the real system. The results, including MP2 calculations on the full system for comparison, are as given in the table below.
Theory Me-CH2 Me-Me H De(Hartree) De(kcal/mol) B3LYP -79.185062 -79.856575 -0.502256 0.169257 106.2 HF -78.620141 -79.251701 -0.499817 0.131741 82.7 MP2 -78.904716 -79.571654 -0.499817 0.167120 104.9 MP2:HF -78.755223 -79.422559 -0.499817 0.167518 105.1
Energies for ONIOM example 1, hydrocarbon bond energy using MP2:HF two-layer model.
The following input first performs a calculation on , and then on . Note that in the second calculation we cannot use the full symmetry since we are breaking the C-C bond in forming the model system (the non-equivalence of the methyl groups is perhaps more apparent if we write ).
start \n\n basis spherical \n H library 6-311++G**; C library 6-311++G** \n end \n\n title \"ONIOM Me-CH2\" \n\n geometry autosym \n H -0.23429328 1.32498565 0.92634814 \n H -0.23429328 1.32498565 -0.92634814 \n C -0.13064265 0.77330370 0.00000000 \n H -1.01618703 -1.19260361 0.00000000 \n H 0.49856072 -1.08196901 -0.88665533 \n H 0.49856072 -1.08196901 0.88665533 \n C -0.02434414 -0.71063687 0.00000000 \n end \n\n scf; uhf; doublet; thresh 1e-6; end \n mp2; freeze atomic; end \n\n oniom \n high mp2 \n low scf \n model 3 3 7 0.724 \n end \n\n task oniom \n\n title \"ONIOM Me-Me\" \n\n geometry # Note cannot use full D3D symmetry here, either specify noautosym, or change an atom tag (here C -> C1) \n H -0.72023641 0.72023641 -1.16373235 \n H 0.98386124 0.26362482 -1.16373235 \n H -0.26362482 -0.98386124 -1.16373235 \n C 0.00000000 0.00000000 -0.76537515 \n H 0.72023641 -0.72023641 1.16373235 \n H -0.98386124 -0.26362482 1.16373235 \n H 0.26362482 0.98386124 1.16373235 \n C1 0.00000000 0.00000000 0.76537515 \n end \n\n scf; rhf; singlet; end \n\n oniom \n high mp2 \n low scf \n model 4 4 8 0.724 \n end \n\n task oniom\n
"},{"location":"ONIOM.html#optimization-and-frequencies","title":"Optimization and frequencies","text":"A two-layer model including modification of theory, basis, ECP and total charge and no link atoms.
This input reproduces the ONIOM optimization and vibrational frequency calculation of Rh(CO)2Cp of Dapprich et al. The model system is Rh(CO)2+. The low theory is the Gaussian LANL2MB model (Hay-Wadt n+1 ECP with minimal basis on Rh, STO-3G on others) with SCF. The high theory is the Gaussian LANL2DZ model (another Hay-Wadt ECP with a DZ basis set on Rh, Dunning split valence on the other atoms) with DFT/B3LYP. Note that different names should be used for the basis set and ECP since the same mechanism is used to store them in the database.
start \n\n ecp LANL2DZ_ECP \n rh library LANL2DZ_ECP \n end \n\n basis LANL2DZ spherical \n rh library LANL2DZ_ECP \n o library SV_(Dunning-Hay); c library SV_(Dunning-Hay); h library SV_(Dunning-Hay) \n end \n\n ecp Hay-Wadt_MB_(n+1)_ECP \n rh library Hay-Wadt_MB_(n+1)_ECP \n end \n\n # This is the minimal basis used by Gaussian. It is not the same \n # as the one in the EMSL basis set library for this ECP. \n basis Hay-Wadt_MB_(n+1) spherical \n Rh s; .264600D+01 -.135541D+01; .175100D+01 .161122D+01; .571300D+00 .589381D+00 \n Rh s; .264600D+01 .456934D+00; .175100D+01 -.595199D+00; .571300D+00 -.342127D+00 \n .143800D+00 .410138D+00; .428000D-01 .780486D+00 \n Rh p; .544000D+01 -.987699D-01; .132900D+01 .743359D+00; .484500D+00 .366846D+00 \n Rh p; .659500D+00 -.370046D-01; .869000D-01 .452364D+00; .257000D-01 .653822D+00 \n Rh d; .366900D+01 .670480D-01; .142300D+01 .455084D+00; .509100D+00 .479584D+00 \n .161000D+00 .233826D+00 \n o library sto-3g; c library sto-3g; h library sto-3g \n end \n\n charge 0 \n geometry autosym \n rh 0.00445705 -0.15119674 0.00000000 \n c -0.01380554 -1.45254070 1.35171818 \n c -0.01380554 -1.45254070 -1.35171818 \n o -0.01805883 -2.26420212 2.20818932 \n o -0.01805883 -2.26420212 -2.20818932 \n c 1.23209566 1.89314720 0.00000000 \n c 0.37739392 1.84262319 -1.15286640 \n c -1.01479160 1.93086461 -0.70666350 \n c -1.01479160 1.93086461 0.70666350 \n c 0.37739392 1.84262319 1.15286640 \n h 2.31251453 1.89903673 0.00000000 \n h 0.70378132 1.86131979 -2.18414218 \n h -1.88154273 1.96919306 -1.35203550 \n h -1.88154273 1.96919306 1.35203550 \n h 0.70378132 1.86131979 2.18414218 \n end \n\n dft; grid fine; convergence gradient 1e-6 density 1e-6; xc b3lyp; end \n scf; thresh 1e-6; end \n\n oniom \n low scf basis Hay-Wadt_MB_(n+1) ecp Hay-Wadt_MB_(n+1)_ECP \n high dft basis LANL2DZ ecp LANL2DZ_ECP \n model 5 charge 1 \n print low \n end \n\n task oniom optimize \n task oniom freq\n
"},{"location":"ONIOM.html#a-three-layer-example","title":"A three-layer example","text":"A three layer example combining CCSD(T), and MP2 with two different quality basis sets, and using multiple link atoms.
The full system is tetra-dimethyl-amino-ethylene (TAME) or (N(Me)2)2-C=C-(N(Me)2)2. The intermediate system is (NH2)2-C=C-(NH2)2 and H2C=CH2 is the model system. CCSD(T)+aug-cc-pvtz is used for the model region, MP2+aug-cc-pvtz for the intermediate region, and MP2+aug-cc-pvdz for everything.
In the real geometry the first two atoms (C, C) are the model system (link atoms will be added automatically). The first six atoms (C, C, N, N, N, N) describe the intermediate system (again with link atoms to be added automatically). The atoms have been numbered using comments to make the bonding input easier to generate.
To make the model system, four C-N bonds are broken between the ethylene fragment and the dimethyl-amino groups and replaced with C-H bonds. To make the intermediate system, eight C-N bonds are broken between the nitrogens and the methyl groups and replaced with N-H bonds. The scaling factor could be chosen differently for each of the bonds.
start \n\n geometry \n C 0.40337795 -0.17516305 -0.51505208 # 1 \n C -0.40328664 0.17555927 0.51466084 # 2 \n N 1.87154979 -0.17516305 -0.51505208 # 3 \n N -0.18694782 -0.60488524 -1.79258692 # 4 \n N 0.18692927 0.60488318 1.79247594 # 5 \n N -1.87148219 0.17564718 0.51496494 # 6 \n C 2.46636552 1.18039452 -0.51505208 # 7 \n C 2.48067731 -1.10425355 0.46161675 # 8 \n C -2.46642715 -1.17982091 0.51473105 # 9 \n C -2.48054940 1.10495864 -0.46156202 # 10 \n C 0.30027136 0.14582197 -2.97072148 # 11 \n C -0.14245927 -2.07576980 -1.96730852 # 12 \n C -0.29948109 -0.14689874 2.97021079 # 13 \n C 0.14140463 2.07558249 1.96815181 # 14 \n H 0.78955302 2.52533887 1.19760764 \n H -0.86543435 2.50958894 1.88075113 \n ... and 22 other hydrogen atoms on the methyl groups \n end \n\n basis aug-cc-pvtz spherical \n C library aug-cc-pvtz; H library aug-cc-pvtz \n end \n\n basis aug-cc-pvdz spherical \n C library aug-cc-pvtz; H library aug-cc-pvtz \n end \n\n oniom \n high ccsd(t) basis aug-cc-pvtz \n medium mp2 basis aug-cc-pvtz \n low mp2 basis aug-cc-pvdz \n model 2 1 3 0.87 1 4 0.87 2 5 0.87 2 6 0.87 \n\n inter 6 3 7 0.69 3 8 0.69 4 11 0.69 4 12 0.69 \\ \n 5 13 0.69 5 14 0.69 6 9 0.69 6 10 0.69 \n end \n\n task oniom\n
"},{"location":"ONIOM.html#dft-with-and-without-charge-fitting","title":"DFT with and without charge fitting","text":"Demonstrates use of general input strings.
A two-layer model for anthracene (a linear chain of three fused benzene rings) using benzene as the model system. The high-level theory is DFT/B3LYP/TZVP with exact Coulomb. The low level is DFT/LDA/DZVP2 with charge fitting.
Note the following.
- The semi-colons and quotation marks inside the input string must be quoted with backslash.
- The low level of theory sets the fitting basis set and the high level of theory unsets it.
start \n geometry \n symmetry d2h \n C 0.71237329 -1.21458940 0.0 \n C -0.71237329 -1.21458940 0.0 \n C 0.71237329 1.21458940 0.0 \n C -0.71237329 1.21458940 0.0 \n C -1.39414269 0.00000000 0.0 \n C 1.39414269 0.00000000 0.0 \n H -2.47680865 0.00000000 0.0 \n H 2.47680865 0.00000000 0.0 \n C 1.40340535 -2.48997027 0.0 \n C -1.40340535 -2.48997027 0.0 \n C 1.40340535 2.48997027 0.0 \n C -1.40340535 2.48997027 0.0 \n C 0.72211503 3.64518615 0.0 \n C -0.72211503 3.64518615 0.0 \n C 0.72211503 -3.64518615 0.0 \n C -0.72211503 -3.64518615 0.0 \n H 2.48612947 2.48094825 0.0 \n H 1.24157357 4.59507342 0.0 \n H -1.24157357 4.59507342 0.0 \n H -2.48612947 2.48094825 0.0 \n H 2.48612947 -2.48094825 0.0 \n H 1.24157357 -4.59507342 0.0 \n H -1.24157357 -4.59507342 0.0 \n H -2.48612947 -2.48094825 0.0 \n end \n\n basis small \n h library DZVP_(DFT_Orbital) \n c library DZVP_(DFT_Orbital) \n end \n\n basis fitting \n h library DGauss_A1_DFT_Coulomb_Fitting \n c library DGauss_A1_DFT_Coulomb_Fitting \n end \n\n basis big \n h library TZVP_(DFT_Orbital) \n c library TZVP_(DFT_Orbital) \n end \n\n oniom \n model 8 1 9 0.75 2 10 0.75 3 11 0.75 4 12 0.75 \n high dft basis big input \"unset \"cd basis\"; dft; xc b3lyp; end\" \n low dft basis small input \"set \"cd basis\" fitting; dft; xc; end\" \n end \n\n task oniom\n
"},{"location":"Ongoing_Projects.html","title":"Ongoing Projects and Future Directions (Obsolete content dating from 2018)","text":""},{"location":"Ongoing_Projects.html#density-functional-theory-dft-time-dependent-dft-td-dft-and-properties","title":"Density functional theory (DFT), time-dependent DFT (TD-DFT) and properties","text":" - Discrete interaction model/quantum mechanical method (DIM/QM) for describing the response properties of molecules adsorbed on metal nanoparticles. Developers: Justin Moore, Lasse Jensen (Penn State University).
- Development of exact two-component relativistic theory and calculations of magnetic response parameters. Developers: Jochen Autschbach (SUNY Buffalo).
- Generalization of real-time TDDFT to include spin-orbit effects . Developers:Niri Govind (PNNL), Ken Lopata (LSU).
"},{"location":"Ongoing_Projects.html#future-projects","title":"Future projects","text":"Dynamics on excited-state surfaces, surface hopping, GW/BSE for molecular systems, Spin-flip TDDFT, Non-collinear DFT, spin-orbit TDDFT, interface to QWalk Quantum Monte-Carlo Program (w/ Lucas Wagner University of Illinois, Urbana-Champaign)
"},{"location":"Ongoing_Projects.html#plane-wave-density-functional-theory-dft-ab-initio-molecular-dynamics-and-nwphys","title":"Plane-Wave Density Functional Theory (DFT), Ab Initio Molecular Dynamics, and NWPhys","text":" - Parallel in Time Algorithms. Developers: Eric J. Bylaska (PNNL), Jonathan Q. Weare (University of Chicago), John H. Weare (UCSD).
- New free energy methods based on diffusion Monte-Carlo algorithm. Developers: Eric J. Bylaska (PNNL), Ying Chen (UCSD), John H. Weare (UCSD).
- Dynamic Mean Field Theory (DMFT). Developers: Duo Song (UCSD), Eric J. Bylaska (PNNL), John H. Weare (UCSD).
- Development of new methods to calculate XPS and XANES spectra. Developers: Eric J. Bylaska (PNNL), Niri Govind (PNNL), John Rehr (University of Washington).
- Implementation of electric field gradients and NMR in NWPW Developers: Eric J. Bylaska (PNNL).
- Implementation of the fast multipole method (FMM) in the combined Ab initio molecular dynamics and molecular dynamics (AIMD/MM) code. Developers: Eric J. Bylaska (PNNL).
- Constant pressure ab initio molecular dynamics. Developers: Eric J. Bylaska (PNNL).
- New implementation of the projector augmented wave method in NWPW. Developers: Eric J. Bylaska (PNNL).
- Initial implementation of orbital free DFT in NWPW. Developers: Eric J. Bylaska (PNNL).
- implementation of Hybrid openmp-mpi and offloading intel MIC algorithms in NWPW. Developers: Eric J. Bylaska (PNNL).
"},{"location":"Ongoing_Projects.html#future-projects_1","title":"Future projects","text":"New NWPhys module development (w/ John Rehr University of Washington) which will include new methods to calculate XPS and XANES spectra. Interface to QWalk Quantum Monte-Carlo Program (w/ Lubos Mitas University of North Carolina).
"},{"location":"Ongoing_Projects.html#high-level-coupled-cluster-methods","title":"High-level Coupled-Cluster methods","text":" - Development of multi-reference coupled-cluster capabilities for quasidegenerate systems. Developers: Jiri Pittner (J Heyrovsky Institute of Physical Chemistry), Karol Kowalski (PNNL).
- Electron-affinity/ionization-potential Equation-of-motion Coupled-Cluster methods. Developers: Kiran Bhaskaran-Nair (LSU), Mark Jarrell (LSU), Juana Moreno (LSU), William Shelton (LSU), Karol Kowalski (PNNL).
- Green function Coupled Cluster formalism. Developers: LSU, PNNL.
"},{"location":"Ongoing_Projects.html#future-projects_2","title":"Future projects","text":"CC/EOMCC analytical gradients, Multi-reference CC formulations employing incomplete model spaces.
"},{"location":"Ongoing_Projects.html#long-term-nwchem-development-plans","title":"Long-term NWChem development plans","text":" - Development of new algorithms for heterogeneous computer system (beyond the existing NWChem GPU implementations).
- Implementation of reduced-scaling methods for electronic structure calculations (local formulations, tensor hypercontractions, resolution-of-identity based approaches),
- Development of novel methodologies for extending temporal scales in ab-initio molecular dynamic and molecular dynamics simulations
- Approximate electronic structure methods for very large-scale simulations (various semi-empirical methods, order N->N2 DFT algorithms - orbital free DFT)
- Integration and extension of existing capabilities towards predictive models for mesoscale systems (for example, aerosol particles, soil chemistry, biosystems, hormone-cofactor functionality in proteins, ionic liquids in cells, large-scale reactions containing multiple steps).
"},{"location":"Other-Capabilities.html","title":"Other Capabilities","text":""},{"location":"Other-Capabilities.html#electron-transfer-calculations","title":"Electron Transfer Calculations","text":""},{"location":"Other-Capabilities.html#controlling-nwchem-with-python","title":"Controlling NWChem with Python","text":""},{"location":"Other-Capabilities.html#quantum-computing","title":"Quantum Computing","text":""},{"location":"Other-Capabilities.html#vscf","title":"VSCF","text":""},{"location":"Other-Capabilities.html#dynamical-nucleation-theory-monte-carlo","title":"Dynamical Nucleation Theory Monte Carlo","text":""},{"location":"Other-Capabilities.html#correlation-consistent-composite-approach-ccca","title":"Correlation consistent Composite Approach (ccCA)","text":""},{"location":"Other-Capabilities.html#interfaces-to-other-programs","title":"Interfaces to Other Programs","text":""},{"location":"Overview.html","title":"NWChem Overview","text":""},{"location":"Overview.html#introduction","title":"Introduction","text":""},{"location":"Overview.html#compiling-nwchem","title":"Compiling NWChem","text":""},{"location":"Overview.html#getting-started","title":"Getting Started","text":""},{"location":"Overview.html#top-level-directives","title":"Top-level Directives","text":""},{"location":"Overview.html#nwchem-architecture","title":"NWChem Architecture","text":""},{"location":"Overview.html#running-nwchem","title":"Running NWChem","text":""},{"location":"P-1.html","title":"P 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a02\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P-1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Triclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a02\n\n+x,+y,+z\n-x,-y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
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"},{"location":"P-3m1.html","title":"P 3m1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0164\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P-3m1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Trigonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n+y,+x,-z\n+x-y,-y,-z\n-x,-x+y,-z\n-x,-y,-z\n+y,-x+y,-z\n+x-y,+x,-z\n-y,-x,+z\n-x+y,+y,+z\n+x,+x-y,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P-4.html","title":"P 4","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a081\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P-4\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n+x,+y,+z\n-x,-y,+z\n+y,-x,-z\n-y,+x,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
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"},{"location":"P-42_1m.html","title":"P 42 1m","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0113\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0P-42_1m\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n+y,-x,-z\n-y,+x,-z\n-x+1/2,+y+1/2,-z\n+x+1/2,-y+1/2,-z\n-y+1/2,-x+1/2,+z\n+y+1/2,+x+1/2,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
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"},{"location":"P1.html","title":"P1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Triclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a01\n\n+x,+y,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n
"},{"location":"P2.html","title":"P2","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a03\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P2\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Monoclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a02\n\n+x,+y,+z\n-x,+y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\ngroup\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a03\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P2\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Monoclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a02\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a02\n\n+x,+y,+z\n-x,-y,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P222.html","title":"P222","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a016\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P222\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z\n+x,-y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P222_1.html","title":"P222 1","text":"\u00a0group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a017\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P222_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n+x,+y,+z\n-x,-y,+z+1/2\n-x,+y,-z+1/2\n+x,-y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P23.html","title":"P23","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0195\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P23\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z\n+x,-y,-z\n+z,+x,+y\n+z,-x,-y\n-z,-x,+y\n-z,+x,-y\n+y,+z,+x\n-y,+z,-x\n+y,-z,-x\n-y,-z,+x\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0 \n
"},{"location":"P2Sc.html","title":"P2Sc","text":" group number = 13\n group name = P2/c\n crystal system = Monoclinic\n setting number = 1\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,+y,-z+1/2\n -x,-y,-z\n +x,-y,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n group number = 13\n group name = P2/c\n crystal system = Monoclinic\n setting number = 2\n number of symmetry operators = 4\n\n +x,+y,+z\n -x+1/2,-y,+z\n -x,-y,-z\n +x+1/2,+y,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n
"},{"location":"P2Sm.html","title":"P2Sm","text":"group name = P2/m\n crystal system = Monoclinic\n setting number = 1\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,+y,-z\n -x,-y,-z\n +x,-y,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n group number = 10\n group name = P2/m\n crystal system = Monoclinic\n setting number = 2\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,-y,+z\n -x,-y,-z\n +x,+y,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n
"},{"location":"P2_1.html","title":"P2 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a04\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P2_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Monoclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a02\n\n+x,+y,+z\n-x,+y+1/2,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\ngroup\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a04\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P2_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Monoclinic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a02\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a02\n\n+x,+y,+z\n-x,-y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"P2_12_12.html","title":"P2 12 12","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a018\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0P2_12_12\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n+x,+y,+z\n-x,-y,+z\n-x+1/2,+y+1/2,-z\n+x+1/2,-y+1/2,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P2_12_12_1.html","title":"P2 12 12 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a019\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0P2_12_12_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P2_13.html","title":"P2 13","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0198\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P2_13\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5 \n
"},{"location":"P2_1Sc.html","title":"P2 1Sc","text":" group number = 14\n group name = P2_1/c\n crystal system = Monoclinic\n setting number = 1\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,+y+1/2,-z+1/2\n -x,-y,-z\n +x,-y+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n group number = 14\n group name = P2_1/c\n crystal system = Monoclinic\n setting number = 2\n number of symmetry operators = 4\n\n +x,+y,+z\n -x+1/2,-y,+z+1/2\n -x,-y,-z\n +x+1/2,+y,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n
"},{"location":"P2_1Sm.html","title":"P2 1Sm","text":" group number = 11\n group name = P2_1/m\n crystal system = Monoclinic\n setting number = 1\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,+y+1/2,-z\n -x,-y,-z\n +x,-y+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n group number = 11\n group name = P2_1/m\n crystal system = Monoclinic\n setting number = 2\n number of symmetry operators = 4\n\n +x,+y,+z\n -x,-y,+z+1/2\n -x,-y,-z\n +x,+y,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 3 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 4 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n
"},{"location":"P3.html","title":"P3","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0143\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P3\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Trigonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a03\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P312.html","title":"P312","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0149\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P312\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Trigonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-y,-x,-z\n-x+y,+y,-z\n+x,+x-y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P31c.html","title":"P31c","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0159\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P31c\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Trigonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n+y,+x,+z+1/2\n+x-y,-y,+z+1/2\n-x,-x+y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"P31m.html","title":"P31m","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0157\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P31m\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Trigonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n+y,+x,+z\n+x-y,-y,+z\n-x,-x+y,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
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"},{"location":"P422.html","title":"P422","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a089\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P422\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z\n+y,-x,+z\n-x,+y,-z\n+x,-y,-z\n+y,+x,-z\n-y,-x,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P42_12.html","title":"P42 12","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a090\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P42_12\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y+1/2,+x+1/2,+z\n+y+1/2,-x+1/2,+z\n-x+1/2,+y+1/2,-z\n+x+1/2,-y+1/2,-z\n+y,+x,-z\n-y,-x,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P432.html","title":"P432","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0207\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P432\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a024\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a013\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a014\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a017\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a018\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a019\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a020\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a021\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a022\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a023\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a024\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0 \n
"},{"location":"P4Sm.html","title":"P4Sm","text":" group number = 83\n group name = P4/m\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 8\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n
"},{"location":"P4Smbm.html","title":"P4Smbm","text":" group number = 127\n group name = P4/mbm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x+1/2,+y+1/2,-z\n +x+1/2,-y+1/2,-z\n +y+1/2,+x+1/2,-z\n -y+1/2,-x+1/2,-z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x+1/2,-y+1/2,+z\n -x+1/2,+y+1/2,+z\n -y+1/2,-x+1/2,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4Smcc.html","title":"P4Smcc","text":" group number = 124\n group name = P4/mcc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z+1/2\n +x,-y,-z+1/2\n +y,+x,-z+1/2\n -y,-x,-z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z+1/2\n -x,+y,+z+1/2\n -y,-x,+z+1/2\n +y,+x,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4Smmm.html","title":"P4Smmm","text":" group number = 123\n group name = P4/mmm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z\n +x,-y,-z\n +y,+x,-z\n -y,-x,-z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z\n -x,+y,+z\n -y,-x,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4Smnc.html","title":"P4Smnc","text":" group number = 128\n group name = P4/mnc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x+1/2,+y+1/2,-z+1/2\n +x+1/2,-y+1/2,-z+1/2\n +y+1/2,+x+1/2,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z\n -y,+x,-z\n +x+1/2,-y+1/2,+z+1/2\n -x+1/2,+y+1/2,+z+1/2\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4Sn.html","title":"P4Sn","text":" group number = 85\n group name = P4/n\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 8\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z\n +y+1/2,-x+1/2,+z\n -x+1/2,-y+1/2,-z\n +x+1/2,+y+1/2,-z\n +y,-x,-z\n -y,+x,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n group number = 85\n group name = P4/n\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 8\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z\n +y,-x+1/2,+z\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z\n -y,+x+1/2,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n
"},{"location":"P4Snbm.html","title":"P4Snbm","text":" group number = 125\n group name = P4/nbm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z\n +x,-y,-z\n +y,+x,-z\n -y,-x,-z\n -x+1/2,-y+1/2,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x+1/2,-z\n -y+1/2,+x+1/2,-z\n +x+1/2,-y+1/2,+z\n -x+1/2,+y+1/2,+z\n -y+1/2,-x+1/2,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n group number = 125\n group name = P4/nbm\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z\n +y,-x+1/2,+z\n -x+1/2,+y,-z\n +x,-y+1/2,-z\n +y,+x,-z\n -y+1/2,-x+1/2,-z\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z\n -y,+x+1/2,-z\n +x+1/2,-y,+z\n -x,+y+1/2,+z\n -y,-x,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4Sncc.html","title":"P4Sncc","text":" group number = 130\n group name = P4/ncc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z\n +y+1/2,-x+1/2,+z\n -x+1/2,+y+1/2,-z+1/2\n +x+1/2,-y+1/2,-z+1/2\n +y,+x,-z+1/2\n -y,-x,-z+1/2\n -x+1/2,-y+1/2,-z\n +x+1/2,+y+1/2,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z+1/2\n -x,+y,+z+1/2\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n group number = 130\n group name = P4/ncc\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z\n +y,-x+1/2,+z\n -x,+y+1/2,-z+1/2\n +x+1/2,-y,-z+1/2\n +y+1/2,+x+1/2,-z+1/2\n -y,-x,-z+1/2\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z\n -y,+x+1/2,-z\n +x,-y+1/2,+z+1/2\n -x+1/2,+y,+z+1/2\n -y+1/2,-x+1/2,+z+1/2\n +y,+x,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4Snmm.html","title":"P4Snmm","text":" group number = 129\n group name = P4/nmm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z\n +y+1/2,-x+1/2,+z\n -x+1/2,+y+1/2,-z\n +x+1/2,-y+1/2,-z\n +y,+x,-z\n -y,-x,-z\n -x+1/2,-y+1/2,-z\n +x+1/2,+y+1/2,-z\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z\n -x,+y,+z\n -y+1/2,-x+1/2,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n group number = 129\n group name = P4/nmm\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z\n +y,-x+1/2,+z\n -x,+y+1/2,-z\n +x+1/2,-y,-z\n +y+1/2,+x+1/2,-z\n -y,-x,-z\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z\n -y,+x+1/2,-z\n +x,-y+1/2,+z\n -x+1/2,+y,+z\n -y+1/2,-x+1/2,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4Snnc.html","title":"P4Snnc","text":" group number = 126\n group name = P4/nnc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z\n +y,-x,+z\n -x,+y,-z\n +x,-y,-z\n +y,+x,-z\n -y,-x,-z\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y+1/2,-x+1/2,-z+1/2\n -y+1/2,+x+1/2,-z+1/2\n +x+1/2,-y+1/2,+z+1/2\n -x+1/2,+y+1/2,+z+1/2\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n group number = 126\n group name = P4/nnc\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z\n +y,-x+1/2,+z\n -x+1/2,+y,-z+1/2\n +x,-y+1/2,-z+1/2\n +y,+x,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z\n -y,+x+1/2,-z\n +x+1/2,-y,+z+1/2\n -x,+y+1/2,+z+1/2\n -y,-x,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4_1.html","title":"P4 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a076\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P4_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n+x,+y,+z\n-x,-y,+z+1/2\n-y,+x,+z+1/4\n+y,-x,+z+3/4\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75 \n
"},{"location":"P4_122.html","title":"P4 122","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a091\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_122\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z+1/2\n-y,+x,+z+1/4\n+y,-x,+z+3/4\n-x,+y,-z\n+x,-y,-z+1/2\n+y,+x,-z+3/4\n-y,-x,-z+1/4\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25 \n
"},{"location":"P4_12_12.html","title":"P4 12 12","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a092\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0P4_12_12\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z+1/2\n-y+1/2,+x+1/2,+z+1/4\n+y+1/2,-x+1/2,+z+3/4\n-x+1/2,+y+1/2,-z+1/4\n+x+1/2,-y+1/2,-z+3/4\n+y,+x,-z\n-y,-x,-z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.25\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.75\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.25\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.75\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5 \n
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"},{"location":"P4_222.html","title":"P4 222","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a093\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_222\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z+1/2\n+y,-x,+z+1/2\n-x,+y,-z\n+x,-y,-z\n+y,+x,-z+1/2\n-y,-x,-z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5 \n
"},{"location":"P4_22_12.html","title":"P4 22 12","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a094\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0P4_22_12\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y+1/2,+x+1/2,+z+1/2\n+y+1/2,-x+1/2,+z+1/2\n-x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,-z+1/2\n+y,+x,-z\n-y,-x,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P4_232.html","title":"P4 232","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0208\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_232\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Cubic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a024\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\n=\u00a0operator\u00a013\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a014\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a015\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a016\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a017\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a018\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a019\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a020\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a021\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a022\u00a0=\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a023\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\n=\u00a0operator\u00a024\u00a0=\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5 \n
"},{"location":"P4_2Sm.html","title":"P4 2Sm","text":" group number = 84\n group name = P4_2/m\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 8\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z+1/2\n +y,-x,+z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z+1/2\n -y,+x,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n
"},{"location":"P4_2Smbc.html","title":"P4 2Smbc","text":" group number = 135\n group name = P4_2/mbc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z+1/2\n +y,-x,+z+1/2\n -x+1/2,+y+1/2,-z\n +x+1/2,-y+1/2,-z\n +y+1/2,+x+1/2,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z+1/2\n -y,+x,-z+1/2\n +x+1/2,-y+1/2,+z\n -x+1/2,+y+1/2,+z\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4_2Smcm.html","title":"P4 2Smcm","text":" group number = 132\n group name = P4_2/mcm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z+1/2\n +y,-x,+z+1/2\n -x,+y,-z+1/2\n +x,-y,-z+1/2\n +y,+x,-z\n -y,-x,-z\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z+1/2\n -y,+x,-z+1/2\n +x,-y,+z+1/2\n -x,+y,+z+1/2\n -y,-x,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4_2Smmc.html","title":"P4 2Smmc","text":" group number = 131\n group name = P4_2/mmc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y,+x,+z+1/2\n +y,-x,+z+1/2\n -x,+y,-z\n +x,-y,-z\n +y,+x,-z+1/2\n -y,-x,-z+1/2\n -x,-y,-z\n +x,+y,-z\n +y,-x,-z+1/2\n -y,+x,-z+1/2\n +x,-y,+z\n -x,+y,+z\n -y,-x,+z+1/2\n +y,+x,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4_2Smnm.html","title":"P4 2Smnm","text":" group number = 136\n group name = P4_2/mnm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,+y+1/2,-z+1/2\n +x+1/2,-y+1/2,-z+1/2\n +y,+x,-z\n -y,-x,-z\n -x,-y,-z\n +x,+y,-z\n +y+1/2,-x+1/2,-z+1/2\n -y+1/2,+x+1/2,-z+1/2\n +x+1/2,-y+1/2,+z+1/2\n -x+1/2,+y+1/2,+z+1/2\n -y,-x,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4_2Sn.html","title":"P4 2Sn","text":" group number = 86\n group name = P4_2/n\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 8\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y,-x,-z\n -y,+x,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n group number = 86\n group name = P4_2/n\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 8\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y,+x+1/2,+z+1/2\n +y+1/2,-x,+z+1/2\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y,-x+1/2,-z+1/2\n -y+1/2,+x,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n
"},{"location":"P4_2Snbc.html","title":"P4 2Snbc","text":" group number = 133\n group name = P4_2/nbc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x,+y,-z+1/2\n +x,-y,-z+1/2\n +y+1/2,+x+1/2,-z\n -y+1/2,-x+1/2,-z\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y,-x,-z\n -y,+x,-z\n +x+1/2,-y+1/2,+z\n -x+1/2,+y+1/2,+z\n -y,-x,+z+1/2\n +y,+x,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n group number = 133\n group name = P4_2/nbc\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z+1/2\n +y,-x+1/2,+z+1/2\n -x+1/2,+y,-z\n +x,-y+1/2,-z\n +y,+x,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z+1/2\n -y,+x+1/2,-z+1/2\n +x+1/2,-y,+z\n -x,+y+1/2,+z\n -y,-x,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4_2Sncm.html","title":"P4 2Sncm","text":" group number = 138\n group name = P4_2/ncm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,+y+1/2,-z\n +x+1/2,-y+1/2,-z\n +y,+x,-z+1/2\n -y,-x,-z+1/2\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z+1/2\n -x,+y,+z+1/2\n -y+1/2,-x+1/2,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n group number = 138\n group name = P4_2/ncm\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z+1/2\n +y,-x+1/2,+z+1/2\n -x,+y+1/2,-z+1/2\n +x+1/2,-y,-z+1/2\n +y+1/2,+x+1/2,-z\n -y,-x,-z\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z+1/2\n -y,+x+1/2,-z+1/2\n +x,-y+1/2,+z+1/2\n -x+1/2,+y,+z+1/2\n -y+1/2,-x+1/2,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4_2Snmc.html","title":"P4 2Snmc","text":" group number = 137\n group name = P4_2/nmc\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x+1/2,+y+1/2,-z+1/2\n +x+1/2,-y+1/2,-z+1/2\n +y,+x,-z\n -y,-x,-z\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y,-x,-z\n -y,+x,-z\n +x,-y,+z\n -x,+y,+z\n -y+1/2,-x+1/2,+z+1/2\n +y+1/2,+x+1/2,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n group number = 137\n group name = P4_2/nmc\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z+1/2\n +y,-x+1/2,+z+1/2\n -x,+y+1/2,-z\n +x+1/2,-y,-z\n +y+1/2,+x+1/2,-z+1/2\n -y,-x,-z+1/2\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z+1/2\n -y,+x+1/2,-z+1/2\n +x,-y+1/2,+z\n -x+1/2,+y,+z\n -y+1/2,-x+1/2,+z+1/2\n +y,+x,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 15 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P4_2Snnm.html","title":"P4 2Snnm","text":" group number = 134\n group name = P4_2/nnm\n crystal system = Tetragonal\n setting number = 1\n number of symmetry operators = 16\n\n +x,+y,+z\n -x,-y,+z\n -y+1/2,+x+1/2,+z+1/2\n +y+1/2,-x+1/2,+z+1/2\n -x,+y,-z\n +x,-y,-z\n +y+1/2,+x+1/2,-z+1/2\n -y+1/2,-x+1/2,-z+1/2\n -x+1/2,-y+1/2,-z+1/2\n +x+1/2,+y+1/2,-z+1/2\n +y,-x,-z\n -y,+x,-z\n +x+1/2,-y+1/2,+z+1/2\n -x+1/2,+y+1/2,+z+1/2\n -y,-x,+z\n +y,+x,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n group number = 134\n group name = P4_2/nnm\n crystal system = Tetragonal\n setting number = 2\n number of symmetry operators = 16\n\n +x,+y,+z\n -x+1/2,-y+1/2,+z\n -y+1/2,+x,+z+1/2\n +y,-x+1/2,+z+1/2\n -x+1/2,+y,-z+1/2\n +x,-y+1/2,-z+1/2\n +y,+x,-z\n -y+1/2,-x+1/2,-z\n -x,-y,-z\n +x+1/2,+y+1/2,-z\n +y+1/2,-x,-z+1/2\n -y,+x+1/2,-z+1/2\n +x+1/2,-y,+z+1/2\n -x,+y+1/2,+z+1/2\n -y,-x,+z\n +y+1/2,+x+1/2,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n -1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n 0.0 -1.0 0.0 0.5\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 4 =\n 0.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n -1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 6 =\n 1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 -1.0 0.0 0.5\n -1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.5\n 0.0 1.0 0.0 0.5\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 1.0 0.0 0.5\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 0.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.5\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n 1.0 0.0 0.0 0.5\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 14 =\n -1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.5\n 0.0 0.0 1.0 0.5\n\n = operator 15 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 16 =\n 0.0 1.0 0.0 0.5\n 1.0 0.0 0.0 0.5\n 0.0 0.0 1.0 0.0\n
"},{"location":"P4_2bc.html","title":"P4 2bc","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0106\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_2bc\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z+1/2\n+y,-x,+z+1/2\n+x+1/2,-y+1/2,+z\n-x+1/2,+y+1/2,+z\n-y+1/2,-x+1/2,+z+1/2\n+y+1/2,+x+1/2,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"P4_2cm.html","title":"P4 2cm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0101\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_2cm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z+1/2\n+y,-x,+z+1/2\n+x,-y,+z+1/2\n-x,+y,+z+1/2\n-y,-x,+z\n+y,+x,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P4_2mc.html","title":"P4 2mc","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0105\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_2mc\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y,+x,+z+1/2\n+y,-x,+z+1/2\n+x,-y,+z\n-x,+y,+z\n-y,-x,+z+1/2\n+y,+x,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"P4_2nm.html","title":"P4 2nm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0102\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P4_2nm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Tetragonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-y+1/2,+x+1/2,+z+1/2\n+y+1/2,-x+1/2,+z+1/2\n+x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,+z+1/2\n-y,-x,+z\n+y,+x,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
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"},{"location":"P6.html","title":"P6","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0168\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P6\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z\n+y,-x+y,+z\n+x-y,+x,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P622.html","title":"P622","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0177\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P622\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z\n+y,-x+y,+z\n+x-y,+x,+z\n+y,+x,-z\n+x-y,-y,-z\n-x,-x+y,-z\n-y,-x,-z\n-x+y,+y,-z\n+x,+x-y,-z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0 \n
"},{"location":"P6Sm.html","title":"P6Sm","text":" group number = 175\n group name = P6/m\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 12\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z\n +y,-x+y,+z\n +x-y,+x,+z\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z\n -y,+x-y,-z\n -x+y,-x,-z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 7 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n
"},{"location":"P6Smcc.html","title":"P6Smcc","text":" group number = 192\n group name = P6/mcc\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 24\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z\n +y,-x+y,+z\n +x-y,+x,+z\n +y,+x,-z+1/2\n +x-y,-y,-z+1/2\n -x,-x+y,-z+1/2\n -y,-x,-z+1/2\n -x+y,+y,-z+1/2\n +x,+x-y,-z+1/2\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z\n -y,+x-y,-z\n -x+y,-x,-z\n -y,-x,+z+1/2\n -x+y,+y,+z+1/2\n +x,+x-y,+z+1/2\n +y,+x,+z+1/2\n +x-y,-y,+z+1/2\n -x,-x+y,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 14 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 15 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 16 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 17 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 18 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 19 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 20 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 21 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 22 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 23 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 24 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P6Smmm.html","title":"P6Smmm","text":" group number = 191\n group name = P6/mmm\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 24\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z\n +y,-x+y,+z\n +x-y,+x,+z\n +y,+x,-z\n +x-y,-y,-z\n -x,-x+y,-z\n -y,-x,-z\n -x+y,+y,-z\n +x,+x-y,-z\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z\n -y,+x-y,-z\n -x+y,-x,-z\n -y,-x,+z\n -x+y,+y,+z\n +x,+x-y,+z\n +y,+x,+z\n +x-y,-y,+z\n -x,-x+y,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 14 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 15 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 16 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 17 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 18 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 19 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 20 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 21 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 22 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 23 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 24 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P6_1.html","title":"P6 1","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0169\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P6_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z+1/3\n-x+y,-x,+z+2/3\n-x,-y,+z+1/2\n+y,-x+y,+z+5/6\n+x-y,+x,+z+1/6\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.833333333333\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.166666666667 \n
"},{"location":"P6_122.html","title":"P6 122","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0178\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P6_122\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z+1/3\n-x+y,-x,+z+2/3\n-x,-y,+z+1/2\n+y,-x+y,+z+5/6\n+x-y,+x,+z+1/6\n+y,+x,-z+1/3\n+x-y,-y,-z\n-x,-x+y,-z+2/3\n-y,-x,-z+5/6\n-x+y,+y,-z+1/2\n+x,+x-y,-z+1/6\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.833333333333\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.166666666667\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.333333333333\n\n=\u00a0operator\u00a08\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.666666666667\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.833333333333\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.166666666667 \n
"},{"location":"P6_2.html","title":"P6 2","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0171\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P6_2\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z+2/3\n-x+y,-x,+z+1/3\n-x,-y,+z\n+y,-x+y,+z+2/3\n+x-y,+x,+z+1/3\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333 \n
"},{"location":"P6_222.html","title":"P6 222","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0180\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P6_222\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z+2/3\n-x+y,-x,+z+1/3\n-x,-y,+z\n+y,-x+y,+z+2/3\n+x-y,+x,+z+1/3\n+y,+x,-z+2/3\n+x-y,-y,-z\n-x,-x+y,-z+1/3\n-y,-x,-z+2/3\n-x+y,+y,-z\n+x,+x-y,-z+1/3\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.666666666667\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.333333333333\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.666666666667\n\n=\u00a0operator\u00a08\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.333333333333\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.666666666667\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.333333333333 \n
"},{"location":"P6_3.html","title":"P6 3","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0173\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0P6_3\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a06\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z+1/2\n+y,-x+y,+z+1/2\n+x-y,+x,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"P6_322.html","title":"P6 322","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0182\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P6_322\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z+1/2\n+y,-x+y,+z+1/2\n+x-y,+x,+z+1/2\n+y,+x,-z\n+x-y,-y,-z\n-x,-x+y,-z\n-y,-x,-z+1/2\n-x+y,+y,-z+1/2\n+x,+x-y,-z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a012\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5 \n
"},{"location":"P6_3Sm.html","title":"P6 3Sm","text":" group number = 176\n group name = P6_3/m\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 12\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z+1/2\n +y,-x+y,+z+1/2\n +x-y,+x,+z+1/2\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z+1/2\n -y,+x-y,-z+1/2\n -x+y,-x,-z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 7 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n
"},{"location":"P6_3Smcm.html","title":"P6 3Smcm","text":" group number = 193\n group name = P6_3/mcm\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 24\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z+1/2\n +y,-x+y,+z+1/2\n +x-y,+x,+z+1/2\n +y,+x,-z+1/2\n +x-y,-y,-z+1/2\n -x,-x+y,-z+1/2\n -y,-x,-z\n -x+y,+y,-z\n +x,+x-y,-z\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z+1/2\n -y,+x-y,-z+1/2\n -x+y,-x,-z+1/2\n -y,-x,+z+1/2\n -x+y,+y,+z+1/2\n +x,+x-y,+z+1/2\n +y,+x,+z\n +x-y,-y,+z\n -x,-x+y,+z\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 8 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 10 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 11 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 12 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 13 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 14 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 15 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 16 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 17 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 18 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 19 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 20 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 21 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 22 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 23 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 24 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n
"},{"location":"P6_3Smmc.html","title":"P6 3Smmc","text":" group number = 194\n group name = P6_3/mmc\n crystal system = Hexagonal\n setting number = 1\n number of symmetry operators = 24\n\n +x,+y,+z\n -y,+x-y,+z\n -x+y,-x,+z\n -x,-y,+z+1/2\n +y,-x+y,+z+1/2\n +x-y,+x,+z+1/2\n +y,+x,-z\n +x-y,-y,-z\n -x,-x+y,-z\n -y,-x,-z+1/2\n -x+y,+y,-z+1/2\n +x,+x-y,-z+1/2\n -x,-y,-z\n +y,-x+y,-z\n +x-y,+x,-z\n +x,+y,-z+1/2\n -y,+x-y,-z+1/2\n -x+y,-x,-z+1/2\n -y,-x,+z\n -x+y,+y,+z\n +x,+x-y,+z\n +y,+x,+z+1/2\n +x-y,-y,+z+1/2\n -x,-x+y,+z+1/2\n\n = operator 1 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 2 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 3 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 4 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 5 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 6 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 7 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 8 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 9 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 10 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 11 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 12 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 13 =\n -1.0 0.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 14 =\n 0.0 1.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 15 =\n 1.0 -1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.0\n\n = operator 16 =\n 1.0 0.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 17 =\n 0.0 -1.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 18 =\n -1.0 1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 -1.0 0.5\n\n = operator 19 =\n 0.0 -1.0 0.0 0.0\n -1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 20 =\n -1.0 1.0 0.0 0.0\n 0.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 21 =\n 1.0 0.0 0.0 0.0\n 1.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.0\n\n = operator 22 =\n 0.0 1.0 0.0 0.0\n 1.0 0.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 23 =\n 1.0 -1.0 0.0 0.0\n 0.0 -1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n\n = operator 24 =\n -1.0 0.0 0.0 0.0\n -1.0 1.0 0.0 0.0\n 0.0 0.0 1.0 0.5\n
"},{"location":"P6_3cm.html","title":"P6 3cm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0185\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P6_3cm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z+1/2\n+y,-x+y,+z+1/2\n+x-y,+x,+z+1/2\n-y,-x,+z+1/2\n-x+y,+y,+z+1/2\n+x,+x-y,+z+1/2\n+y,+x,+z\n+x-y,-y,+z\n-x,-x+y,+z\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a011\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a012\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
"},{"location":"P6_3mc.html","title":"P6 3mc","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0186\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0P6_3mc\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Hexagonal\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a012\n\n+x,+y,+z\n-y,+x-y,+z\n-x+y,-x,+z\n-x,-y,+z+1/2\n+y,-x+y,+z+1/2\n+x-y,+x,+z+1/2\n-y,-x,+z\n-x+y,+y,+z\n+x,+x-y,+z\n+y,+x,+z+1/2\n+x-y,-y,+z+1/2\n-x,-x+y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a09\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a010\u00a0=\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a011\u00a0=\n\u00a01.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a012\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a0-1.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
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"},{"location":"Pcca.html","title":"Pcca","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a054\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pcca\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x+1/2,-y,+z\n-x,+y,-z+1/2\n+x+1/2,-y,-z+1/2\n-x,-y,-z\n+x+1/2,+y,-z\n+x,-y,+z+1/2\n-x+1/2,+y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Pccm.html","title":"Pccm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a049\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pccm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z+1/2\n+x,-y,-z+1/2\n-x,-y,-z\n+x,+y,-z\n+x,-y,+z+1/2\n-x,+y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Pccn.html","title":"Pccn","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a056\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pccn\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z\n-x,+y+1/2,-z+1/2\n+x+1/2,-y,-z+1/2\n-x,-y,-z\n+x+1/2,+y+1/2,-z\n+x,-y+1/2,+z+1/2\n-x+1/2,+y,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Permanent_Dir.html","title":"Permanent Dir","text":""},{"location":"Permanent_Dir.html#permanent_dir","title":"PERMANENT_DIR","text":"This start-up directive allows the user to specify the directory location of permanent files created by NWChem. NWChem distinguishes between permanent (or persistent) files and scratch (or temporary) files, and allows the user the option of putting them in different locations. In most installations, however, permanent and scratch files are all written to the current directory by default. What constitutes \u201clocal\u201d disk space may also differ from machine to machine.
The PERMANENT_DIR directive enable the user to specify a single directory for all processes or different directories for different processes. The general form of the directive is as follows:
(PERMANENT_DIR)\u00a0[(<string\u00a0host>||<integer process>):]\u00a0\u00a0<string directory>\u00a0\u00a0[...]\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html","title":"Plane-Wave Density Functional Theory","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#contents","title":"Contents","text":" - 1 Pseudopotential plane-wave density functional theory (NWPW)
- 1.1 PSPW Tasks - Gamma Point Calculations
- 1.1.1 PAW Potentials
- 1.1.1.1 PAW Implementation Notes
- 1.1.2 Exchange-Correlation Potentials
- 1.1.2.1 DFT + U Corrections
- 1.1.2.2 Langreth style vdw and vdw2 van der Wall functionals
- 1.1.2.3 Grimme Dispersion Corrections
- 1.1.2.4 Using Exchange-Correlation Potentials Available in the DFT Module
- 1.1.2.4 Exact Exchange
- 1.1.2.5 Self-Interaction Corrections
- 1.1.3 Wannier
- 1.1.4 Mulliken Analysis
- 1.1.5 Density of States
- 1.1.6 Projected Density of States
- 1.1.7 Point Charge Analysis
- 1.1.8 PSPW_DPLOT - Generate Gaussian Cube Files
- 1.2 Band Tasks - Multiple k-point Calculations
- 1.2.1 Brillouin Zone
- 1.2.1.1 Band Structure Paths
- 1.2.1.2 Special Points of Different Space Groups (Conventional Cells)
- 1.2.2 Screened Exchange
- 1.2.3 Density of States and Projected Density of States
- 1.2.4 Two-Component Wavefunctions (Spin-Orbit ZORA)
- 1.2.5 BAND_DPLOT - Generate Gaussian Cube Files
- 1.3 Car-Parrinello
- 1.3.1 Adding Geometry Constraints to a Car-Parrinello Simulation
- 1.3.2 Car-Parrinello Output Datafiles
- 1.3.2.1 XYZ motion file
- 1.3.2.2 ION_MOTION motion file
- 1.3.2.3 EMOTION motion file
- 1.3.2.4 HMOTION motion file
- 1.3.2.5 EIGMOTION motion file
- 1.3.2.6 OMOTION motion file
- 1.4 Born-Oppenheimer Molecular Dynamics
- 1.5 Metropolis Monte-Carlo
- 1.6 Free Energy Simulations
- 1.6.1 MetaDynamics
- 1.6.2 TAMD - Temperature Accelerated Molecular Dynamics
- 1.6.3 Collective Variables
- 1.6.3.1 Bond Distance Collective Variable
- 1.6.3.2 Angle Collective Variable
- 1.6.3.3 Coordination Collective Variable
- 1.6.3.4 N-Plane Collective Variable
- 1.6.3.5 User defined Collective Variable
- 1.7 Extended X-Ray Absorption Fine Structure (EXAFS) - Integration with FEFF6L
- 1.8 Frozen Phonon Calculations
- 1.9 Steepest Descent
- 1.10 Simulation Cell
- 1.11 Unit Cell Optimization
- 1.12 SMEAR - Fractional Occupation of the Molecular Orbitals
- 1.13 Spin Penalty Functions
- 1.14 AIMD/MM (QM/MM)
- 1.15 PSP_GENERATOR
- 1.15.1 ATOMIC_FILLING Block
- 1.15.2 CUTOFF
- 1.15.3 SEMICORE_RADIUS
- 1.16 PAW Tasks - Legacy Implementation
- 1.17 Pseudopotential and PAW basis Libraries
- 1.18 NWPW RTDB Entries and Miscellaneous DataFiles
- 1.18.1 Ion Positions
- 1.18.2 Ion Velocities
- 1.18.3 Wavefunction Datafile
- 1.18.4 Velocity Wavefunction Datafile
- 1.18.5 Formatted Pseudopotential Datafile
- 1.18.6 One-Dimensional Pseudopotential Datafile
- 1.19 Car-Parrinello Scheme for Ab Initio Molecular Dynamics
- 1.19.1 Verlet Algorithm for Integration
- 1.19.2 Constant Temperature Simulations: Nose-Hoover Thermostats
- 1.20 NWPW Tutorial 1: S2 dimer examples with PSPW
- 1.20.1 Total energy of S2 dimer with LDA approximation
- 1.20.2 Structural optimization of S2 dimer with LDA approximation
- 1.20.3 Frequency calculation of S2 dimer with LDA approximation
- 1.20.4 Ab initio molecular dynamics simulation (Car-Parrinello) of S2 dimer using the LDA approximation
- 1.20.5 Ab initio molecular dynamics simulation (Born-Oppenheimer) of S2 dimer using the LDA approximation
- 1.21 NWPW Tutorial 2: Using PSPW Car-Parrinello Simulated Annealing Simulations to Optimize Structures
- 1.21.1 Simulated Annealing Using Constant Energy Simulation
- 1.21.2 Simulated Annealing Using Constant Temperature Simulation
- 1.22 NWPW Tutorial 3: using isodesmic reaction energies to estimate gas-phase thermodynamics
- 1.23 NWPW Tutorial 4: AIMD/MM simulation of CCl4 + 64 H2O
- 1.24 NWPW Tutorial 5: Optimizing the Unit Cell and Geometry of Diamond
- 1.24.1 Optimizing the Unit Cell and Geometry for an 8 Atom Supercell of Diamond with PSPW
- 1.24.2 Optimizing the Unit Cell for an 8 Atom Supercell of Diamond with BAND
- 1.24.3 Using BAND to Optimize the Unit Cell for a 2 Atom Primitive Cell of Diamond
- 1.24.4 Using BAND to Calculate the Band Structures of Diamond
- 1.24.5 Using BAND to Calculate the Density of States of Diamond
- 1.24.6 Calculate the Phonon Spectrum of Diamond
- 1.25 NWPW Tutorial 6: optimizing the unit cell of nickel with fractional occupation
- 1.26 NWPW Tutorial 7: Optimizing the unit cells with symmetry: Diamond with Fd-3m symmetry and Brucite with P-3m1 symmetry
- 1.27 NWPW Tutorial 8: NVT Metropolis Monte-Carlo Simulations
- 1.28 NWPW Tutorial 9: NPT Metropolis Monte-Carlo Simulations
- 1.29 NWPW Tutorial 9: Free Energy Simulations
- 1.30 PAW Tutorial
- 1.30.1 Optimizing a water molecule
- 1.30.2 Optimizing a unit cell and geometry for Silicon-Carbide
- 1.30.3 Running a Car-Parrinello Simulation
- 1.31 NWPW Capabilities and Limitations
- 1.32 Development Blog
- 1.33 Questions and Difficulties
"},{"location":"Plane-Wave-Density-Functional-Theory.html#pseudopotential-plane-wave-density-functional-theory-nwpw","title":"Pseudopotential plane-wave density functional theory (NWPW)","text":"The NWChem plane-wave (NWPW) module uses pseudopotentials and plane-wave basis sets to perform Density Functional Theory calculations (simple introduction pw-lecture.pdf). This module complements the capabilities of the more traditional Gaussian function based approaches by having an accuracy at least as good for many applications, yet is still fast enough to treat systems containing hundreds of atoms. Another significant advantage is its ability to simulate dynamics on a ground state potential surface directly at run-time using the Car-Parrinello algorithm. This method\u2019s efficiency and accuracy make it a desirable first principles method of simulation in the study of complex molecular, liquid, and solid state systems. Applications for this first principles method include the calculation of free energies, search for global minima, explicit simulation of solvated molecules, and simulations of complex vibrational modes that cannot be described within the harmonic approximation.
The NWPW module is a collection of three modules.
- PSPW - (PSeudopotential Plane-Wave) A gamma point code for calculating molecules, liquids, crystals, and surfaces.
- Band - A band structure code for calculating crystals and surfaces with small band gaps (e.g. semi-conductors and metals).
- PAW - a (gamma point) projector augmented plane-wave code for calculating molecules, crystals, and surfaces ( This module will be deprecated in the future releases since PAW potentials have been added to PSPW )
The PSPW, Band, and PAW modules can be used to compute the energy and optimize the geometry. Both the PSPW and Band modules can also be used to find saddle points, and compute numerical second derivatives. In addition the PSPW module can also be used to perform Car-Parrinello molecular dynamics. Section PSPW Tasks describes the tasks contained within the PSPW module, section Band Tasks describes the tasks contained within the Band module, section PAW Tasks describes the tasks contained within the PAW module, and section Pseudopotential and PAW basis Libraries describes the pseudopotential library included with NWChem. The datafiles used by the PSPW module are described in section NWPW RTDB Entries and DataFiles. Car-Parrinello output data files are described in section Car-Parrinello Output Datafiles, and the minimization and Car-Parrinello algorithms are described in section Car-Parrinello Scheme for Ab Initio Molecular Dynamics. Examples of how to setup and run a PSPW geometry optimization, a Car-Parrinello simulation, a band structure minimization, and a PAW geometry optimization are presented at the end. Finally in section NWPW Capabilities and Limitations the capabilities and limitations of the NWPW module are discussed.
As of NWChem 6.6 to use PAW potentials the user is recommended to use the implementation contained in the PSPW module (see Sections ). PAW potentials are also being integrated into the BAND module. Unfortunately, the porting to BAND was not completed for the NWChem 6.6 release.
If you are a first time user of this module it is recommended that you skip the next five sections and proceed directly to the tutorials.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#pspw-tasks-gamma-point-calculations","title":"PSPW Tasks: Gamma Point Calculations","text":"All input to the PSPW Tasks is contained within the compound PSPW block,
PSPW \n ...\nEND\n
To perform an actual calculation a TASK PSPW directive is used (Section Task).
TASK PSPW
In addition to the directives listed in Task, i.e.
TASK PSPW energy \nTASK PSPW gradient \nTASK PSPW optimize \nTASK PSPW saddle \nTASK PSPW freqencies\nTASK PSPW vib \n
there are additional directives that are specific to the PSPW module, which are:
TASK PSPW [Car-Parrinello || \n Born-Oppenheimer ||\n Metropolis ||\n pspw_et ||\n noit_energy ||\n stress ||\n pspw_dplot || \n wannier ||\n expand_cell || \n exafs ||\n ionize ||\n lcao ||\n rdf ||\n aimd_properties ||\n translate ||\n psp_generator || \n steepest_descent || \n psp_formatter || \n wavefunction_initializer || \n v_wavefunction_initializer || \n wavefunction_expander ]\n
Once a user has specified a geometry, the PSPW module can be invoked with no input directives (defaults invoked throughout). However, the user will probably always specify the simulation cell used in the computation, since the default simulation cell is not well suited for most systems. There are sub-directives which allow for customized application; those currently provided as options for the PSPW module are:
NWPW \n SIMULATION_CELL ... (see section [Simulation Cell](#Simulation_Cell)) END\n CELL_NAME <string cell_name default 'cell_default'>\n VECTORS [[input (<string input_wavefunctions default file_prefix.movecs>) || \n [output(<string output_wavefunctions default file_prefix.movecs>)]] \n XC (Vosko || LDA || PBE96 || revPBE || PBEsol || \n LDA-SIC || LDA-SIC/2 || LDA-0.4SIC || LDA-SIC/4 || LDA-0.2SIC || \n PBE96-SIC || PBE96-SIC/2 || PBE96-0.4SIC || PBE96-SIC/4 || PBE96-0.2SIC || \n revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || \n PBE96-Grimme2 || PBE96-Grimme3 || PBE96-Grimme4 || BLYP-Grimme2 || BLYP-Grimme3 || BLYP-Grimme4 || \n revPBE-Grimme2 || revPBE-Grimme3 || revPBE-Grimme4 || PBEsol-Grimme2 || PBEsol-Grimme3 || PBEsol-Grimme4 || \n PBE0-Grimme2 || PBE0-Grimme3 || PBE0-Grimme4 || B3LYP-Grimme2 || B3LYP-Grimme3 || B3LYP-Grimme4 ||\n revPBE0-Grimme2 || revPBE0-Grimme3 || revPBE0-Grimme4 ||\n PBE0 || revPBE0 || HSE || HF || default Vosko) \n XC new ...(see section [Using Exchange-Correlation Potentials Available in the DFT Module](#Using_Exchange-Correlation_Potentials_Available_in_the_DFT_Module))\n DFT||ODFT||RESTRICTED||UNRESTRICTED \n MULT <integer mult default 1> \n CG \n LMBFGS \n SCF [Anderson|| simple || Broyden] \n [CG || RMM-DIIS] \n [density || potential]\n [ALPHA real alpha default 0.25]\n [Kerker real ekerk nodefault] \n [ITERATIONS integer inner_iterations default 5] \n [OUTER_ITERATIONS integer outer_iterations default 0]\n LOOP <integer inner_iteration outer_iteration default 10 100> \n TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> \n FAKE_MASS <real fake_mass default 400000.0> \n TIME_STEP <real time_step default 5.8> \n EWALD_NCUT <integer ncut default 1> \n EWALD_RCUT <real rcut default (see input description)> \n CUTOFF <real cutoff> \n ENERGY_CUTOFF <real ecut default (see input description)> \n WAVEFUNCTION_CUTOFF <real wcut default (see input description)> \n ALLOW_TRANSLATION \n TRANSLATION (ON || OFF)\n ROTATION (ON || OFF) \n MULLIKEN [OFF]\n EFIELD \n\n BO_STEPS <integer bo_inner_iteration bo_outer_iteration default 10 100> \n MC_STEPS <integer mc_inner_iteration mc_outer_iteration default 10 100>\n BO_TIME_STEP <real bo_time_step default 5.0> \n BO_ALGORITHM [verlet|| velocity-verlet || leap-frog]\n BO_FAKE_MASS <real bo_fake_mass default 500.0> \n\n SOCKET (UNIX || IPI_CLIENT) <string socketname default (see input description)> \n\n MAPPING <integer mapping default 1> \n NP_DIMENSIONS <integer npi npj default -1 -1> \n CAR-PARRINELLO ... (see section [Car-Parrinello](#Car-Parrinello)) END \n STEEPEST_DESCENT ... (see section [Steepest Descent](#STEEPEST_DESCENT)) END\n DPLOT ... (see section [DPLOT](#DPLOT)) END \n WANNIER ... (see section [Wannier](#Wannier)) END \n PSP_GENERATOR ... (see section [PSP Generator](#PSP_GENERATOR))) END \n\n WAVEFUNCTION_INITIALIZER ... (see section [Wavefunction Initializer](NWPW_RETIRED.md#WAVEFUNCTION_INITIALIZER) - retired) END \n V_WAVEFUNCTION_INITIATIZER ... (see section [Wavefunction Velocity Initializer (NWPW_RETIRED#V_WAVEFUNCTION_INITIALIZER) - retired) END \n WAVEFUNCTION_EXPANDER ... (see section [Wavefunction Expander](NWPW_RETIRED.md#WAVEFUNCTION_EXPANDER) - retired) END \n INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default file_prefix.movecs> \n OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default file_prefix.movecs> \nEND\n
The following list describes the keywords contained in the PSPW input block.
cell_name - name of the simulation_cell named cell_name. See section Simulation Cell.input_wavefunctions - name of the file containing one-electron orbitalsoutput_wavefunctions - name of the file that will contain the one-electron orbitals at the end of the run.fake_mass - value for the electronic fake mass This parameter is not presently used in a conjugate gradient simulation.time_step - value for the time step . This parameter is not presently used in a conjugate gradient simulation.inner_iteration - number of iterations between the printing out of energies and tolerancesouter_iteration - number of outer iterationstole - value for the energy tolerance.tolc - value for the one-electron orbital tolerance.cutoff - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.ecut - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell cell_name.wcut - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell cell_name.ncut - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.rcut - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
Default set to be .
- (Vosko || PBE96 || revPBE || \u2026) - Choose between Vosko et al\u2019s LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options.
- MULT - optional keyword which if specified allows the user to define the spin multiplicity of the system
- MULLIKEN - optional keyword which if specified causes a Mulliken analysis to be performed at the end of the simulation.
- EFIELD - optional keyword which if specified causes an atomic electric field analysis to be performed at the end of the simulation.
- ALLOW_TRANSLATION - By default the the center of mass forces are projected out of the computed forces. This optional keyword if specified allows the center of mass forces to not be zero.
- TRANSLATION - By default the the center of mass forces are projected out of the computed forces. TRANSLATION ON allows the center of mass forces to not be zero.
- ROTATION - By default the overall rotation is not projected out of the computed forces. ROTATION OFF projects out the overal rotation of the molecule.
- CG - optional keyword which sets the minimizer to 1
- LMBFGS - optional keyword which sets the minimizer to 2
- SCF - optional keyword which sets the minimizer to be a band by band minimizer. Several options are available for setting the density or potential mixing, and the type of Kohn-Sham minimizer.
mapping - for a value of 1 slab FFT is used, for a value of 2 a 2d-hilbert FFT is used.
A variety of prototype minimizers can be used to minimize the energy. To use these other optimizers the following SET directive needs to be specified:
set nwpw:mimimizer 1 # Default - Grassman conjugate gradient minimizer is used to minimize the energy. \nset nwpw:mimimizer 2 # Grassman LMBFGS minimimzer is used to minimize the energy.\nset nwpw:minimizer 4 # Stiefel conjugate gradient minimizer is used to minimize the energy. \nset nwpw:minimizer 5 # Band-by-band (potential) minimizer is used to minimize the energy.\nset nwpw:minimizer 6 # Projected Grassman LMBFGS minimizer is used to minimize the energy.\nset nwpw:minimizer 7 # Stiefel LMBFGS minimizer is used to minimize the energy.\nset nwpw:minimizer 8 # Band-by-band (density) minimizer is used to minimize the energy.\n
Limited testing suggests that the Grassman LMBFGS minimizer is about twice as fast as the conjugate gradient minimizer. However, there are several known cases where this optimizer fails, so it is currently not a default option, and should be used with caution.
In addition the following SET directives can be specified:
set nwpw:lcao_skip .false. # Initial wavefunctions generated using an LCAO guess. \nset nwpw:lcao_skip .true. # Default - Initial wavefunctions generated using a random plane-wave guess.\nset nwpw:lcao_print .false. # Default - Output not produced during the generation of the LCAO guess. \nset nwpw:lcao_print .true. # Output produced during the generation of the LCAO guess.\nset nwpw:lcao_iterations 2 #specifies the number of LCAO iterations.\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#paw-potentials","title":"PAW Potentials","text":"The PSPW code can now handle PAW potentials. To use them the pseudopotentials input block is used to redirect the code to use the paw potentials located in the default paw potential library ($NWCHEM_TOP/src/nwpw/libraryp/paw_default). For example, to redirect the code to use PAW potentials for carbon and hydrogen, the following input would be used.
nwpw \n pseudopotentials \n C library paw_default \n H library paw_default \n end \nend\n
Most of the capabilities of PSPW will work with PAW potentials including geometry optimization, Car-Parrinello ab initio molecular dynamics, Born-Oppenheimer ab initio molecular dynamics, Metropolis Monte-Carlo, and AIMD/MM. Unfortunately, some of the functionality is missing at this point in time such as Mulliken analysis, and analytic stresses. However these small number of missing capabilities should become available over the next couple of months in the development tree of NWChem.
Even though analytic stresses are not currently available with PAW potentials unit cell optimization can still be carried out using numerical stresses. The following SET directives can be used to tell the code to calculate stresses numerically.
set includestress .true. #this option tells driver to optimize the unit cell \nset includelattice .true. #this option tells driver to optimize cell using a,b,c,alpha,beta,gamma \nset nwpw:frozen_lattice:thresh 999.0 #large number guarentees the lattice gridding does not adjust during optimization\nset nwpw:cif_filename pspw_corundum\nset nwpw:stress_numerical .true. \nset nwpw:lstress_numerical .true.\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#paw-implementation-notes","title":"PAW Implementation Notes","text":"The main idea in the PAW method(Blochl 1994) is to project out the high-frequency components of the wavefunction in the atomic sphere region. Effectively this splits the original wavefunction into two parts:
The first part is smooth and can be represented using a plane wave basis set of practical size. The second term is localized with the atomic spheres and is represented on radial grids centered on the atoms as
where the coefficients are given by
This decomposition can be expressed using an invertible linear transformation, , is defined which relates the stiff one-electron wavefunctions to a set of smooth one-electron wavefunctions
which can be represented by fairly small plane-wave basis. The transformation is defined using a local PAW basis, which consists of atomic orbitals, , smooth atomic orbitals, \u03b1I(r) which coincide with the atomic orbitals outside a defined atomic sphere, and projector functions, . Where I is the atomic index and \u03b1 is the orbital index. The projector functions are constructed such that they are localized within the defined atomic sphere and in addition are orthonormal to the atomic orbitals. Bl\u00f6chl defined the invertible linear transformations by
The main effect of the PAW transformation is that the fast variations of the valence wave function in the atomic sphere region are projected out using local basis set, thereby producing a smoothly varying wavefunction that may be expanded in a plane wave basis set of a manageable size.
The expression for the total energy in PAW method can be separated into the following 15 terms.
The first five terms are essentially the same as for a standard pseudopotential plane-wave program, minus the non-local pseudopotential, where
The local potential in the term is the Fourier transform of
It turns out that for many atoms needs to be fairly small. This results in being stiff. However, since in the integral above this function is multiplied by a smooth density the expansion of Vlocal(G) only needs to be the same as the smooth density. The auxiliary pseudoptential is defined to be localized within the atomic sphere and is introduced to remove ghost states due to local basis set incompleteness.
The next four terms are atomic based and they essentially take into account the difference between the true valence wavefunctions and the pseudowavefunctions.
The next three terms are the terms containing the compensation charge densities.
In the first two formulas the first terms are computed using plane-waves and the second terms are computed using Gaussian two center integrals. The smooth local potential in the term is the Fourier transform of
The stiff and smooth compensation charge densities in the above formula are
where
The decay parameter is defined the same as above, and I is defined to be smooth enough in order that \u03c1\u0303cmp(r) and local(r) can readily be expanded in terms of plane-waves.
The final three terms are the energies that contain the core densities
The matrix elements contained in the above formula are
"},{"location":"Plane-Wave-Density-Functional-Theory.html#exchange-correlation-potentials","title":"Exchange-Correlation Potentials","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#dft-u-corrections","title":"DFT + U Corrections","text":"TO DO
nwpw \n uterm d 0.13634 0.0036749 1 \nend\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#langreth-style-vdw-and-vdw-van-der-wall-functionals","title":"Langreth style vdw and vdw van der Wall functionals","text":"These potenials that are used to augment standard exchange-correlation potentials area calculated from a double integral over a nonlocal interaction kernel,
that is evaluated using the fast Fourier transformation method of Roman-Perez and Soler.
G. Roman-Perez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
Langreth vdw and vdw2 van der Wall functionals are currently available for the BEEF, PBE96, revPBE, PBEsol, BLYP, PBE0, revPBE0, HSE, and B3LYP exchange-correlation functionals. To use them the following keywords BEEF-vdw, BEEF-vdw2, PBE96-vdw, PBE96-vdw2, BLYP-vdw, BLYP-vdw2, revPBE-vdw, revPBE-vdw, PBEsol-vdw PBEsol-vdw2, PBE0-vdw, PBE0-vdw2, revPBE0-vdw, revPBE0-vdw2, HSE-vdw, HSE-vdw2, B3LYP-vdw, and B3LYP-vdw2 can be used in the XC input directive, e.g.
nwpw\n xc beef-vdw \nend\n
nwpw\n xc beef-vdw2 \nend\n
the vdw and vdw2 functionals are defined in
(vdw) Dion M, Rydberg H, Schr\u00f6der E, Langreth DC, Lundqvist BI. Van der Waals density functional for general geometries. Physical review letters. 2004 Jun 16;92(24):246401.
(vdw2) K. Lee, E. D. Murray, L. Kong, B. I. Lundqvist, and D. C. Langreth, Phys. Rev. B 82, 081101 (2010).
"},{"location":"Plane-Wave-Density-Functional-Theory.html#grimme-dispersion-corrections","title":"Grimme Dispersion Corrections","text":"Grimme dispersion corrections are currently available for the PBE96, revPBE, PBEsol, BLYP, PBE0, revPBE0, HSE, and B3LYP exchange-correlation functionals. To use them the following keywords PBE96-Grimme2, PBE96-Grimme3, PBE96-Grimme4, BLYP-Grimme2, BLYP-Grimme3, BLYP-Grimme4, revPBE-Grimme2, revPBE-Grimme3, revPBE-Grimme4, PBEsol-Grimme2, PBEsol-Grimme3, PBEsol-Grimme4, PBE0-Grimme2, PBE0-Grimme3, PBE0-Grimme4, revPBE0-Grimme2, revPBE0-Grimme3, revPBE0-Grimme4, HSE-Grimme2, HSE-Grimme3, HSE-Grimme4, B3LYP-Grimme2, B3LYP-Grimme3, and B3LYP-Grimme4 can be used in the XC input directive, e.g.
nwpw\n xc pbe96-grimme2 \nend\n
In these functionals Grimme2, Grimme3 and Grimme4 are defined in the following papers by S. Grimme.
Grimme2 - Commonly known as DFT-D2, S. Grimme, J. Comput. Chem., 27 (2006), 1787-1799.
Grimme3 - Commonly known as DFT-D3, S. Grimme, J. Antony, S. Ehrlich and H. Krieg A consistent and accurate ab initio parameterization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys, 132 (2010), 154104
Grimme4 - Commonly known as DFT-D3 with BJ damping. This correction augments the Grimme3 correction by including BJ-damping, S. Grimme, J. Antony, S. Ehrlich and H. Krieg A consistent and accurate ab initio parameterization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys, 132 (2010), 154104. S. Grimme, S. Ehrlich and L. Goerigk, J. Comput. Chem, 32 (2011), 1456-1465. This correction augments the Grimme3 correction by including BJ-damping.
If these functionals are used in a publication please include in your citations the references to Grimme\u2019s work.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#using-exchange-correlation-potentials-available-in-the-dft-module","title":"Using Exchange-Correlation Potentials Available in the DFT Module","text":"(Warning - To use this capability in NWChem 6.6 the user must explicitly include the nwxc module in the NWCHEM_MODULES list when compiling. Unfortunately, there was too much uncertainty in how the nwxc computed higher-order derivatives used by some of the functionality in nwdft module to include it in a release for all the functionality in NWChem. We are planning to have a debug release in winter 2016 to take fix this problem. This capability is still included by default in NWChem 6.5)
The user has the option of using many of the exchange-correlation potentials available in DFT Module (see Section XC and DECOMP \u2013 Exchange-Correlation Potentials).
XC [[acm] [b3lyp] [beckehandh] [pbe0] [bhlyp]\\\n [becke97] [becke97-1] [becke97-2] [becke97-3] [becke98] [hcth] [hcth120] [hcth147] \\ \n [hcth407] [becke97gga1] [hcth407p] \\\n [optx] [hcthp14] [mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\\\n [HFexch <real prefactor default 1.0>] \\\n [becke88 [nonlocal] <real prefactor default 1.0>] \\\n [xperdew91 [nonlocal] <real prefactor default 1.0>] \\\n [xpbe96 [nonlocal] <real prefactor default 1.0>] \\\n [gill96 [nonlocal] <real prefactor default 1.0>] \\\n [lyp <real prefactor default 1.0>] \\\n [perdew81 <real prefactor default 1.0>] \\\n [perdew86 [nonlocal] <real prefactor default 1.0>] \\\n [perdew91 [nonlocal] <real prefactor default 1.0>] \\\n [cpbe96 [nonlocal] <real prefactor default 1.0>] \\\n [pw91lda <real prefactor default 1.0>] \\\n [slater <real prefactor default 1.0>] \\\n [vwn_1 <real prefactor default 1.0>] \\\n [vwn_2 <real prefactor default 1.0>] \\\n [vwn_3 <real prefactor default 1.0>] \\\n [vwn_4 <real prefactor default 1.0>] \\\n [vwn_5 <real prefactor default 1.0>] \\\n [vwn_1_rpa <real prefactor default 1.0>]]\n
These functional can be invoked by prepending the \u201cnew\u201d directive before the exchange correlation potetntials in the input directive, XC new slater vwn_5.
That is, this statement in the input file
nwpw \n XC new slater vwn_5 \nend \ntask pspw energy\n
Using this input the user has ability to include only the local or nonlocal contributions of a given functional. The user can also specify a multiplicative prefactor (the variable prefactor in the input) for the local/nonlocal component or total (for more details see Section XC and DECOMP \u2013 Exchange-Correlation Potentials). An example of this might be,
XC new becke88 nonlocal 0.72
The user should be aware that the Becke88 local component is simply the Slater exchange and should be input as such.
Any combination of the supported exchange functional options can be used. For example the popular Gaussian B3 exchange could be specified as:
XC new slater 0.8 becke88 nonlocal 0.72 HFexch 0.2
Any combination of the supported correlation functional options can be used. For example B3LYP could be specified as:
XC new vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20 slater 0.80 becke88 nonlocal 0.72
and X3LYP as:
xc new vwn_1_rpa 0.129 lyp 0.871 hfexch 0.218 slater 0.782 \\ \nbecke88 nonlocal 0.542 xperdew91 nonlocal 0.167\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#exact-exchange","title":"Exact Exchange","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#self-interaction-corrections","title":"Self-Interaction Corrections","text":"The SET directive is used to specify the molecular orbitals contribute to the self-interaction-correction (SIC) term.
set pspw:SIC_orbitals <integer list_of_molecular_orbital_numbers>\n
This defines only the molecular orbitals in the list as SIC active. All other molecular orbitals will not contribute to the SIC term. For example the following directive specifies that the molecular orbitals numbered 1,5,6,7,8, and 15 are SIC active.
set pspw:SIC_orbitals 1 5:8 15
or equivalently
set pspw:SIC_orbitals 1 5 6 7 8 15
The following directive turns on self-consistent SIC.
set pspw:SIC_relax .false. # Default - Perturbative SIC calculation \nset pspw:SIC_relax .true. # Self-consistent SIC calculation\n
Two types of solvers can be used and they are specified using the following SET directive
set pspw:SIC_solver_type 1 # Default - cutoff coulomb kernel \nset pspw:SIC_solver_type 2 # Free-space boundary condition kernel\n
The parameters for the cutoff coulomb kernel are defined by the following SET directives:
set pspw:SIC_screening_radius <real rcut> \nset pspw:SIC_screening_power <real rpower>\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#wannier","title":"Wannier","text":"The pspw wannier task is generate maximally localized (Wannier) molecular orbitals. The algorithm proposed by Silvestrelli et al is use to generate the Wannier orbitals.
Input to the Wannier task is contained within the Wannier sub-block.
NWPW \n... \n Wannier \n ... \n END \n... \nEND\n
To run a Wannier calculation the following directive is used:
TASK PSPW Wannier
Listed below is the format of a Wannier sub-block.
NWPW \n... \n Wannier \n OLD_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> \n NEW_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> \n END\n... \nEND\n
The following list describes the input for the Wannier sub-block.
input_wavefunctions - name of pspw wavefunction file.output_wavefunctions - name of pspw wavefunction file that will contain the Wannier orbitals.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#mulliken-analysis","title":"Mulliken Analysis","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#density-of-states","title":"Density of States","text":"The \u201cdos\u201d option is used to turn on a density of states analysis. This option can be specified without additional parameters, i.e.
nwpw \n dos \nend\n
in which case default values are used, or it can be specified with additional parameters, e.g.
nwpw\n dos 0.002 700 -0.80000 0.8000 \nend\n
The parameters are
nwpw \n dos [<alpha> <npoints> <emin> <emax>] \nend\n
where
alpha value for the broadening the eigenvalues, default 0.05/27.2116 aunpoints number of plotting points in dos files, default 500emin minimum energy in dos plots, default min(eigenvalues)-0.1 auemax maximimum energy in dos plots, default max(eigenvalues)+0.1 au
The units for dos parameters are in atomic units. Note that if virtual states are specified in the pspw calculation then the virtual density of states will also be generated in addition to the filled density of states.
The following files are generated and written to the permanent_dir for restricted calculations
- file_prefix.smear_dos_both - total density of states
- file_prefix.smear_fdos_both - density of states of filled states
- file_prefix.smear_vdos_both - density of states of virtual states
For unrestricted calculations
- file_prefix.smear_dos_alpha - total density of states for up electrons
- file_prefix.smear_dos_beta - total density of states for down electrons
- file_prefix.smear_fdos_alpha - density of states for filled up electrons
- file_prefix.smear_fdos_beta - density of states for filled down electrons
- file_prefix.smear_vdos_alpha - density of states for virtual up electrons
- file_prefix.smear_vdos_beta - density of states for virtual down electrons
The nwpw:dos:actlist variable is used to specify the atoms used to determine weights for dos generation. If the variable is not set then all the atoms are used, e.g.
set nwpw:dos:actlist 1 2 3 4
"},{"location":"Plane-Wave-Density-Functional-Theory.html#projected-density-of-states","title":"Projected Density of States","text":"For projected density of states the \u201cMulliken\u201d keyword needs to be set, e.g.
nwpw \n Mulliken \n dos\nend\n
The following additional files are generated and written to the permanent_dir for restricted calculations
- file_prefix.mulliken_dos_both_s - total s projected density of restricted states
- file_prefix.mulliken_fdos_both_s - s projected density of states of filled restricted states
- file_prefix.mulliken_vdos_both_s - s projected density of states of virtual restricted states
- file_prefix.mulliken_dos_both_p - total p projected density of states
- file_prefix.mulliken_fdos_both_p - p projected density of states of filled states
- file_prefix.mulliken_vdos_both_p - p projected density of states of virtual states
\u2026
- file_prefix.mulliken_dos_both_all - total of projected density of filled and virtual restricted states
- file_prefix.mulliken_fdos_both_all - total of projected density of filled restricted states
- file_prefix.mulliken_vdos_both_all - total of projected density of states of virtual restricted states
Similarly for unrestricted calculations
- file_prefix.mulliken_dos_alpha_s - total s projected density of up states
- file_prefix.mulliken_fdos_alpha_s - s projected density of states of filled up states
- file_prefix.mulliken_vdos_alpha_s - s projected density of states of virtual up states
- file_prefix.mulliken_dos_alpha_p - total p projected density of up states
- file_prefix.mulliken_fdos_alpha_p - p projected density of states of filled up states
- file_prefix.mulliken_vdos_alpha_p - p projected density of states of virtual up states
\u2026
- file_prefix.mulliken_dos_alpha_all - total of projected density of filled up states
- file_prefix.mulliken_fdos_alpha_all - total of projected density of filled up states
- file_prefix.mulliken_vdos_alpha_all - total of projected density of states of virtual up states
\u2026
- file_prefix.mulliken_dos_beta_s - total s projected density of down states
- file_prefix.mulliken_fdos_beta_s - s projected density of states of filled down states
- file_prefix.mulliken_vdos_beta_s - s projected density of states of virtual down states
- file_prefix.mulliken_dos_beta_p - total p projected density of down states
- file_prefix.mulliken_fdos_beta_p - p projected density of states of filled down states
- file_prefix.mulliken_vdos_beta_p - p projected density of states of virtual down states
\u2026
- file_prefix.mulliken_dos_beta_all - total of projected density of filled down states
- file_prefix.mulliken_fdos_beta_all - total of projected density of filled down states
- file_prefix.mulliken_vdos_beta_all - total of projected density of states of virtual down states
"},{"location":"Plane-Wave-Density-Functional-Theory.html#point-charge-analysis","title":"Point Charge Analysis","text":"The MULLIKEN option can be used to generate derived atomic point charges from a plane-wave density. This analysis is based on a strategy suggested in the work of P.E. Blochl, J. Chem. Phys. vol. 103, page 7422 (1995). In this strategy the low-frequency components a plane-wave density are fit to a linear combination of atom centered Gaussian functions.
The following SET directives are used to define the fitting.
set nwpw_APC:Gc <real Gc_cutoff> # specifies the maximum frequency component of the density to be used in the fitting in units of au. \nset nwpw_APC:nga <integer number_gauss> # specifies the the number of Gaussian functions per atom.\nset nwpw_APC:gamma <real gamma_list> # specifies the decay lengths of each atom centered Gaussian. \n
We suggest using the following parameters.
set nwpw_APC:Gc 2.5\nset nwpw_APC:nga 3 \nset nwpw_APC:gamma 0.6 0.9 1.35 \n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#pspw_dplot-generate-gaussian-cube-files","title":"PSPW_DPLOT: Generate Gaussian Cube Files","text":"The pspw dplot task is used to generate plots of various types of electron densities (or orbitals) of a molecule. The electron density is calculated on the specified set of grid points from a PSPW calculation. The output file generated is in the Gaussian Cube format. Input to the DPLOT task is contained within the DPLOT sub-block.
NWPW \n... \n DPLOT \n ... \n END \n... \nEND\n
To run a DPLOT calculation the following directive is used:
TASK PSPW PSPW_DPLOT
Listed below is the format of a DPLOT sub-block.
NWPW \n... \n DPLOT \n VECTORS <string input_wavefunctions default input_movecs> \n DENSITY [total||diff||alpha||beta||laplacian||potential default total] \n <string density_name no default> \n ELF [restricted|alpha|beta] <string elf_name no default>\n ORBITAL <integer orbital_number no default> <string orbital_name no default> \n [LIMITXYZ [units <string Units default au>] \n <real X_From> <real X_To> <integer No_Of_Spacings_X> \n <real Y_From> <real Y_To> <integer No_Of_Spacings_Y> \n <real Z_From> <real Z_To> <integer No_Of_Spacings_Z>] \n NCELL <integer nx default 0> <integer ny default 0> <integer nz default 0>\n POSITION_TOLERANCE <real rtol default 0.001>\n END \n... \nEND\n
The following list describes the input for the DPLOT sub-block.
VECTORS <string input_wavefunctions default input_movecs>\n
This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.
DENSITY [total||difference||alpha||beta||laplacian||potential default total] \n <string density_name no default>\n
This sub-directive specifies, what kind of density is to be plotted. The known names for total, difference, alpha, beta, laplacian, and potential.
ELF [restricted|alpha|beta] <string elf_name no default>\n
This sub-directive specifies that an electron localization function (ELF) is to be plotted.
ORBITAL <integer orbital_number no default> <string orbital_name no default>\n
This sub-directive specifies the molecular orbital number that is to be plotted.
LIMITXYZ [units <string Units default angstroms>] \n<real X_From> <real X_To> <integer No_Of_Spacings_X> \n<real Y_From> <real Y_To> <integer No_Of_Spacings_Y> \n<real Z_From> <real Z_To> <integer No_Of_Spacings_Z>\n
By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#band-tasks-multiple-k-point-calculations","title":"Band Tasks: Multiple k-point Calculations","text":"All input to the Band Tasks is contained within the compound NWPW block,
NWPW \n ... \nEND\n
To perform an actual calculation a Task Band directive is used (Section Task).
Task Band
Once a user has specified a geometry, the Band module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the Band module are:
NWPW \n CELL_NAME <string cell_name default cell_default> \n ZONE_NAME <string zone_name default zone_default> \n INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> \n OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> \n FAKE_MASS <real fake_mass default 400000.0> \n TIME_STEP <real time_step default 5.8> \n LOOP <integer inner_iteration outer_iteration default 10 100> \n TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> \n CUTOFF <real cutoff> \n ENERGY_CUTOFF <real ecut default (see input description)> \n WAVEFUNCTION_CUTOFF <real wcut default (see input description)> \n EWALD_NCUT <integer ncut default 1>] \n EWALD_RCUT <real rcut default (see input description)> \n\n XC (Vosko || LDA || PBE96 || revPBE || PBEsol || ` \n || HSE || default Vosko) ` \n #Note that HSE is the only hybrid functional implemented in BAND\n\n DFT||ODFT||RESTRICTED||UNRESTRICTED \n MULT <integer mult default 1> \n CG \n LMBFGS \n SCF [Anderson|| simple || Broyden] \n [CG || RMM-DIIS] [density || potential] \n [ALPHA real alpha default 0.25] \n [ITERATIONS integer inner_iterations default 5] \n [OUTER_ITERATIONS integer outer_iterations default 0]\n\n SIMULATION_CELL [units <string units default bohrs>]\n ... (see input description) \n END \n BRILLOUIN_ZONE \n ... (see input description) \n END \n MONKHORST-PACK <real n1 n2 n3 default 1 1 1>\n BAND_DPLOT \n ... (see input description) \n END \n MAPPING <integer mapping default 1> \n SMEAR <sigma default 0.001> \n [TEMPERATURE <temperature>] \n [FERMI || GAUSSIAN || MARZARI-VANDERBILT default FERMI] \n [ORBITALS <integer orbitals default 4>] \nEND \n
The following list describes these keywords.
cell_name - name of the simulation_cell named cell_name. See Simulation Cell.input_wavefunctions - name of the file containing one-electron orbitalsoutput_wavefunctions - name that will point to file containing the one-electron orbitals at the end of the run.fake_mass - value for the electronic fake mass . This parameter is not presently used in a conjugate gradient simulationtime_step - value for the time step . This parameter is not presently used in a conjugate gradient simulation.inner_iteration - number of iterations between the printing out of energies and tolerancesouter_iteration - number of outer iterationstole - value for the energy tolerance.tolc - value for the one-electron orbital tolerance.cutoff - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.ecut - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell cell_name.wcut - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fix within the simulation_cell cell_name.ncut - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.rcut - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
Default set to be .
- (Vosko || PBE96 || revPBE) - Choose between Vosko et al\u2019s LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional.
- SIMULATION_CELL (see section -sec:pspw_cell-)
- BRILLOUIN_ZONE (see section -sec:band_brillouin_zone-)
- MONKHORST-PACK - Alternatively, the MONKHORST-PACK keyword can be used to enter a MONKHORST-PACK sampling of the Brillouin zone.
smear - value for smearing broadendingtemperature - same as smear but in units of K.- CG - optional keyword which sets the minimizer to 1
- LMBFGS - optional keyword which sets the minimizer to 2
- SCF - optional keyword which sets the minimizer to be a band by band minimizer. Several options are available for setting the density or potential mixing, and the type of Kohn-Sham minimizer.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#brillouin-zone","title":"Brillouin Zone","text":"To supply the special points of the Brillouin zone, the user defines a brillouin_zone sub-block within the NWPW block. Listed below is the format of a brillouin_zone sub-block.
NWPW \n... \n BRILLOUIN_ZONE \n ZONE_NAME <string name default zone_default> \n (KVECTOR <real k1 k2 k3 no default> <real weight default (see input description)> \n ...) \n END \n... \nEND\n
The user enters the special points and weights of the Brillouin zone. The following list describes the input in detail.
name - user-supplied name for the simulation block.k1 k2 k3 - user-supplied values for a special point in the Brillouin zone.weight - user-supplied weight. Default is to set the weight so that the sum of all the weights for the entered special points adds up to unity.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#band-structure-paths","title":"Band Structure Paths","text":"SC: gamma, m, r, x
FCC: gamma, k, l, u, w, x
BCC: gamma, h, n, p
Rhombohedral: not currently implemented
Hexagonal: gamma, a, h, k, l, m
Simple Tetragonal: gamma, a, m, r, x, z
Simple Orthorhombic: gamma, r, s, t, u, x, y, z
Body-Centered Tetragonal: gamma, m, n, p, x
"},{"location":"Plane-Wave-Density-Functional-Theory.html#special-points-of-different-space-groups-conventional-cells","title":"Special Points of Different Space Groups (Conventional Cells)","text":"(1) P1
(2) P-1
(3)
"},{"location":"Plane-Wave-Density-Functional-Theory.html#screened-exchange","title":"Screened Exchange","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#density-of-states-and-projected-density-of-states","title":"Density of States and Projected Density of States","text":"The \u201cdos\u201d option is used to calculate density of states using broadening of the eigenvalues . This option can be specified without additional parameters, i.e.
nwpw \n dos\nend\n
in which case default values are used, or it can be specified with additional parameters, e.g.
nwpw \n dos 0.002 700 -0.80000 0.8000\nend\n
The parameters are
nwpw \n dos [<alpha> <npoints> <emin> <emax>]\nend\n
where
alpha - value for the broadening the eigenvalues, default 0.05/27.2116 aunpoints - number of plotting points in dos files, default 500emin - minimum energy in dos plots, default min(eigenvalues)-0.1 auemax - maximimum energy in dos plots, default max(eigenvalues)+0.1 au
The units for dos parameters are in atomic units. Note that if virtual states are specified in the pspw calculation then the virtual density of states will also be generated in addition to the filled density of states.
The following files are generated and written to the permanent_dir for restricted calculations
- file_prefix.smear_dos_both - total density of states
- file_prefix.smear_fdos_both - density of states of filled states
- file_prefix.smear_vdos_both - density of states of virtual states
For unrestricted calculations
- file_prefix.smear_dos_alpha - total density of states for up electrons
- file_prefix.smear_dos_beta - total density of states for down electrons
- file_prefix.smear_fdos_alpha - density of states for filled up electrons
- file_prefix.smear_fdos_beta - density of states for filled down electrons
- file_prefix.smear_vdos_alpha - density of states for virtual up electrons
- file_prefix.smear_vdos_beta - density of states for virtual down electrons
The nwpw:dos:actlist variable is used to specify the atoms used to determine weights for dos generation. If the variable is not set then all the atoms are used, e.g.
set nwpw:dos:actlist 1 2 3 4
For projected density of states the \u201cMulliken\u201d keyword needs to be set, e.g.
nwpw\n Mulliken\n dos \nend\n
The following additional files are generated and written to the permanent_dir for restricted calculations
- file_prefix.mulliken_dos_both_s - total s projected density of restricted states
- file_prefix.mulliken_fdos_both_s - s projected density of states of filled restricted states
- file_prefix.mulliken_vdos_both_s - s projected density of states of virtual restricted states
- file_prefix.mulliken_dos_both_p - total p projected density of states
- file_prefix.mulliken_fdos_both_p - p projected density of states of filled states
- file_prefix.mulliken_vdos_both_p - p projected density of states of virtual states
\u2026
- file_prefix.mulliken_dos_both_all - total of projected density of filled and virtual restricted states
- file_prefix.mulliken_fdos_both_all - total of projected density of filled restricted states
- file_prefix.mulliken_vdos_both_all - total of projected density of states of virtual restricted states
Similarly for unrestricted calculations
- file_prefix.mulliken_dos_alpha_s - total s projected density of up states
- file_prefix.mulliken_fdos_alpha_s - s projected density of states of filled up states
- file_prefix.mulliken_vdos_alpha_s - s projected density of states of virtual up states
- file_prefix.mulliken_dos_alpha_p - total p projected density of up states
- file_prefix.mulliken_fdos_alpha_p - p projected density of states of filled up states
- file_prefix.mulliken_vdos_alpha_p - p projected density of states of virtual up states
\u2026
- file_prefix.mulliken_dos_alpha_all - total of projected density of filled up states
- file_prefix.mulliken_fdos_alpha_all - total of projected density of filled up states
- file_prefix.mulliken_vdos_alpha_all - total of projected density of states of virtual up states
\u2026
- file_prefix.mulliken_dos_beta_s - total s projected density of down states
- file_prefix.mulliken_fdos_beta_s - s projected density of states of filled down states
- file_prefix.mulliken_vdos_beta_s - s projected density of states of virtual down states
- file_prefix.mulliken_dos_beta_p - total p projected density of down states
- file_prefix.mulliken_fdos_beta_p - p projected density of states of filled down states
- file_prefix.mulliken_vdos_beta_p - p projected density of states of virtual down states
\u2026
- file_prefix.mulliken_dos_beta_all - total of projected density of filled down states
- file_prefix.mulliken_fdos_beta_all - total of projected density of filled down states
- file_prefix.mulliken_vdos_beta_all - total of projected density of states of virtual down states
"},{"location":"Plane-Wave-Density-Functional-Theory.html#two-component-wavefunctions-spin-orbit-zora","title":"Two-Component Wavefunctions (Spin-Orbit ZORA)","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#band_dplot-generate-gaussian-cube-files","title":"BAND_DPLOT: Generate Gaussian Cube Files","text":"The BAND BAND_DPLOT task is used to generate plots of various types of electron densities (or orbitals) of a crystal. The electron density is calculated on the specified set of grid points from a Band calculation. The output file generated is in the Gaussian Cube format. Input to the BAND_DPLOT task is contained within the BAND_DPLOT sub-block.
NWPW \n... \n BAND_DPLOT \n ... \n END \n...\nEND\n
To run a BAND_DPLOT calculation the following directive is used:
TASK BAND BAND_DPLOT
Listed below is the format of a BAND_DPLOT sub-block.
NWPW\n... \n BAND_DPLOT \n VECTORS <string input_wavefunctions default input_movecs>\n DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default>\n ELF [restricted|alpha|beta] <string elf_name no default> \n ORBITAL (density || real || complex default density) \n <integer orbital_number no default> \n <integer brillion_number default 1> \n <string orbital_name no default> \n [LIMITXYZ [units <string Units default angstroms>] \n <real X_From> <real X_To> <integer No_Of_Spacings_X> \n <real Y_From> <real Y_To> <integer No_Of_Spacings_Y> \n <real Z_From> <real Z_To> <integer No_Of_Spacings_Z>] \n END\n...\nEND\n
The following list describes the input for the BAND_DPLOT sub-block.
VECTORS <string input_wavefunctions default input_movecs>
This sub-directive specifies the name of the molecular orbital file. If the second file is optionally given the density is computed as the difference between the corresponding electron densities. The vector files have to match.
DENSITY [total||difference||alpha||beta||laplacian||potential default total] <string density_name no default>\n
This sub-directive specifies, what kind of density is to be plotted. The known names for total, difference, alpha, beta, laplacian, and potential.
ELF [restricted|alpha|beta] <string elf_name no default>\n
This sub-directive specifies that an electron localization function (ELF) is to be plotted.
ORBITAL (density || real || complex default density) <integer orbital_number no default><integer brillion_number default 1> <string orbital_name no default>\n
This sub-directive specifies the molecular orbital number that is to be plotted.
LIMITXYZ [units <string Units default angstroms>] \n<real X_From> <real X_To> <integer No_Of_Spacings_X> \n<real Y_From> <real Y_To> <integer No_Of_Spacings_Y> \n<real Z_From> <real Z_To> <integer No_Of_Spacings_Z>\n
By default the grid spacing and the limits of the cell to be plotted are defined by the input wavefunctions. Alternatively the user can use the LIMITXYZ sub-directive to specify other limits. The grid is generated using No_Of_Spacings + 1 points along each direction. The known names for Units are angstroms, au and bohr.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#car-parrinello","title":"Car-Parrinello","text":"The Car-Parrinello task is used to perform ab initio molecular dynamics using the scheme developed by Car and Parrinello. In this unified ab initio molecular dynamics scheme the motion of the ion cores is coupled to a fictitious motion for the Kohn-Sham orbitals of density functional theory. Constant energy or constant temperature simulations can be performed. A detailed description of this method is described in section Car-Parrinello Scheme for Ab Initio Molecular Dynamics.
Input to the Car-Parrinello simulation is contained within the Car-Parrinello sub-block.
NWPW \n... \n Car-Parrinello \n ... \n END \n...\nEND\n
To run a Car-Parrinello calculation the following directives are used:
TASK PSPW Car-Parrinello \n TASK BAND Car-Parrinello\n TASK PAW Car-Parrinello\n
The Car-Parrinello sub-block contains a great deal of input, including pointers to data, as well as parameter input. Listed below is the format of a Car-Parrinello sub-block.
NWPW \n... \n Car-Parrinello \n CELL_NAME <string cell_name default 'cell_default'>\n INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default file_prefix.movecs> \n OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default file_prefix.movecs> \n INPUT_V_WAVEFUNCTION_FILENAME <string input_v_wavefunctions default file_prefix.vmovecs> \n OUTPUT_V_WAVEFUNCTION_FILENAME <string output_v_wavefunctions default file_prefix.vmovecs> \n FAKE_MASS <real fake_mass default default 1000.0>\n TIME_STEP <real time_step default 5.0> \n LOOP <integer inner_iteration outer_iteration default 10 1> \n SCALING <real scale_c scale_r default 1.0 1.0> \n ENERGY_CUTOFF <real ecut default (see input description)> \n WAVEFUNCTION_CUTOFF <real wcut default (see input description)> \n EWALD_NCUT <integer ncut default 1> \n EWALD_RCUT <real rcut default (see input description)> \n XC (Vosko || LDA || PBE96 || revPBE || HF || \n LDA-SIC || LDA-SIC/2 || LDA-0.4SIC || LDA-SIC/4 || LDA-0.2SIC || \n PBE96-SIC || PBE96-SIC/2 || PBE96-0.4SIC || PBE96-SIC/4 || PBE96-0.2SIC || \n revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || \n PBE0 || revPBE0 || default Vosko) \n [Nose-Hoover <real Period_electron real Temperature_electron \n real Period_ion real Temperature_ion \n integer Chainlength_electron integer Chainlength_ion default 100.0 298.15 100.0 298.15 1 1>] \n [TEMPERATURE <real Temperature_ion real Period_ion \n real Temperature_electron real Period_electron \n integer Chainlength_ion integer Chainlength_electron default 298.15 1200 298.15 1200.0 1 1>] \n [SA_decay <real sa_scale_c sa_scale_r default 1.0 1.0>] \n XYZ_FILENAME <string xyz_filename default file_prefix.xyz> \n ION_MOTION_FILENAME <string ion_motion_filename default file_prefix.ion_motion\n EMOTION_FILENAME <string emotion_filename default file_prefix.emotion> \n HMOTION_FILENAME <string hmotion_filename nodefault>\n OMOTION_FILENAME <string omotion_filename nodefault>\n EIGMOTION_FILENAME <string eigmotion_filename nodefault> \n END \n... \nEND\n
The following list describes the input for the Car-Parrinello sub-block.
cell_name - name of the the simulation_cell named cell_name. See section Simulation Cell.input_wavefunctions - name of the file containing one-electron orbitalsoutput_wavefunctions - name of the file that will contain the one-electron orbitals at the end of the run.input_v_wavefunctions - name of the file containing one-electron orbital velocities.output_v_wavefunctions - name of the file that will contain the one-electron orbital velocities at the end of the run.fake_mass - value for the electronic fake mass ( ).time_step - value for the Verlet integration time step ().inner_iteration - number of iterations between the printing out of energies.outer_iteration - number of outer iterationsscale_c - value for the initial velocity scaling of the one-electron orbital velocities.scale_r - value for the initial velocity scaling of the ion velocities.ecut - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell cell_name.wcut - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell cell_name.ncut - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.rcut - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
Default set to be .
- (Vosko || PBE96 || revPBE || \u2026) - Choose between Vosko et al\u2019s LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options.
- Nose-Hoover or Temperature - optional subblock which if specified causes the simulation to perform Nose-Hoover dynamics. If this subblock is not specified the simulation performs constant energy dynamics. See section -sec:pspw_nose- for a description of the parameters. Note that the Temperature subblock is just a reordering of the Nose-Hoover subblock.
Period_electron - estimated period for fictitious electron thermostat.Temperature_electron - temperature for fictitious electron motionPeriod_ion - estimated period for ionic thermostatTemperature_ion - temperature for ion motionChainlength_electron - number of electron thermostat chainsChainlength_ion - number of ion thermostat chains
- SA_decay - optional subblock which if specified causes the simulation to run a simulated annealing simulation. For simulated annealing to work the Nose-Hoover subblock needs to be specified. The initial temperature are taken from the Nose-Hoover subblock. See section -sec:pspw_nose- for a description of the parameters.
sa_scale_c - decay rate in atomic units for electronic temperature.sa_scale_r - decay rate in atomic units for the ionic temperature.
xyz_filename - name of the XYZ motion file generatedemotion_filename - name of the emotion motion file. See section EMOTION motion file for a description of the datafile.hmotion_filenameh - name of the hmotion motion file. See section HMOTION motion file for a description of the datafile.eigmotion_filename - name of the eigmotion motion file. See section EIGMOTION motion file for a description of the datafile.ion_motion_filename - name of the ion_motion motion file. See section ION_MOTION motion file- for a description of the datafile.- MULLIKEN - optional keyword which if specified causes an omotion motion file to be created.
omotion_filename - name of the omotion motion file. See section OMOTION motion file for a description of the datafile.
When a DPLOT sub-block is specified the following SET directive can be used to output dplot data during a PSPW Car-Parrinello simulation:
set pspw_dplot:iteration_list <integer list_of_iteration_numbers>\n
The Gaussian cube files specified in the DPLOT sub-block are appended with the specified iteration number.
For example, the following directive specifies that at the 3,10,11,12,13,14,15, and 50 iterations Gaussian cube files are to be produced.
set pspw_dplot:iteration_list 3,10:15,50
"},{"location":"Plane-Wave-Density-Functional-Theory.html#adding-geometry-constraints-to-a-car-parrinello-simulation","title":"Adding Geometry Constraints to a Car-Parrinello Simulation","text":"The Car-Parrinello module allows users to freeze the cartesian coordinates in a simulation (Note - the Car-Parrinello code recognizes Cartesian constraints, but it does not recognize internal coordinate constraints). The +SET+ directive (Section Applying constraints in geometry optimizations) is used to freeze atoms, by specifying a directive of the form:
set geometry:actlist <integer list_of_center_numbers>\n
This defines only the centers in the list as active. All other centers will have zero force assigned to them, and will remain frozen at their starting coordinates during a Car-Parrinello simulation.
For example, the following directive specifies that atoms numbered 1, 5, 6, 7, 8, and 15 are active and all other atoms are frozen:
set geometry:actlist 1 5:8 15
or equivalently,
set geometry:actlist 1 5 6 7 8 15
If this option is not specified by entering a +SET+ directive, the default behavior in the code is to treat all atoms as active. To revert to this default behavior after the option to define frozen atoms has been invoked, the +UNSET+ directive must be used (since the database is persistent, see Section NWChem Architecture). The form of the +UNSET+ directive is as follows:
unset geometry:actlist
In addition, the Car-Parrinello module allows users to freeze bond lengths via a Shake algorithm. The following +SET+ directive shows how to do this.
set nwpw:shake_constraint \"2 6 L 6.9334\"
This input fixes the bond length between atoms 2 and 6 to be 6.9334 bohrs. Note that this input only recognizes bohrs.
When using constraints it is usually necessary to turn off center of mass shifting. This can be done by the following +SET+ directive.
set nwpw:com_shift .false.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#car-parrinello-output-datafiles","title":"Car-Parrinello Output Datafiles","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#xyz-motion-file","title":"XYZ motion file","text":"Data file that stores ion positions and velocities as a function of time in XYZ format.
[line 1: ] n_ion\n[line 2: ] do ii=1,n_ion\n[line 2+ii: ] atom_name(ii), x(ii),y(ii),z(ii),vx(ii),vy(ii),vz(ii)\nend do \n[line n_ion+3 ] n_nion \n do ii=1,n_ion\n[line n_ion+3+ii: ] atom_name(ii), x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii) \nend do\n[line 2*n_ion+4: ] ....\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#ion_motion-motion-file","title":"ION_MOTION motion file","text":"Datafile that stores ion positions and velocities as a function of time
[line 1: ] it_out, n_ion, omega, a1.x,a1.y,a1.z, a2.x,a2,y,a2.z, a3.x,a3.y,a3.z \n[line 2: ] time \ndo ii=1,n_ion\n[line 2+ii: ] ii, atom_symbol(ii),atom_name(ii), x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii) \nend do\n[line n_ion+3 ] time \ndo do ii=1,n_ion \n[line n_ion+3+ii: ] ii, atom_symbol(ii),atom_name(ii), x(ii),y(ii),z(ii), vx(ii),vy(ii),vz(ii) \nend do \n[line 2*n_ion+4: ] ....\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#emotion-motion-file","title":"EMOTION motion file","text":"Datafile that store energies as a function of time.
[line 1: ] time, E1,E2,E3,E4,E5,E6,E7,E8,(E9,E10, if Nose-Hoover),eave,evar,have,hvar,ion_Temp \n[line 2: ] ...\n
where
E1 = total energy\nE2 = potential energy\nE3 = ficticious kinetic energy\nE4 = ionic kinetic energy\nE5 = orbital energy\nE6 = hartree energy\nE7 = exchange-correlation energy \nE8 = ionic energy\neave = average potential energy \nevar = variance of potential energy\nhave = average total energy\nhvar = variance of total energy\nion_Temp = temperature\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#hmotion-motion-file","title":"HMOTION motion file","text":"Datafile that stores the rotation matrix as a function of time.
[line 1: ] time\n[line 2: ] ms,ne(ms),ne(ms)\ndo i=1,ne(ms)\n[line 2+i: ] (hml(i,j), j=1,ne(ms)\nend do\n[line 3+ne(ms): ] time\n[line 4+ne(ms): ] ....\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#eigmotion-motion-file","title":"EIGMOTION motion file","text":"Datafile that stores the eigenvalues for the one-electron orbitals as a function of time.
[line 1: ] time, (eig(i), i=1,number_orbitals) \n[line 2: ] ...\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#omotion-motion-file","title":"OMOTION motion file","text":"Datafile that stores a reduced representation of the one-electron orbitals. To be used with a molecular orbital viewer that will be ported to NWChem in the near future.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#born-oppenheimer-molecular-dynamics","title":"Born-Oppenheimer Molecular Dynamics","text":"NWPW\n...\n BO_STEPS <integer bo_inner_iteration bo_outer_iteration default 10 100> \n BO_TIME_STEP <real bo_time_step default 5.0> \n BO_ALGORITHM [verlet|| velocity-verlet || leap-frog]\n BO_FAKE_MASS <real bo_fake_mass default 500.0> \nEND\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#i-pi-socket-communication","title":"i-PI Socket Communication","text":"NWPW\n SOCKET (UNIX || IPI_CLIENT) <string socketname default (see input description)>\nEND\n
The NWPW module provides native communication via the i-PI socket protocol. The behavior is identical to the i-PI socket communication provided by the DRIVER module. The NWPW implementation of the SOCKET directive is better optimized for plane-wave calculations.
For proper behavior, the TASK directive should be set to GRADIENT, e.g. TASK PSPW GRADIENT or TASK BAND GRADIENT.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#metropolis-monte-carlo","title":"Metropolis Monte-Carlo","text":"NWPW\n...\n MC_STEPS <integer mc_inner_iteration mc_outer_iteration default 10 100> \nEND\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#free-energy-simulations","title":"Free Energy Simulations","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#metadynamics","title":"MetaDynamics","text":" Metadynamics234 is a powerful, non-equilibrium molecular dynamics method which accelerates the sampling of the multidimensional free energy surfaces of chemical reactions. This is achieved by adding an external time-dependent bias potential that is a function of user defined collective variables, . The bias potential discourages the system from sampling previously visited values of (i.e., encourages the system to explore new values of . During the simulation the bias potential accumulates in low energy wells which then allows the system to cross energy barriers much more quickly than would occur in standard dynamics. The collective variable is a generic function of the system coordinates, (e.g. bond distance, bond angle, coordination numbers, etc.) that is capable of describing the chemical reaction of interest. can be regarded as a reaction coordinate if it can distinguish between the reactant, transition, and products states, and also capture the kinetics of the reaction.
The biasing is achieved by \u201cflooding\u201d the energy landscape with repulsive Gaussian \u201chills\u201d centered on the current location of at a constant time interval . If the height of the Gaussians is constant in time then we have standard metadynamics; if the heights vary (slowly decreased) over time then we have well-tempered metadynamics. In between the addition of Gaussians, the system is propagated by normal (but out of equilibrium) dynamics. Suppose that the dimension of the collective space is , i.e. and that prior to any time during the simulation, Gaussians centered on are deposited along the trajectory of at times . Then, the value of the bias potential, , at an arbitrary point, , along the trajectory of at time is given by
where is the time-dependent Gaussian height. and are width and initial height respectively of Gaussians, and is the tempered metadynamics temperature. corresponds to standard molecular dynamics because and therfore there is no bias. corresponds to standard metadynamics since in this case =constant. A positive, finite value of (eg. >=1500 K) corresponds to well-tempered metadynamics in which .
For sufficiently large , the history potential will nearly flatten the free energy surface, , along and an unbiased estimator of F(s) is given by
"},{"location":"Plane-Wave-Density-Functional-Theory.html#input","title":"Input","text":"Input to a metadynamics simulation is contained within the METADYNAMICS sub-block. Listed below is the the format of a METADYNAMICS sub-block,
NWPW \n METADYNAMICS\n [\n BOND <integer atom1_index no default> <integer atom2_index no default> \n [W <real w default 0.00005>] \n [SIGMA <real sigma default 0.1>] \n [RANGE <real a b default (see input description)>] \n [NRANGE <integer nrange default 501>] \n ...] \n [\n ANGLE <integer atom1_index no default> <integer atom2_index no default> <integer atom3_index no default> \n [W <real w default 0.00005>] \n [SIGMA <real sigma default 0.1>]\n [RANGE <real a b default 0]\n [NRANGE <integer nrange default 501>] \n ...]\n [\n COORD_NUMBER [INDEX1 <integer_list atom1_indexes no default>][INDEX2 <integer_list atom2_indexes no default>] \n [SPRIK] \n [N <real n default 6.0>]\n [M <real m default 12.0>]\n [R0 <real r0 default 3.0>] \n\n [W <real w default 0.00005>] \n [SIGMA <real sigma default 0.1>] \n [RANGE <real a b no default>] \n [NRANGE <integer nrange default 501>] \n ...] \n [ \n N-PLANE <integer atom1_index no default> <integer_list atom_indexes no default> \n [W <real w default 0.00005>] \n [SIGMA <real sigma default 0.1>] \n [RANGE <real a b no default>] \n [NRANGE <integer nrange default 501>] \n [NVECTOR <real(3) nx ny nz>] \n ...] \n [UPDATE <integer meta_update default 1>] \n [PRINT_SHIFT <integer print_shift default 0>]\n [TEMPERED <real tempered_temperature no default>] \n [BOUNDARY <real w_boundary sigma_boundary no default>]\n END\nEND\n
Multiple collective variables can be defined at the same time, e.g.
NWPW \n METADYNAMICS \n BOND 1 8 W 0.0005 SIGMA 0.1 \n BOND 1 15 W 0.0005 SIGMA 0.1 \n END\nEND\n
will produce a two-dimensional potential energy surface.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#tamd-temperature-accelerated-molecular-dynamics","title":"TAMD - Temperature Accelerated Molecular Dynamics","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#input_1","title":"Input","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#collective-variables","title":"Collective Variables","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#bond-distance-collective-variable","title":"Bond Distance Collective Variable","text":"This describes the bond distance between any pair of atoms and :
"},{"location":"Plane-Wave-Density-Functional-Theory.html#angle-collective-variable","title":"Angle Collective Variable","text":"This describes the bond angle formed at by the triplet
"},{"location":"Plane-Wave-Density-Functional-Theory.html#coordination-collective-variable","title":"Coordination Collective Variable","text":"The coordination number collective variable is defined as
where the summation over and runs over two types of atoms, is the weighting function, and is the cut-off distance. In the standard procedure for computing the coordination number, =1 if , otherwise =0, implying that is not continuous when . To ensure a smooth and continuous definition of the coordination number, we adopt two variants of the weighting function. The first variant is
where and are integers (m > n) chosen such that when and when is much larger than . For example, the parameters of the O-H coordination in water is well described by =1.6 \u00c5, and . In practice, and must tuned for a given to ensure that is smooth and satisfies the above mentioned properties, particularly the large
The second form of the weighting function, which is due to Sprik, is
In this definition is analogous to the Fermi function and its width is controlled by the parameter . Large and small values of respectively correspond to sharp and soft transitions at . Furthermore should approach 1 and 0 when and respectively. In practice =6-10 \u00c5 . For example, a good set of parameters of the O-H coordination in water is =1.4 \u00c5 and =10 \u00c5 .
"},{"location":"Plane-Wave-Density-Functional-Theory.html#n-plane-collective-variable","title":"N-Plane Collective Variable","text":"The N-Plane collective variable is useful for probing the adsorption of adatom/admolecules to a surface. It is defined as the average distance of the adatom/admolecule from a given layer in the slab along the surface normal:
where denotes the position of the adatom/admolecule/impurity along the surface normal (here, we assume the surface normal to be the z-axis) and the summation over runs over atoms at which form the layer. The layer could be on the face or in the interior of the slab.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#user-defined-collective-variable","title":"User defined Collective Variable","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#extended-x-ray-absorption-fine-structure-exafs-integration-with-feff6l","title":"Extended X-Ray Absorption Fine Structure (EXAFS) - Integration with FEFF6L","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#frozen-phonon-calculations","title":"Frozen Phonon Calculations","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#steepest-descent","title":"Steepest Descent","text":"The functionality of this task is now performed automatically by the PSPW and BAND. For backward compatibility, we provide a description of the input to this task.
The steepest_descent task is used to optimize the one-electron orbitals with respect to the total energy. In addition it can also be used to optimize geometries. This method is meant to be used for coarse optimization of the one-electron orbitals.
Input to the steepest_descent simulation is contained within the steepest_descent sub-block.
NWPW \n... \n STEEPEST_DESCENT \n ... \n END \n... \nEND\n
To run a steepest_descent calculation the following directive is used:
TASK PSPW steepest_descent \nTASK BAND steepest_descent \n
The steepest_descent sub-block contains a great deal of input, including pointers to data, as well as parameter input. Listed below is the format of a STEEPEST_DESCENT sub-block.
NWPW \n... \n STEEPEST_DESCENT \n CELL_NAME <string cell_name> \n [GEOMETRY_OPTIMIZE] \n INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default file_prefix.movecs> \n OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default file_prefix.movecs> \n FAKE_MASS <real fake_mass default 400000.0> \n TIME_STEP <real time_step default 5.8> \n LOOP <integer inner_iteration outer_iteration default 10 1> \n TOLERANCES <real tole tolc tolr default 1.0d-9 1.0d-9 1.0d-4> \n ENERGY_CUTOFF <real ecut default (see input desciption)> \n WAVEFUNCTION_CUTOFF <real wcut default (see input description)> \n EWALD_NCUT <integer ncut default 1> \n EWALD_RCUT <real rcut default (see input description)> \n XC (Vosko || LDA || PBE96 || revPBE || HF || \n LDA-SIC || LDA-SIC/2 || LDA-0.4SIC || LDA-SIC/4 || LDA-0.2SIC || \n PBE96-SIC || PBE96-SIC/2 || PBE96-0.4SIC || PBE96-SIC/4 || PBE96-0.2SIC || \n revPBE-SIC || revPBE-SIC/2 || revPBE-0.4SIC || revPBE-SIC/4 || revPBE-0.2SIC || \n PBE0 || revPBE0 || default Vosko) \n [MULLIKEN] \n END \n... \nEND\n
The following list describes the input for the STEEPEST_DESCENT sub-block.
cell_name - name of the simulation_cell named cell_name. See Simulation Cell.- GEOMETRY_OPTIMIZE - optional keyword which if specified turns on geometry optimization.
input_wavefunctions - name of the file containing one-electron orbitalsoutput_wavefunctions - name of the file tha will contain the one-electron orbitals at the end of the run.fake_mass - value for the electronic fake mass time_step - value for the time step .inner_iteration - number of iterations between the printing out of energies and tolerancesouter_iteration - number of outer iterationstole - value for the energy tolerance.tolc - value for the one-electron orbital tolerance.tolr - value for the ion position tolerance.ecut - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell cell_name.wcut - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fit within the simulation_cell cell_name.ncut - value for the number of unit cells to sum over (in each direction) for the real space part of the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.rcut - value for the cutoff radius used in the Ewald summation. Note Ewald summation is only used if the simulation_cell is periodic.
Default set to be .
- (Vosko || PBE96 || revPBE || \u2026) - Choose between Vosko et al\u2019s LDA parameterization or the orginal and revised Perdew, Burke, and Ernzerhof GGA functional. In addition, several hybrid options (hybrid options are not available in BAND).
- MULLIKEN - optional keyword which if specified causes a Mulliken analysis to be performed at the end of the simulation.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#simulation-cell","title":"Simulation Cell","text":"The simulation cell parameters are entered by defining a simulation_cell sub-block within the PSPW block. Listed below is the format of a simulation_cell sub-block.
NWPW \n... \n SIMULATION_CELL [units <string units default bohrs>]\n CELL_NAME <string name default 'cell_default'> \n BOUNDARY_CONDITIONS (periodic || aperiodic default periodic) \n LATTICE_VECTORS \n <real a1.x a1.y a1.z default 20.0 0.0 0.0> \n <real a2.x a2.y a2.z default 0.0 20.0 0.0> \n <real a3.x a3.y a3.z default 0.0 0.0 20.0> \n NGRID <integer na1 na2 na3 default 32 32 32> \n END \n... \nEND\n
Basically, the user needs to enter the dimensions, gridding and boundary conditions of the simulation cell. The following list describes the input in detail.
name - user-supplied name for the simulation block.- periodic - keyword specifying that the simulation cell has periodic boundary conditions.
- aperiodic - keyword specifying that the simulation cell has free-space boundary conditions.
a1.x a1.y a1.z - user-supplied values for the first lattice vectora2.x a2.y a2.z - user-supplied values for the second lattice vectora3.x a3.y a3.z - user-supplied values for the third lattice vectorna1 na2 na3 - user-supplied values for discretization along lattice vector directions.
Alternatively, instead of explicitly entering lattice vectors, users can enter the unit cell using the standard cell parameters, a, b, c, , , and , by using the LATTICE block. The format for input is as follows:
NWPW \n... \n SIMULATION_CELL [units <string units default bohrs>] \n ... \n LATTICE \n [lat_a <real a default 20.0>] \n [lat_b <real b default 20.0>] \n [lat_c <real c default 20.0>] \n [alpha <real alpha default 90.0>] \n [beta <real beta default 90.0>] \n [gamma <real gamma default 90.0>] \n END \n ... \n END\n...\nEND\n
The user can also enter the lattice vectors of standard unit cells using the keywords SC, FCC, BCC, for simple cubic, face-centered cubic, and body-centered cubic respectively. Listed below is an example of the format of this type of input.
NWPW \n... \n SIMULATION_CELL [units <string units default bohrs>]\n SC 20.0 \n .... \n END\n...\nEND\n
Finally, the lattice vectors from the unit cell can also be defined using the fractional coordinate input in the GEOMETRY input (see section Geometry Lattice Parameters). Listed below is an example of the format of this type of input for an 8 atom silicon carbide unit cell.
geometry units au \n system crystal \n lat_a 8.277\n lat_b 8.277 \n lat_c 8.277 \n alpha 90.0 \n beta 90.0 \n gamma 90.0 \n end\n Si -0.50000 -0.50000 -0.50000\n Si 0.00000 0.00000 -0.50000 \n Si 0.00000 -0.50000 0.00000\n Si -0.50000 0.00000 0.00000 \n C -0.25000 -0.25000 -0.25000 \n C 0.25000 0.25000 -0.25000 \n C 0.25000 -0.25000 0.25000 \n C -0.25000 0.25000 0.25000 \nend\n
Warning - Currently only the \u201csystem crystal\u201d option is recognized by NWPW. The \u201csystem slab\u201d and \u201csystem polymer\u201d options will be supported in the future.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#unit-cell-optimization","title":"Unit Cell Optimization","text":"The PSPW module using the DRIVER geometry optimizer can optimize a crystal unit cell. Currently this type of optimization works only if the geometry is specified in fractional coordinates. The following SET directive is used to tell the DRIVER geometry optimizer to optimize the crystal unit cell in addition to the geometry.
set includestress .true.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#smear-fractional-occupation-of-the-molecular-orbitals","title":"SMEAR - Fractional Occupation of the Molecular Orbitals","text":"The smear keyword to turn on fractional occupation of the molecular orbitals in PSPW and BAND calculations
SMEAR <sigma default 0.001> [TEMPERATURE <temperature>]\n [FERMI || GAUSSIAN || MARZARI-VANDERBILT default FERMI]\n [ORBITALS <integer orbitals default 4>]\n
Fermi-Dirac (FERMI), Gaussian, and Marzari-Vanderbilt broadening functions are available. The ORBITALS keyword is used to change the number of virtual orbitals to be used in the calculation. Note to use this option the user must currently use the SCF minimizer. The following SCF options are recommended for running fractional occupation
SCF Anderson outer_iterations 0 Kerker 2.0
"},{"location":"Plane-Wave-Density-Functional-Theory.html#spin-penalty-functions","title":"Spin Penalty Functions","text":"Spin-penalty functions makes it easier to define antiferromagnetic structures. These functions are implemented by adding a scaling factor to the non-local psp for up/down spins on atoms and angular momentum that you specify.
Basically, the pseudopotential energy
was modified to
An example input is as follows:
title \"hematite 10 atoms\"\n\nstart hema10\n\nmemory 1900 mb\n\npermanent_dir ./perm\nscratch_dir ./perm\n\ngeometry center noautosym noautoz print\n system crystal\n lat_a 5.42 \n lat_b 5.42 \n lat_c 5.42 \n alpha 55.36 \n beta 55.36 \n gamma 55.36 \n end\nFe 0.355000 0.355000 0.355000\nFe 0.145000 0.145000 0.145000 \nFe -0.355000 -0.355000 -0.355000 \nFe 0.855000 0.855000 0.855000 \nO 0.550000 -0.050000 0.250000 \nO 0.250000 0.550000 -0.050000 \nO -0.050000 0.250000 0.550000 \nO -0.550000 0.050000 -0.250000 \nO -0.250000 -0.550000 0.050000 \nO 0.050000 -0.250000 -0.550000\\ \nend \n\nnwpw\n virtual 8\n odft\n ewald_rcut 3.0\n ewald_ncut 8 \n xc pbe96\n lmbfgs \n mult 1\n dplot\n density diff diff1.cube\n end\n\n #spin penalty functions \n pspspin up d -1.0 1:2 \n pspspin down d -1.0 3:4 \nend\ntask pspw energy \ntask pspw pspw_dplot \n\nnwpw\n pspspin off\n dplot\n density diff diff2.cube\n end \nend \ntask pspw energy\ntask pspw pspw_dplot\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#aimdmm-qmmm","title":"AIMD/MM (QM/MM)","text":"A QM/MM capability is available that is integrated with PSPW module and can be used with Car-Parrinello simulations. Currently, the input is not very robust but it is straightforward. The first step to run a QM/MM simulations is to define the MM atoms in the geometry block. The MM atoms must be at the end of the geometry and a carat, \u201d ^ \u201c, must be appended to the end of the atom name, e.g.
geometry units angstrom nocenter noautosym noautoz print xyz \n C -0.000283 0.000106 0.000047 \n Cl -0.868403 1.549888 0.254229 \n Cl 0.834043 -0.474413 1.517103 \n Cl -1.175480 -1.275747 -0.460606 \n Cl 1.209940 0.200235 -1.310743 \n O^ 0.3226E+01 -0.4419E+01 -0.5952E+01 \n H^ 0.3193E+01 -0.4836E+01 -0.5043E+01 \n H^ 0.4167E+01 -0.4428E+01 -0.6289E+01 \n O^ 0.5318E+01 -0.3334E+01 -0.1220E+01 \n H^ 0.4978E+01 -0.3040E+01 -0.2113E+01 \n H^ 0.5654E+01 -0.2540E+01 -0.7127E+00 \nend\n
Another way to specify the MM atoms is to use the mm_tags option which appends the atoms with a \u201d ^ \u201c.
geometry units angstrom nocenter noautosym noautoz print xyz \n C -0.000283 0.000106 0.000047 \n Cl -0.868403 1.549888 0.254229 \n Cl 0.834043 -0.474413 1.517103 \n Cl -1.175480 -1.275747 -0.460606 \n Cl 1.209940 0.200235 -1.310743 \n O 0.3226E+01 -0.4419E+01 -0.5952E+01 \n H 0.3193E+01 -0.4836E+01 -0.5043E+01 \n H 0.4167E+01 -0.4428E+01 -0.6289E+01 \n O 0.5318E+01 -0.3334E+01 -0.1220E+01 \n H 0.4978E+01 -0.3040E+01 -0.2113E+01 \n H 0.5654E+01 -0.2540E+01 -0.7127E+00 \nend \nNWPW \n QMMM \n mm_tags 6:11 \n END \nEND\n
The option \u201cmm_tags off\u201d can be used to remove the \u201d ^ \u201d from the atoms, i.e.
NWPW \n QMMM \n mm_tags 6:11 off \n END \nEND \n
Next the pseudopotentials have be defined for the every type of MM atom contained in the geometry blocks. The following local pseudopotential suggested by Laio, VandeVondele and Rothlisberger can be automatically generated.
The following input To define this pseudopo the O^ MM atom using the following input
NWPW \n QMMM \n mm_psp O^ -0.8476 4 0.70 \n END \nEND\n
defines the local pseudopotential for the O^ MM atom , where , , and . The following input can be used to define the local pseudopotentials for all the MM atoms in the geometry block defined above
NWPW \n QMMM \n mm_psp O^ -0.8476 4 0.70 \n mm_psp H^ 0.4238 4 0.40 \n END \nEND\n
Next the Lenard-Jones potentials for the QM and MM atoms need to be defined. This is done as as follows
NWPW \n QMMM \n lj_ion_parameters C 3.41000000d0 0.10d0 \n lj_ion_parameters Cl 3.45000000d0 0.16d0 \n lj_ion_parameters O^ 3.16555789d0 0.15539425d0 \n END \nEND\n
Note that the Lenard-Jones potential is not defined for the MM H atoms in this example. The final step is to define the MM fragments in the simulation. MM fragments are a set of atoms in which bonds and angle harmonic potentials are defined, or alternatively shake constraints are defined. The following input defines the fragments for the two water molecules in the above geometry,
NWPW \n QMMM \n fragment spc \n size 3 #size of fragment \n index_start 6:9:3 #atom index list that defines the start of \n # the fragments (start:final:stride) \n bond_spring 1 2 0.467307856 1.889726878 #bond i j Kspring r0 \n bond_spring 1 3 0.467307856 1.889726878 #bond i j Kspring r0 \n angle_spring 2 1 3 0.07293966 1.910611932 #angle i j k Kspring theta0 \n end \n END \nEND\n
The fragments can be defined using shake constraints as
NWPW \n QMMM \n fragment spc \n size 3 #size of fragment \n index_start 6:9:3 #atom index list that defines the start of \n # the fragments (start:final:stride) \n shake units angstroms 1 2 3 cyclic 1.0 1.632993125 1.0 \n end \n END \nEND\n
Alternatively, each water could be defined independently as follows.
NWPW \n QMMM \n fragment spc1 \n size 3 #size of fragment \n index_start 6 #atom index list that defines the start of \n #the fragments \n bond_spring 1 2 0.467307856 1.889726878 #bond i j Kspring r0 \n bond_spring 1 3 0.467307856 1.889726878 #bond i j Kspring r0 \n angle_spring 2 1 3 0.07293966 1.910611932 #angle i j k Kspring theta0 \n end \n fragment spc2 \n size 3 #size of fragment \n index_start 9 #atom index list that defines the start of \n #the fragments \n shake units angstroms 1 2 3 cyclic 1.0 1.632993125 1.0 \n end \n END \nEND\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#psp_generator","title":"PSP_GENERATOR","text":"A one-dimensional pseudopotential code has been integrated into NWChem. This code allows the user to modify and develop pseudopotentials. Currently, only the Hamann and Troullier-Martins norm-conserving pseudopotentials can be generated. In future releases, the pseudopotential library (section Pseudopotential and PAW basis Libraries) will be more complete, so that the user will not have explicitly generate pseudopotentials using this module.
Input to the PSP_GENERATOR task is contained within the PSP_GENERATOR sub-block.
NWPW \n... \n PSP_GENERATOR \n ... \n END \n... \nEND\n
To run a PSP_GENERATOR calculation the following directive is used:
TASK PSPW PSP_GENERATOR
Listed below is the format of a PSP_GENERATOR sub-block.
NWPW \n... \n PSP_GENERATOR \n PSEUDOPOTENTIAL_FILENAME: <string psp_name> \n ELEMENT: <string element> \n CHARGE: <real charge> \n MASS_NUMBER: <real mass_number> \n ATOMIC_FILLING: <integer ncore nvalence> ( (1||2||...) (s||p||d||f||...) <real filling> ...)\n\n [CUTOFF: <integer lmax> ( (s||p||d||f||g) <real rcut> ...) ] \n\n PSEUDOPOTENTIAL_TYPE: (TROULLIER-MARTINS || HAMANN default HAMANN) \n SOLVER_TYPE: (PAULI || SCHRODINGER default PAULI) \n EXCHANGE_TYPE: (dirac || PBE96 default DIRAC) \n CORRELATION_TYPE: (VOSKO || PBE96 default VOSKO) \n [SEMICORE_RADIUS: <real rcore>]\n\n END \n... \nEND\n
The following list describes the input for the PSP_GENERATOR sub-block.
psp_name - name that points to a.element - Atomic symbol.charge - charge of the atommass - mass number for the atomncore - number of core statesnvalence - number of valence states.- ATOMIC_FILLING:.....(see below)
filling - occupation of atomic state- CUTOFF:....(see below)
rcore - value for the semicore radius (see below)
"},{"location":"Plane-Wave-Density-Functional-Theory.html#atomic_filling-block","title":"ATOMIC_FILLING Block","text":"This required block is used to define the reference atom which is used to define the pseudopotential. After the ATOMIC_FILLING: line, the core states are listed (one per line), and then the valence states are listed (one per line). Each state contains two integer and a value. The first integer specifies the radial quantum number, , the second integer specifies the angular momentum quantum number, , and the third value specifies the occupation of the state.
For example to define a pseudopotential for the Neon atom in the state could have the block
ATOMIC_FILLING: 1 2 \n 1 s 2.0 #core state - 1s^2 \n 2 s 2.0 #valence state - 2s^2 \n 2 p 6.0 #valence state - 2p^6\n
for a pseudopotential with a and valence electrons or the block
ATOMIC_FILLING: 3 0 \n 1 s 2.0 #core state \n 2 s 2.0 #core state \n 2 p 6.0 #core state\n
could be used for a pseudopotential with no valence electrons.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#cutoff","title":"CUTOFF","text":"This optional block specifies the cutoff distances used to match the all-electron atom to the pseudopotential atom. For Hamann pseudopotentials defines the distance where the all-electron potential is matched to the pseudopotential, and for Troullier-Martins pseudopotentials defines the distance where the all-electron orbital is matched to the pseudowavefunctions. Thus the definition of the radii depends on the type of pseudopotential. The cutoff radii used in Hamann pseudopotentials will be smaller than the cutoff radii used in Troullier-Martins pseudopotentials.
For example to define a softened Hamann pseudopotential for Carbon would be
ATOMIC_FILLING: 1 2 \n 1 s 2.0 \n 2 s 2.0 \n 2 p 2.0 \nCUTOFF: 2 \n s 0.8 \n p 0.85 \n d 0.85\n
while a similarly softened Troullier-Marting pseudopotential for Carbon would be
ATOMIC_FILLING: 1 2 \n 1 s 2.0 \n 2 s 2.0 \n 2 p 2.0 \nCUTOFF: 2 \n s 1.200 \n p 1.275 \n d 1.275\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#semicore_radius","title":"SEMICORE_RADIUS","text":"Specifying the SEMICORE_RADIUS option turns on the semicore correction approximation proposed by Louie et al (S.G. Louie, S. Froyen, and M.L. Cohen, Phys. Rev. B, 26(, 1738, (1982)). This approximation is known to dramatically improve results for systems containing alkali and transition metal atoms.
The implementation in the PSPW module defines the semi-core density, , by using the sixth-order polynomial
This expansion was suggested by Fuchs and Scheffler (M. Fuchs, and M. Scheffler, Comp. Phys. Comm.,119,67 (1999)), and is better behaved for taking derivatives (i.e. calculating ionic forces) than the expansion suggested by Louie et al.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#paw-tasks-legacy-implementation","title":"PAW Tasks: Legacy Implementation","text":"(This capability is now available in PSPW. It is recommended that this module only be used for testing purposes. )
All input to the PAW Tasks is contained within the compound NWPW block,
NWPW \n ... \nEND\n
To perform an actual calculation a TASK PAW directive is used (Task).
TASK PAW
In addition to the directives listed in Task, i.e.
TASK paw energy \nTASK paw gradient \nTASK paw optimize \nTASK paw saddle \nTASK paw freqencies \nTASK paw vib\n
there are additional directives that are specific to the PSPW module, which are:
TASK PAW [Car-Parrinello || steepest_descent ]
Once a user has specified a geometry, the PAW module can be invoked with no input directives (defaults invoked throughout). There are sub-directives which allow for customized application; those currently provided as options for the PAW module are:
NWPW \n CELL_NAME <string cell_name default 'cell_default'> \n [GEOMETRY_OPTIMIZE] \n INPUT_WAVEFUNCTION_FILENAME <string input_wavefunctions default input_movecs> \n OUTPUT_WAVEFUNCTION_FILENAME <string output_wavefunctions default input_movecs> \n FAKE_MASS <real fake_mass default 400000.0> \n TIME_STEP <real time_step default 5.8> \n LOOP <integer inner_iteration outer_iteration default 10 100> \n TOLERANCES <real tole tolc default 1.0e-7 1.0e-7> \n CUTOFF <real cutoff> \n ENERGY_CUTOFF <real ecut default (see input description)> \n WAVEFUNCTION_CUTOFF <real wcut default (see input description)> \n EWALD_NCUT <integer ncut default 1>] \n EWALD_RCUT <real rcut default (see input description)> \n XC (Vosko || PBE96 || revPBE default Vosko) \n DFT||ODFT||RESTRICTED||UNRESTRICTED \n MULT <integer mult default 1> \n INTEGRATE_MULT_L <integer imult default 1> \n SIMULATION_CELL \n ... (see input description) \n END \n CAR-PARRINELLO \n ... (see input description) \n END \n MAPPING <integer mapping default 1> \nEND \n
The following list describes these keywords.
cell_name - name of the the simulation_cell named cell_name. The current version of PAW only accepts periodic unit cells. See Simulation Cell.- GEOMETRY_OPTIMIZE - optional keyword which if specified turns on geometry optimization.
input_wavefunctions - name of the file containing one-electron orbitalsoutput_wavefunctions - name of the file that will contain the one-electron orbitals at the end of the run.fake_mass - value for the electronic fake mass . This parameter is not presently used in a conjugate gradient simulationtime_step - value for the time step (). This parameter is not presently used in a conjugate gradient simulation.inner_iteration - number of iterations between the printing out of energies and tolerancesouter_iteration - number of outer iterationstole - value for the energy tolerance.tolc - value for the one-electron orbital tolerance.cutoff - value for the cutoff energy used to define the wavefunction. In addition using the CUTOFF keyword automatically sets the cutoff energy for the density to be twice the wavefunction cutoff.ecut - value for the cutoff energy used to define the density. Default is set to be the maximum value that will fit within the simulation_cell cell_name.wcut - value for the cutoff energy used to define the one-electron orbitals. Default is set to be the maximum value that will fix within the simulation_cell cell_name.ncuth - value for the number of unit cells to sum over (in each direction) for the real space part of the smooth compensation summation.rcut - value for the cutoff radius used in the smooth compensation summation.
Default set to be .
- (Vosko || PBE96 || revPBE) - Choose between Vosko et al\u2019s LDA parametrization or the original and revised Perdew, Burke, and Ernzerhof GGA functional.
- MULT - optional keyword which if specified allows the user to define the spin multiplicity of the system
- INTEGRATE_MULT_L - optional keyword which if specified allows the user to define the angular XC integration of the augmented region
- SIMULATION_CELL (see Simulation Cell )
- CAR-PARRINELLO (see Car-Parrinello )
mapping - for a value of 1 slab FFT is used, for a value of 2 a 2d-Hilbert FFT is used.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#pseudopotential-and-paw-basis-libraries","title":"Pseudopotential and PAW basis Libraries","text":"A library of pseudopotentials used by PSPW and BAND is currently available in the directory $NWCHEM_TOP/src/nwpw/libraryp/pspw_default
The elements listed in the following table are present:
H He \n------- ------------------ \n Li Be B C N O F Ne \n------- ------------------- \n Na Mg Al Si P S Cl Ar \n------------------------------------------------------- \n K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr \n------------------------------------------------------- \n Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe \n------------------------------------------------------- \n Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn \n------------------------------------------------------- \n Fr Ra . \n----------------- \n ------------------------------------------ \n . . . . . . Gd . . . . . . . \n ------------------------------------------ \n . . U . Pu . . . . . . . . . \n ------------------------------------------\n
The pseudopotential libraries are continually being tested and added. Also, the PSPW program can read in pseudopotentials in CPI and TETER format generated with pseudopotential generation programs such as the OPIUM package of Rappe et al. The user can request additional pseudopotentials from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).
Similarly, a library of PAW basis used by PAW is currently available in the directory $NWCHEM_TOP/src/nwpw/libraryp/paw_default
H He \n------- ----------------- \n Li Be B C N O F Ne \n------- ------------------ \n Na Mg Al Si P S Cl Ar \n------------------------------------------------------ \n K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr \n------------------------------------------------------ \n . . . . . . . . . . . . . . . . . . \n------------------------------------------------------ \n . . . . . . . . . . . . . . . . . . \n------------------------------------------------------ \n . . . \n----------------- \n ------------------------------------------ \n . . . . . . . . . . . . . . \n ------------------------------------------ \n . . . . . . . . . . . . . . \n ------------------------------------------\n
Currently there are not very many elements available for PAW. However, the user can request additional basis sets from Eric J. Bylaska at (Eric.Bylaska@pnl.gov).
A preliminary implementation of the HGH pseudopotentials (Hartwigsen, Goedecker, and Hutter) has been implemented into the PSPW module. To access the pseudopotentials the pseudopotentials input block is used. For example, to redirect the code to use HGH pseudopotentials for carbon and hydrogen, the following input would be used.
nwpw \n... \n pseudopotentials \n C library HGH_LDA \n H library HGH_LDA \n end \n... \nend\n
The implementation of HGH pseudopotentials is rather limited in this release. HGH pseudopotentials cannot be used to optimize unit cells, and they do not work with the MULLIKEN option. They also have not yet been implemented into the BAND structure code. To read in pseudopotentials in CPI format the following input would be used.
nwpw \n... \n pseudopotentials \n C CPI c.cpi \n H CPI h.cpi \n end \n... \nend\n
In order for the program to recognize the CPI format the CPI files, e.g. c.cpi have to be prepended with the \u201c\u201d keyword.
To read in pseudopotentials in TETER format the following input would be used.
nwpw \n... \n pseudopotentials \n C TETER c.teter \n H TETER h.teter \n end \n... \nend\n
In order for the program to recognize the TETER format the TETER files, e.g. c.teter have to be prepended with the \u201c\u201d keyword.
If you wish to redirect the code to a different directory other than the default one, you need to set the environmental variable NWCHEM_NWPW_LIBRARY to the new location of the libraryps directory.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-rtdb-entries-and-miscellaneous-datafiles","title":"NWPW RTDB Entries and Miscellaneous DataFiles","text":"Input to the PSPW and Band modules are contained in both the RTDB and datafiles. The RTDB is used to store input that the user will need to directly specify. Input of this kind includes ion positions, ion velocities, and simulation cell parameters. The datafiles are used to store input, such the one-electron orbitals, one-electron orbital velocities, formatted pseudopotentials, and one-dimensional pseudopotentials, that the user will in most cases run a program to generate.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#ion-positions","title":"Ion Positions","text":"The positions of the ions are stored in the default geometry structure in the RTDB and must be specified using the GEOMETRY directive.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#ion-velocities","title":"Ion Velocities","text":"The velocities of the ions are stored in the default geometry structure in the RTDB, and must be specified using the GEOMETRY directive.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#wavefunction-datafile","title":"Wavefunction Datafile","text":"The one-electron orbitals are stored in a wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is used by steepest_descent and Car-Parrinello tasks and can be generated using the wavefunction_initializer or wavefunction_expander tasks.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#velocity-wavefunction-datafile","title":"Velocity Wavefunction Datafile","text":"The one-electron orbital velocities are stored in a velocity wavefunction datafile. This is a binary file and cannot be directly edited. This datafile is automatically generated the first time a Car-Parrinello task is run.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#formatted-pseudopotential-datafile","title":"Formatted Pseudopotential Datafile","text":"The pseudopotentials in Kleinman-Bylander form expanded on a simulation cell (3d grid) are stored in a formatted pseudopotential datafile (PSPW-\u201catomname.vpp\u201d, BAND-\u201catomname.cpp\u201d, PAW-\u201catomname.jpp\u201d). These are binary files and cannot be directly edited. These datafiles are automatically generated.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#one-dimensional-pseudopotential-datafile","title":"One-Dimensional Pseudopotential Datafile","text":"The one-dimensional pseudopotentials are stored in a one-dimensional pseudopotential file (\u201catomname.psp\u201d). This is an ASCII file and can be directly edited with a text editor or can be generated using the pspw_generator task. However, these datafiles are usually atomatically generated.
The data stored in the one-dimensional pseudopotential file is
character*2 element :: element name \ninteger charge :: valence charge of ion \nreal mass :: mass of ion \ninteger lmax :: maximum angular component \nreal rcut(lmax) :: cutoff radii used to define pseudopotentials \ninteger nr :: number of points in the radial grid \nreal dr :: linear spacing of the radial grid \nreal r(nr):: one-dimensional radial grid \nreal Vpsp(nr,lmax) :: one-dimensional pseudopotentials \nreal psi(nr,lmax) :: one-dimensional pseudowavefunctions \nreal r_semicore :: semicore radius \nreal rho_semicore(nr) :: semicore density \n
and the format of it is:
[line 1: ] element [line 2: ] charge mass lmax \n[line 3: ] (rcut(l), l=1,lmax) \n[line 4: ] nr dr \n[line 5: ] r(1) (Vpsp(1,l), l=1,lmax) \n[line 6: ] .... \n[line nr+4: ] r(nr) (Vpsp(nr,l), l=1,lmax) \n[line nr+5: ] r(1) (psi(1,l), l=1,lmax) [line nr+6: ] .... \n[line 2*nr+4:] r(nr) (psi(nr,l), l=1,lmax) \n[line 2*nr+5:] r_semicore \nif (r_semicore read) then \n [line 2*nr+6:] r(1) rho_semicore(1) \n [line 2*nr+7:] .... \n [line 3*nr+5:] r(nr) rho_semicore(nr) \nend if\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#car-parrinello-scheme-for-ab-initio-molecular-dynamics","title":"Car-Parrinello Scheme for Ab Initio Molecular Dynamics","text":"Car and Parrinello developed a unified scheme for doing ab initio molecular dynamics by combining the motion of the ion cores and a fictitious motion for the Kohn-Sham orbitals of density-functional theory (R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471, (1985) - simple introduction cpmd-lecture.pdf). At the heart of this method they introduced a fictitious kinetic energy functional for the Kohn-Sham orbitals.
Given this kinetic energy the constrained equations of motion are found by taking the first variation of the auxiliary Lagrangian.
Which generates a dynamics for the wavefunctions and atoms positions through the constrained equations of motion:
where is the fictitious mass for the electronic degrees of freedom and are the ionic masses. The adjustable parameter is used to describe the relative rate at which the wavefunctions change with time. are the Lagrangian multipliers for the orthonormalization of the single-particle orbitals . They are defined by the orthonormalization constraint conditions and can be rigorously found. However, the equations of motion for the Lagrange multipliers depend on the specific algorithm used to integrate the Eqns. above.
For this method to give ionic motions that are physically meaningful the kinetic energy of the Kohn-Sham orbitals must be relatively small when compared to the kinetic energy of the ions. There are two ways where this criterion can fail. First, the numerical integrations for the Car-Parrinello equations of motion can often lead to large relative values of the kinetic energy of the Kohn-Sham orbitals relative to the kinetic energy of the ions. This kind of failure is easily fixed by requiring a more accurate numerical integration, i.e. use a smaller time step for the numerical integration. Second, during the motion of the system a the ions can be in locations where there is an Kohn-Sham orbital level crossing, i.e. the density-functional energy can have two states that are nearly degenerate. This kind of failure often occurs in the study of chemical reactions. This kind of failure is not easily fixed and requires the use of a more sophisticated density-functional energy that accounts for low-lying excited electronic states.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#verlet-algorithm-for-integration","title":"Verlet Algorithm for Integration","text":"Integrating the Eqns. above using the Verlet algorithm results in
In this molecular dynamic procedure we have to know variational derivative
and the matrix . The variational derivative
can be analytically found and is
To find the matrix impose the orthonormality constraint on obtain a matrix Riccatti equation, and then Riccatti equation is solved by an iterative solution.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#constant-temperature-simulations-nose-hoover-thermostats","title":"Constant Temperature Simulations: Nose-Hoover Thermostats","text":"Nose-Hoover Thermostats for the electrons and ions can also be added to the Car-Parrinello simulation. In this type of simulation thermostats variables and are added to the simulation by adding the auxiliary energy functionals to the total energy.
In these equations, the average kinetic energy for the ions is
where is the number of atomic degrees of freedom, \u201d is Boltzmann\u2019s constant, and T is the desired t emperature. Defining the average fictitious kinetic energy of the electrons is not as straightforward. Bl\u00f6chl and Parrinello (P.E. Bl\u00f6chl and M. Parrinello, Phys. Rev. B, 45, 9413, (1992)) have suggested the following formula for determining the average fictitious kinetic energy
where is the fictitious electronic mass, is average mass of one atom, and is the kinetic energy of the electrons.
Bl\u00f6chl and Parrinello suggested that the choice of mass parameters, , and should be made such that the period of oscillating thermostats should be chosen larger than the typical time scale for the dynamical events of interest but shorter than the simulation time.
where and are the periods of oscillation for the ionic and fictitious electronic thermostats.
In simulated annealing simulations the electronic and ionic Temperatures are scaled according to an exponential cooling schedule,
where and are the initial temperatures, and and are the cooling rates in atomic units.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-1-s2-dimer-examples-with-pspw","title":"NWPW Tutorial 1: S2 dimer examples with PSPW","text":"A description of all the examples in NWPW Tutorial 1 can be found in the attached pdf nwpwexample1.pdf
"},{"location":"Plane-Wave-Density-Functional-Theory.html#total-energy-of-s2-dimer-with-lda-approximation","title":"Total energy of S2 dimer with LDA approximation","text":"(input:Media:s2-example1.nw, output:Media:s2-example1.nwout)
In this example, the total energy of the S2 dimer using LDA approximation for the exchange-correlation functional is calculated.
echo \n title \"total energy of s2-dimer LDA/30Ry with PSPW method\" \n scratch_dir ./scratch \n permanent_dir ./perm \n start s2-pspw-energy \n geometry \n S 0.0 0.0 0.0 \n S 0.0 0.0 1.88 \n end \n nwpw \n simulation_cell \n SC 20.0 \n end \n cutoff 15.0 \n mult 3 \n xc lda \n lmbfgs \n end \n task pspw energy\n
The energies from the simulation will be
... \n == Summary Of Results == \n\n number of electrons: spin up= 7.00000 down= 5.00000 (real space) \n\n total energy : -0.2041363137E+02 ( -0.10207E+02/ion) \n total orbital energy: -0.4944372503E+01 ( -0.41203E+00/electron) \n hartree energy : 0.1680529987E+02 ( 0.14004E+01/electron) \n exc-corr energy : -0.4320620600E+01 ( -0.36005E+00/electron) \n ion-ion energy : 0.8455644190E-02 ( 0.42278E-02/ion) \n\n kinetic (planewave) : 0.7529965882E+01 ( 0.62750E+00/electron) \n V_local (planewave) : -0.4506036741E+02 ( -0.37550E+01/electron) \n V_nl (planewave) : 0.4623635248E+01 ( 0.38530E+00/electron) \n V_Coul (planewave) : 0.3361059973E+02 ( 0.28009E+01/electron) \n V_xc. (planewave) : -0.5648205953E+01 ( -0.47068E+00/electron) \n Virial Coefficient : -0.1656626150E+01 \n\n orbital energies: \n -0.2001309E+00 ( -5.446eV) \n -0.2001309E+00 ( -5.446eV) \n -0.3294434E+00 ( -8.965eV) -0.2991148E+00 ( -8.139eV) \n -0.3294435E+00 ( -8.965eV) -0.2991151E+00 ( -8.139eV) \n -0.3582269E+00 ( -9.748eV) -0.3352434E+00 ( -9.123eV) \n -0.5632339E+00 ( -15.326eV) -0.5246249E+00 ( -14.276eV) \n -0.7642738E+00 ( -20.797eV) -0.7413909E+00 ( -20.174eV) \n\n Total PSPW energy : -0.2041363137E+02 \n ...\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#structural-optimization-of-s2-dimer-with-lda-approximation","title":"Structural optimization of S2 dimer with LDA approximation","text":"(input:Media:s2-example2.nw, output:Media:s2-example2.nwout)
In this example, the structure of the S2 dimer using results generated from prior energy calculation is calculated. Since most of the parameters are already stored in the run-time database the input is very simple.
echo \n title \"optimization of s2-dimer LDA/30Ry with PSPW method\" \n scratch_dir ./scratch \n permanent_dir ./perm \n restart s2-pspw-energy \n driver \n maxiter 20 \n xyz s2 \n end \n task pspw optimize\n
As the optimization process consists of series of total energy evaluations the contents of the output file are very much similar to that in Example I. At each step the total energy and force information will be outputed as follows
Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n ---- ---------------- -------- -------- -------- -------- -------- -------- \n @ 1 -20.41364254 -7.1D-05 0.00004 0.00004 0.00605 0.01048 7.8\n
The best way to keep track of the optimization calculation is to run the following grep command on the output file.
grep @ outputfile \n\n @ Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n @ ---- ---------------- -------- -------- -------- -------- -------- -------- \n @ 0 -20.41357202 0.0D+00 0.00672 0.00672 0.00000 0.00000 1.5 \n @ 1 -20.41364254 -7.1D-05 0.00004 0.00004 0.00605 0.01048 7.8 \n @ 2 -20.41364256 -2.3D-08 0.00020 0.00020 0.00003 0.00005 9.7 \n @ 2 -20.41364256 -2.3D-08 0.00020 0.00020 0.00003 0.00005 9.7\n
The optimized energy and geometry will be
... \n ---------------------- \n Optimization converged \n ---------------------- \n\n\n Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n ---- ---------------- -------- -------- -------- -------- -------- -------- \n @ 2 -20.41364256 -2.3D-08 0.00020 0.00020 0.00003 0.00005 9.7 \n ok ok ok ok \n\n\n\n Z-matrix (autoz) \n -------- \n\n Units are Angstrom for bonds and degrees for angles \n\n Type Name I J K L M Value Gradient \n ----------- -------- ----- ----- ----- ----- ----- ---------- ---------- \n 1 Stretch 1 2 1.89115 0.00020 \n\n\n\n Geometry \"geometry\" -> \"geometry\" \n --------------------------------- \n\n Output coordinates in angstroms (scale by 1.889725989 to convert to a.u.) \n\n No. Tag Charge X Y Z \n ---- ---------------- ---------- -------------- -------------- -------------- \n 1 S 16.0000 0.00000000 0.00000000 -0.94557591 \n 2 S 16.0000 0.00000000 0.00000000 0.94557591 \n\n ...\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#frequency-calculation-of-s2-dimer-with-lda-approximation","title":"Frequency calculation of S2 dimer with LDA approximation","text":"(input:Media:s2-example3.nw, output:Media:s2-example3.nwout)
In this example, the vibrational frequency of the S2 dimer using results generated from prior geometry optimization is calculated. Since most of the parameters are already stored in the run-time database the input is very simple.
echo \n title \"frequency calculation of s2-dimer LDA/30Ry with PSPW method\" \n scratch_dir ./scratch \n permanent_dir ./perm \n restart s2-pspw-energy \n freq \n animate \n end \n task pspw freq\n
The frequency and thermodynamic analysis generated
... \n Temperature = 298.15K \n frequency scaling parameter = 1.0000 \n\n\n Linear Molecule \n\n Zero-Point correction to Energy = 1.034 kcal/mol ( 0.001647 au) \n Thermal correction to Energy = 2.579 kcal/mol ( 0.004110 au) \n Thermal correction to Enthalpy = 3.171 kcal/mol ( 0.005054 au) \n\n Total Entropy = 52.277 cal/mol-K \n - Translational = 38.368 cal/mol-K (mol. weight = 63.9441) \n - Rotational = 13.630 cal/mol-K (symmetry # = 2) \n - Vibrational = 0.279 cal/mol-K \n\n Cv (constant volume heat capacity) = 5.750 cal/mol-K \n - Translational = 2.979 cal/mol-K \n - Rotational = 1.986 cal/mol-K \n - Vibrational = 0.785 cal/mol-K \n ... \n ---------------------------------------------------------------------------- \n Normal Eigenvalue || Projected Infra Red Intensities \n Mode [cm**-1] || [atomic units] [(debye/angs)**2] [(KM/mol)] [arbitrary] \n ------ ---------- || -------------- ----------------- ---------- ----------- \n 1 0.000 || 0.000030 0.001 0.029 0.000 \n 2 0.000 || 2.466908 56.914 2404.864 15.000 \n 3 0.000 || 2.466908 56.914 2404.864 15.000 \n 4 0.000 || 2.466908 56.914 2404.864 15.000 \n 5 0.000 || 2.466908 56.914 2404.864 15.000 \n 6 723.419 || 0.000000 0.000 0.000 0.000 \n ---------------------------------------------------------------------------- \n ...\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#ab-initio-molecular-dynamics-simulation-car-parrinello-of-s2-dimer-using-the-lda-approximation","title":"Ab initio molecular dynamics simulation (Car-Parrinello) of S2 dimer using the LDA approximation","text":"(input:Media:s2-example4.nw, output:Media:s2-example4.nwout Media:s2-md.xyz Media:s2-md.emotion.dat )
In this example, a constant energy Car-Parrinello simulation of S2 dimer using LDA approximation is calculated. A brief introduction to the Car-Parrinello method can be found in cpmd-lecture.pdf
echo \n title \"AIMD simulation of s2-dimer\" \n scratch_dir ./scratch \n permanent_dir ./perm \n start s2-md \n geometry \n S 0.0 0.0 0.0 \n S 0.0 0.0 1.95 \n end \n nwpw \n simulation_cell \n SC 20.0 \n end \n cutoff 15.0 \n mult 3 \n xc lda \n lmbfgs \n car-parrinello \n time_step 5.0 \n fake_mass 600.0 \n loop 1 1000 \n xyz_filename s2-md.xyz \n end \n end \n task pspw energy \n task pspw car-parrinello\n
A plotting program (e.g. gnuplot, xmgrace) can be used to look at the total, potential, kinetic energies, contained in the s2-md.emotion file (see section EMOTION motion file for datafile format) i.e.,
seattle-1604% gnuplot \n\n G N U P L O T \n Version 4.0 patchlevel 0 \n last modified Thu Apr 15 14:44:22 CEST 2004 \n System: Linux 2.6.18-194.8.1.el5 \n\n Copyright (C) 1986 - 1993, 1998, 2004 \n Thomas Williams, Colin Kelley and many others \n\n This is gnuplot version 4.0. Please refer to the documentation \n for command syntax changes. The old syntax will be accepted \n throughout the 4.0 series, but all save files use the new syntax. \n\n Type help to access the on-line reference manual. \n The gnuplot FAQ is available from \n <http://www.gnuplot.info/faq/> \n\n Send comments and requests for help to \n <gnuplot-info@lists.sourceforge.net> \n Send bugs, suggestions and mods to \n <gnuplot-bugs@lists.sourceforge.net> \n\n\n Terminal type set to 'x11' \n gnuplot> plot \"s2-md.emotion\",\"s2-md.emotion\" using 1:3 \n gnuplot> \n
The following plot shows the Car-Parrinello S energy surface generated from the simulation.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#ab-initio-molecular-dynamics-simulation-born-oppenheimer-of-ssub2-dimer-using-the-lda-approximation","title":"Ab initio molecular dynamics simulation (Born-Oppenheimer) of S<sub2 dimer using the LDA approximation","text":"(input:Media:s2-example5.nw, output:Media:s2-example5.nwout Media:s2-bomd.xyz Media:s2-bomd.emotion.dat ) In this example, a constant energy Born-Oppenheimer simulation of S2 dimer using LDA approximation is calculated.
title \"AIMD simulation of s2-dimer\" \necho\n\nscratch_dir ./scratch\npermanent_dir ./perm\n\nstart s2-bomd \n\ngeometry\nS 0.0 0.0 0.0\nS 0.0 0.0 1.95\nend\n\nnwpw \n simulation_cell\n SC 20.0 \n end\n cutoff 15.0 \n mult 3 \n xc lda \n lmbfgs \nend\ntask pspw energy \n\nnwpw \n bo_steps 1 500 \n bo_time_step 10.0 \nend \ntask pspw born-oppenheimer\n
The following plot shows the energy surface generated from the simulation.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-2-using-pspw-car-parrinello-simulated-annealing-simulations-to-optimize-structures","title":"NWPW Tutorial 2: Using PSPW Car-Parrinello Simulated Annealing Simulations to Optimize Structures","text":"In principle quantum mechanical calculations can be used to determine the structure of any chemical system. One chooses a structure, calculates the total energy of the system, and repeats the calculation for all possible geometries. Of course the major limitation of this approach is that the number of local minima structures increases dramatically with system size and the cost of quantum mechanical calculations also increases dramatically with system size. Not surprisingly most quantum mechanical calculations limit the number of structures to be calculated by using experimental results or chemical intuition. One could speed up the calculations by using simplified inter-atomic force fields instead of quantum mechanical calculations. However, inter-atomic forces fields have many simplifying assumptions that can severely limit their predictability. Another approach is to use ab initio molecular dynamics methods combined with simulated annealing. These methods are quite robust and allow strongly interacting many body systems to be studied by direct dynamics simulation without the introduction of empirical interactions. In these methods, the atomic forces are calculated from ab initio calculations that are performed \u201con-the-fly\u201d as the molecular dynamics trajectory is generated.
The following examples demonstrate how to use the ab initio molecular dynamics methods and simulated annealing strategies of NWChem to determine the lowest energy structures of the B12 cluster. This example is based on a study performed by Kiran Boggavarapu et al.. One might expect from chemical intuition that lowest energy structure of B12 will be an icosahedron, since B12 icosahedra are a common structural unit found in many boron rich materials. Despite this prevalence, ab initio calculations performed by several researchers have suggested that B12, as well as B12+ and B12-, will have a more open geometry.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#simulated-annealing-using-constant-energy-simulation","title":"Simulated Annealing Using Constant Energy Simulation","text":"(input:Media:b12-example2a.nw, output:Media:b12-example2a.nwout Media:b12.00.xyz Media:b12.00.emotion.dat Media:b12.01.xyz Media:b12.01.emotion.dat)
This example uses a series of constant energy Car-Parrinello simulations with velocity scaling to do simulated annealing. The initial four Car-Parrinello simulations are used to heat up the system to several thousand Kelvin. Then the system is cooled down thru a series of constant energy simulations in which the electronic and ionic velocities are scaled by 0.99 at the start of each Car-Parrinello simulation. Energy minimization calculations are used periodically in this simulation to bring the system back down to Born-Oppenheimer surface. This is necessary because of electronic heating.
The Car-Parrinello keyword \u201cscaling\u201d scales the wavefunction and ionic velocities at the start of the simulation. The following input is used to increase the ionic velocities by a factor of two at the start of the Car-Parrinello simulation.
Key Input
...\nCar-Parrinello \nfake_mass 500.0\ntime_step 5.0 \nloop 10 100 \n** scaling 1.0 2.0** \nemotion_filename b12.00.emotion\nxyz_filename b12.00.xyz\nend \n...\n
Output
... \n wavefnc cutoff= 10.000 fft= 42x 42x 42( 6027 waves 1004 per task) \n\ntechnical parameters: \n translation contrained \n time step= 5.00 ficticious mass= 500.0 \n **cooling/heatting rates: 0.10000E+01 (psi)\n0.20000E+01\n(ion)** \n maximum iterations = 1000 ( 10 inner 100 outer ) \n initial kinetic energy: 0.99360E-05 (psi) 0.27956E-03 (ion) \n 0.20205E-28 (c.o.m.) \n **after scaling: 0.99360E-05 (psi) 0.11182E-02\n(ion)** \n **increased energy: 0.00000E+00 (psi)\n0.83868E-03 (ion)** \n\nConstant Energy Simulation \n...\n
The program checks to see if the initial input ionic velocities have a non-zero center of mass velocity. If there is a non-zero center of mass velocity in the system then by default the program removes it. To turn off this feature set the following
nwpw \n translation on \n end\n
or
set nwpw:com_shift .false.\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#simulated-annealing-using-constant-temperature-simulation","title":"Simulated Annealing Using Constant Temperature Simulation","text":"(input:Media:b12-example2b.nw, output:Media:b12-example2b.nwout Media:b12.10.xyz Media:b12.10.emotion.dat Media:b12.11.xyz.gz Media:b12.11.emotion.dat)
(mpeg movie of simulation: Media:boron.mpg)
The simulated annealing calculation in this example uses a constant temperature Car-Parrinello simulation with an exponential cooling schedule,
where T0 and \u03c4 are an initial temperature and a time scale of cooling, respectively. In the present calculations T0=3500K and \u03c4=4.134e+4 au (1.0 ps) were used and the thermostat masses were kept fixed to the initial values determined by T=Te=3500K and (2\u03c0/\u03c9)=250 a.u. (6 fs). Annealing proceeded for 50000 steps, until a temperature of 10K was reached. After which, the metastable structure is optimized using the driver optimizer. The keyword SA_decay is used to enter the decay rates, \u03c4electron and \u03c4ion, used in the simulated annealing algorithm in the constant temperature car-parrinello simulation. The decay rates are in units of au (conversion 1 au = 2.41889e-17 seconds).
Key Input
\u2026.\n Car-Parrinello \n SA_decay 4.134d4 4.134d4 #decay rate in units of au (1au=2.41889e-17seconds) \n \u2026.\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-3-using-isodesmic-reaction-energies-to-estimate-gas-phase-thermodynamics","title":"NWPW Tutorial 3: using isodesmic reaction energies to estimate gas-phase thermodynamics","text":"(isodesmic.pdf isodesmic.tgz)
The development of a computational scheme that can accurately predict reaction energies requires some care. As shown in Table 1 energy errors associated with ab initio calculations can be quite high. Even though ab initio electronic structure methods are constantly being developed and improved upon, these methods are rarely able to give heat of formations of a broad class of molecules with error limits of less than a few kcal/mol. Only when very large basis sets such as the correlation-consistent basis sets, high level treatments of correlation energy such as coupled cluster methods (CCSD(T)), and small correction factors such as core-valence correlation energies and relativistic effects, are included will the heat of formation from ab initio electronic structure methods be accurate to within one kcal/mol. Although one can now accurately calculate the heats of formation of molecules with up to 6 first row atoms, such high-level calculations are extremely demanding and scale computationally as for basis functions.
Examples of these types of large errors are shown in the following Table, where the enthalpies of formation of CClSH are calculated by using atomization energies from different levels of ab initio theory.
MP2/cc-pVDZ LDA/DZVP2 BP91/DZVP2 B3LYP/DZVP2 G2 Theory \u0394H +4.9 -80.0 -2.6 +26.5 -13.0 Table 1: Standard enthalpy of formation (\u0394H(298K) for CClSH in kcal/mol from atomization energies with various electronic structure methods. Results taken from reference [2].
Differences of up to 106.5 kcal/mol are found between different levels of theory. This example demonstrates that care must be taken in choosing the appropriate method for calculating the heats of formation from total atomization energies.
The difficulties associated with calculating absolute heats of formation from atomization energies can be avoided by using a set of isodesmic reactions[1]. The defining property of an isodesmic reaction - that there are an equal number of like bonds on the left-hand and right-hand sides of the reaction - helps to minimize the error in the reaction energy. These reactions are designed to separate out the interactions between molecular subsistents and non-bonding electrons from the direct bonding interactions by having the direct bonding interactions largely canceling one another. This separation is quite attractive. Most ab initio methods give substantial errors when estimating direct bonding interactions due to the computational difficulties associated with electron pair correlation, whereas ab initio methods are expected to be more accurate for estimating neighboring interactions and long-range through-bond effects.
The following isodesmic reaction can be used determine the enthalpy of formation for CClSH that is significantly more accurate than the estimates based on atomization energies.
CClSH + CH CHSH + CClH, \u0394H(calc).
The first step is to calculate the reaction enthalpy of this reaction from electronic, thermal and vibrational energy differences at 298.15K at a consistent level of theory. The defining property of an isodesmic reaction that there are an equal number of like bonds on the left-hand and right-hand sides of the reaction helps to minimize the error in the calculation of the reaction energy. The enthalpy of formation of CClSH can then be calculated by using Hess\u2019s law with the calculated enthalpy change and the experimentally known heats of formation of the other 3 species (see Table 3).
\u0394H(CClSH) = \u0394H(CHSH)(exp) + \u0394H(CClH)(exp) - \u0394H(CH)(exp)- \u0394H(calc).
In this example, try to design and run NWPW simulations that can be used to estimate the enthalpy of formation for CClSH using its atomization energy and using the reaction enthalpy of the isodesmic reaction and compare your results to Table 2. Be careful to make sure that you use the same cutoff energy for all the simulations (.e.g. cutoff 35.0). You might also try to estimate enthalpies of formation for CHClSH and CHClSH. Also try designing simulations that use the SCF, DFT, MP2, and TCE modules.
CClSH + CH CHSH + CClH
Un-optimized geometries for CClSH, CHSH, CClH and CH which are needed to design your simulations are contained in the file Media:thermodynamics.xyz. You will also need to calculate the energies for the H, C, S, and Cl atoms to calculate the atomization energies. The multiplicities for these atoms are 2, 3, 3 and 2 respectively. You will also need to calculate the enthalpy of a molecule. The enthalpy of a molecule at 298.15K is sum of the total energy and a thermal correction to the enthalpy. A good estimate for the thermal correction to the enthalpy can be obtained from a frequency calculation, i.e.
H = E + H
Thermodynamic output from a frequency calculation:
Temperature = 298.15K \nfrequency scaling parameter = 1.0000 \n\nZero-Point correction to Energy = 27.528 kcal/mol ( 0.043869 au) \nThermal correction to Energy = 29.329 kcal/mol ( 0.046739 au)\n
The following line contains the value for H
Thermal correction to Enthalpy = 29.922 kcal/mol ( 0.047683 au)\n\nTotal Entropy = 44.401 cal/mol-K \n - Translational = 34.246 cal/mol-K (mol. weight = 16.0313) \n - Rotational = 10.060 cal/mol-K (symmetry # = 12) \n - Vibrational = 0.095 cal/mol-K \n\nCv (constant volume heat capacity) = 6.503 cal/mol-K \n - Translational = 2.979 cal/mol-K \n - Rotational = 2.979 cal/mol-K \n - Vibrational = 0.544 cal/mol-K\n
Compounds MP2/cc-pVDZ LDA/DZVP2 BP91/DZVP2 B3LYP/DZVP2 G2 Experiment (isodesmic) (isodesmic) (isodesmic) (isodesmic) (atomization) CCl$_3SH -13.40 -11.86 -8.68 -7.64 -12.95 CHClSH -11.48 -11.07 -8.66 -7.92 -11.52 CHClSH -7.01 -6.66 -5.44 -5.20 -6.98 CHSH -4.76 -5.34 Table 2: Gas-phase standard enthalpies of formation ( \u0394H(298K)) in kcal/mol from isodesmic reactions and G2 Theory calculations taken from [3].
Compounds \u0394H(298K) H 52.095 C 171.291 S 66.636 Cl 29.082 CCl -24.59 CClH -24.65 CClH -22.10 CClH -19.32 CH -17.88 CHSH -5.34 Table 3: Miscellaneous experimental gas-phase enthalpies of formation (kcal/mol) taken from [3].
- Hehre, W. J., L. Radom, P.v.R. Schleyer, and J.A. Pople Ab Initio Molecular Orbital Theory; John Wiley & Sons: New York, 1986).
- E.J. Bylaska, D.A. Dixon, and A.R. Felmy(2000), \u201cThe Free Energies of Reactions of Chlorinated Methanes with Aqueous Monovalent Anions: Application of ab initio Electronic Structure Theory\u201d, J. Phys. Chem. A, 104(3), 610-617.
- Chase, M. W., Jr. Phys. Chem. Ref. Data, Monograph No. 9 1998, 9, 1-1951.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-4-aimdmm-simulation-of-ccl_4-64-h_2o","title":"NWPW Tutorial 4: AIMD/MM simulation of CCl + 64 HO","text":"(input:Media:ccl4-64water.nw, output:Media:ccl4-64water.nwout)
In this section we show how use the PSPW module to perform a Car-Parrinello AIMD/MM simulation for a CCl molecule in a box of 64 HO. Before running a PSPW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). In this example, default pseudopotentials from the pseudopotential library are used for C, Cl, O^ and H^, exchange correlation functional is PBE96, The boundary condition is periodic, and with a side length of 23.577 Bohrs and has a cutoff energy is 50 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-5-optimizing-the-unit-cell-and-geometry-of-diamond","title":"NWPW Tutorial 5: Optimizing the Unit Cell and Geometry of Diamond","text":" The PSPW and BAND codes can be used to determine structures and energies for a wide range of crystalline systems. It can also be used to generate band structure and density of state plots.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#optimizing-the-unit-cell-and-geometry-for-an-8-atom-supercell-of-diamond-with-pspw","title":"Optimizing the Unit Cell and Geometry for an 8 Atom Supercell of Diamond with PSPW","text":"(input:Media:diamond-pspw.nw, output:Media:diamond-pspw.nwout, Media:diamond.opt.cif)
(input:Media:catom-pspw.nw, output:Media:catom-pspw.nwout)
The following example uses the PSPW module to optimize the unit cell and geometry for a diamond crystal. The fractional coordinates and the unit cell are defined in the geometry block. The simulation_cell block is not needed since NWPW automatically uses the unit cell defined in the geometry block.
title \"Diamond 8 atom cubic cell - geometry and unit cell optimization\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamond \n\nmemory 950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 3.56d0 \n lat_b 3.56d0 \n lat_c 3.56d0 \n alpha 90.0d0 \n beta 90.0d0 \n gamma 90.0d0 \n end \n C -0.50000d0 -0.50000d0 -0.50000d0 \n C 0.00000d0 0.00000d0 -0.50000d0 \n C 0.00000d0 -0.50000d0 0.00000d0 \n C -0.50000d0 0.00000d0 0.00000d0 \n C -0.25000d0 -0.25000d0 -0.25000d0 \n C 0.25000d0 0.25000d0 -0.25000d0 \n C 0.25000d0 -0.25000d0 0.25000d0 \n C -0.25000d0 0.25000d0 0.25000d0 \nend \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased for small cells \n lmbfgs \n xc pbe96 \nend \n\ndriver \n clear \n maxiter 40 \nend \n\nset nwpw:cif_filename diamond.opt # create a CIF file containing optimization history \nset includestress .true. # this option tells driver to optimize the unit cell \ntask pspw optimize ignore\n
The optimized energy and geometry will be
... \n ---------------------- \n Optimization converged \n ---------------------- \n\n Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n ---- ---------------- -------- -------- -------- -------- -------- -------- \n@ 6 -45.07688304 -1.1D-07 0.00037 0.00021 0.00002 0.00003 174.5 \n ok ok ok ok \n\n\n\n Geometry \"geometry\" -> \"geometry\" \n --------------------------------- \n\nOutput coordinates in angstroms (scale by 1.889725989 to convert to a.u.) \n\n No. Tag Charge X Y Z \n---- ---------------- ---------- -------------- -------------- -------------- \n 1 C 6.0000 1.82723789 1.82729813 1.82705440 \n 2 C 6.0000 0.00000857 -0.00006053 1.82730027 \n 3 C 6.0000 -0.00000584 1.82706061 0.00002852 \n 4 C 6.0000 1.82712018 0.00006354 -0.00002544 \n 5 C 6.0000 2.74074195 2.74072805 2.74088522 \n 6 C 6.0000 0.91366407 0.91370055 2.74064976 \n 7 C 6.0000 0.91351181 2.74080771 0.91352917 \n 8 C 6.0000 2.74078843 0.91348115 0.91365446 \n\n Lattice Parameters \n ------------------ \n\n lattice vectors in angstroms (scale by 1.889725989 to convert to a.u.) \n\n a1=< 3.654 0.000 0.000 > \n a2=< 0.000 3.654 0.000 > \n a3=< 0.000 0.000 3.654 > \n a= 3.654 b= 3.654 c= 3.654 \n alpha= 90.000 beta= 90.000 gamma= 90.000 \n omega= 48.8 \n\n reciprocal lattice vectors in a.u. \n\n b1=< 0.910 0.000 0.000 > \n b2=< 0.000 0.910 0.000 > \n b3=< 0.000 0.000 0.910 > \n\n Atomic Mass \n ----------- \n\n C 12.000000 \n\n\n============================================================================== \n internuclear distances \n------------------------------------------------------------------------------ \n center one | center two | atomic units | angstroms \n------------------------------------------------------------------------------ \n 5 C | 1 C | 2.99027 | 1.58238 \n 6 C | 1 C | 2.99027 | 1.58238 \n 6 C | 2 C | 2.99027 | 1.58238 \n 7 C | 1 C | 2.99026 | 1.58238 \n 7 C | 3 C | 2.99027 | 1.58238 \n 8 C | 1 C | 2.99027 | 1.58238 \n 8 C | 4 C | 2.99027 | 1.58238 \n------------------------------------------------------------------------------ \n number of included internuclear distances: 7 \n============================================================================== \n\n============================================================================== \n internuclear angles \n------------------------------------------------------------------------------ \n center 1 | center 2 | center 3 | degrees \n------------------------------------------------------------------------------ \n 5 C | 1 C | 6 C | 109.46 \n 5 C | 1 C | 7 C | 109.48 \n 5 C | 1 C | 8 C | 109.48 \n 6 C | 1 C | 7 C | 109.47 \n 6 C | 1 C | 8 C | 109.46 \n 7 C | 1 C | 8 C | 109.48 \n 1 C | 6 C | 2 C | 109.48 \n 1 C | 7 C | 3 C | 109.47 \n 1 C | 8 C | 4 C | 109.47 \n------------------------------------------------------------------------------ \n number of included internuclear angles: 9 \n============================================================================== ...\n
The C-C bond distance after the geometry optimization is 1.58 Angs. and agrees very well with the experimental value of 1.54 Angs.. Another quantity that can be calculated from this simulation is the cohesive energy.The cohesive energy of a crystal is the energy needed to separate the atoms of the solid into isolated atoms, i.e.
where is the energy of the solid and are the energies of the isolated atoms. In order to calculate the cohesive energy the energy of an isolated carbon atom at the same level of theory and cutoff energy will need to be calculated. The following input can be used to the energy of an isolated carbon atom.
(input:file:catom-pspw.nw, output:file:catom-pspw.nwout)
title \"triplet carbon atom at pbe96 level using a large unit cell\" \nstart c1-pspw \nmemory 1400 mb \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\ngeometry \nC 0 0 0 \nend \n\nnwpw \n simulation_cell \n FCC 38.0 #large unit cell \n boundary_conditions periodic # periodic boundary conditions are used by default. \n #boundary_conditions aperiodic # free-space (or aperiodic) boundary conditions could also be used. \n end \n xc pbe96 \n mult 3 \n lmbfgs \nend \ntask pspw energy\n
The total energy from the simulation will be
Total PSPW energy : -0.5421213534E+01
Using this energy and energy of diamond the cohesive energy per atom is calculated to be
This value is substantially lower than the experimental value of ! It turns out this error is a result of the unit cell being too small for the diamond calculation (or too small of a Brillioun zone sampling). In the next section, we show how increasing the Brillouin zone sampling reduces the error in the calculated cohesive energy.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#optimizing-the-unit-cell-for-an-8-atom-supercell-of-diamond-with-band","title":"Optimizing the Unit Cell for an 8 Atom Supercell of Diamond with BAND","text":"(input:Media:diamond-band.nw, output:Media:diamond-band.nwout)
In this example the BAND module is used to optimize the unit cell and geometry for a diamond crystal at different Brillouin zone samplings.
title \"Diamond 8 atom cubic cell - geometry and unit cell optimization\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamond-band \n\nmemory 1950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 3.58d0 \n lat_b 3.58d0 \n lat_c 3.58d0 \n alpha 90.0d0 \n beta 90.0d0 \n gamma 90.0d0 \n end \n C -0.50000d0 -0.50000d0 -0.50000d0 \n C 0.00000d0 0.00000d0 -0.50000d0 \n C 0.00000d0 -0.50000d0 0.00000d0 \n C -0.50000d0 0.00000d0 0.00000d0 \n C -0.25000d0 -0.25000d0 -0.25000d0 \n C 0.25000d0 0.25000d0 -0.25000d0 \n C 0.25000d0 -0.25000d0 0.25000d0 \n C -0.25000d0 0.25000d0 0.25000d0 \nend \nset includestress .true. # option tells driver to optimize the unit cell \nset nwpw:zero_forces .true. # option zeros the forces on the atoms--> only lattice parameters optimized \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased \n lmbfgs \n xc pbe96 \nend \n\n#1x1x1 k-point mesh \nnwpw \n monkhorst-pack 1 1 1 \nend \nset nwpw:cif_filename diamond111.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#2x2x2 k-point mesh \nnwpw \n monkhorst-pack 2 2 2 \nend \nset nwpw:cif_filename diamond222.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#3x3x3 k-point mesh \nnwpw \n monkhorst-pack 3 3 3 \nend \nset nwpw:cif_filename diamond333.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#4x4x4 k-point mesh \nnwpw \n monkhorst-pack 4 4 4 \nend \nset nwpw:cif_filename diamond444.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#5x5x5 k-point mesh \nnwpw \n monkhorst-pack 5 5 5 \nend \nset nwpw:cif_filename diamond555.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n
The following figure shows a plot of the cohesive energy and C-C bond distance versus the Brillouin zone sampling. As can be seen in this figure the cohesive energy (w/o zero-point correction) and C-C bond distance agree very well with the experimental values of 7.37 eV (including zero-point correction) and 1.54 Angs.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#using-band-to-optimize-the-unit-cell-for-a-2-atom-primitive-cell-of-diamond","title":"Using BAND to Optimize the Unit Cell for a 2 Atom Primitive Cell of Diamond","text":"(input:Media:diamond-fcc.nw, output:Media:diamond-fcc.nwout.gz)
In this example the BAND module is used to optimize a 2 atom unit cell for a diamond crystal at different Brillouin zone samplings. The optimized energy and geometry will be (Monkhorst-Pack sampling of 11x11x11)
---------------------- \n Optimization converged \n ---------------------- \n\n Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n ---- ---------------- -------- -------- -------- -------- -------- -------- \n@ 1 -11.40586236 5.2D-07 0.00039 0.00018 0.00002 0.00003 662.0 \n ok ok ok ok \n\n\n\n Geometry \"geometry\" -> \"geometry\" \n --------------------------------- \n\n Output coordinates in angstroms (scale by 1.889725989 to convert to a.u.) \n\n No. Tag Charge X Y Z \n ---- ---------------- ---------- -------------- -------------- -------------- \n 1 C 6.0000 0.00000000 0.00000000 0.00000000 \n 2 C 6.0000 0.72201500 1.25056532 0.51054180 \n\n Lattice Parameters \n ------------------ \n\n lattice vectors in angstroms (scale by 1.889725989 to convert to a.u.) \n\n a1=< 2.165 1.251 0.001 > \n a2=< 0.001 2.500 0.001 > \n a3=< 0.722 1.251 2.041 > \n a= 2.500 b= 2.500 c= 2.500 \n alpha= 59.966 beta= 59.966 gamma= 59.966 \n omega= 11.0 \n\n reciprocal lattice vectors in a.u. \n\n b1=< 1.536 -0.768 0.000 > \n b2=< 0.000 1.330 0.000 > \n b3=< -0.543 -0.543 1.629 > \n\n Atomic Mass \n ----------- \n\n C 12.000000 \n\n\n ============================================================================== \n internuclear distances \n ------------------------------------------------------------------------------ \n center one | center two | atomic units | angstroms \n ------------------------------------------------------------------------------ \n 2 C | 1 C | 2.89435 | 1.53162 \n ------------------------------------------------------------------------------ \n number of included internuclear distances: 1 \n ==============================================================================\n
The following figure shows a plot of the cohesive energy and C-C bond distance versus the Brillouin zone sampling for the 8 atom SC unit cell and the 2 atom FCC unit cell.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#using-band-to-calculate-the-band-structures-of-diamond","title":"Using BAND to Calculate the Band Structures of Diamond","text":"(input:Media:diamond-structure.nw, output:Media:diamond-structure.nwout, file:diamondfcc.restricted_band.dat)
The following example uses the BAND module to calculate the band structure for the FCC cell of the a diamond crystal. The fractional coordinates and the unit cell are defined in the geometry block. The simulation_cell block is not needed since NWPW automatically uses the unit cell defined in the geometry block.
title \"Diamond 2 atom fcc cell Brillouin sampling=9x9x9 M-P - Band structure plot\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamondfcc \n\nmemory 1950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 2.500d0 \n lat_b 2.500d0 \n lat_c 2.500d0 \n alpha 60.0d0 \n beta 60.0d0 \n gamma 60.0d0 \n end \n C 0.00000d0 0.00000d0 0.00000d0 \n C 0.25000d0 0.25000d0 0.25000d0 \nend \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased \n lmbfgs \n xc pbe96 \n\n monkhorst-pack 9 9 9 \nend \n\n#need to run \"task band energy\" before \"task band structure\" can be run \ntask band energy \n\nnwpw \n virtual 16 \n brillouin_zone \n zone_name fccpath \n path fcc l gamma x w k gamma \n end \n zone_structure_name fccpath \nend \ntask band structure\n
This calculation outputs the file:diamondfcc.restricted_band.dat) data file in the permanent_directory. A plotting (e.g. gnuplot or xmgrace) can be used to display the band structure.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#using-band-to-calculate-the-density-of-states-of-diamond","title":"Using BAND to Calculate the Density of States of Diamond","text":"(2 atom cell - input:diamond-dos.nw output:diamond-dos.nwout, diamond-dos.dos.dat (8 atom cell - input:diamond-dos8.nw output: diamond-dos8.nwout.gz, diamond-dos8.dos.dat
There are two possible ways to use the BAND module to calculate the density and projected density of states. The first approach just uses the eigenvalues generated from an energy calculation to generate a density of states. The following example uses this strategy to calculate the density of states and projected density of states of diamond.
title \"Diamond 2 atom fcc cell Brillouin sampling=9x9x9 M-P - density of states plot\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamond-dos \n\nmemory 1950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 2.500d0 \n lat_b 2.500d0 \n lat_c 2.500d0 \n alpha 60.0d0 \n beta 60.0d0 \n gamma 60.0d0 \n end \n C 0.00000d0 0.00000d0 0.00000d0 \n C 0.25000d0 0.25000d0 0.25000d0 \nend \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased \n lmbfgs \n xc pbe96 \n\n monkhorst-pack 9 9 9 \n dos # dos keyword tells the code to calculate dos at the end of an energy calculation\n mulliken # turn on projected density of states\n virtual 8 # include 8 virtual states\nend \n\ntask band energy \n
The other approach uses the band structure code to calculate the eigenvalues given a precomputed density. The approach is slower than the first approach, however, it can be used to substantially increase the number of k-points and virtual orbitals used to generate the density of states. The following example demonstrates this capability to calculate the density of states and projected density of states of the diamond crystal.
title \"Diamond 2 atom fcc cell Brillouin sampling=9x9x9 M-P - density of states plot\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamond-dos \n\nmemory 1950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 2.500d0 \n lat_b 2.500d0 \n lat_c 2.500d0 \n alpha 60.0d0 \n beta 60.0d0 \n gamma 60.0d0 \n end \n C 0.00000d0 0.00000d0 0.00000d0 \n C 0.25000d0 0.25000d0 0.25000d0 \nend \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased \n lmbfgs \n xc pbe96 \n\n monkhorst-pack 9 9 9 \nend \n\n#need to run \"task band energy\" before \"task band dos\" can be run \ntask band energy \n\nnwpw \n virtual 26 #26 virtual orbitals included in the DOS calculation \n dos 0.002 700 -1.00000 2.0000 #alpha npoints emin emax,....,change default energy range and gridding. note alpha not used in task band dos calculations\n dos-grid 11 11 11 \n mulliken # mulliken keyword used to turn on projected density of states\nend \ntask band dos\n
This calculation outputs the data file in the permanent_directory. A plotting (e.g. gnuplot or xmgrace) can be used to display the density of states.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#calculate-the-phonon-spectrum-of-diamond","title":"Calculate the Phonon Spectrum of Diamond","text":"title \"Diamond 2 atom fcc cell Brillouin sampling=9x9x9 M-P - Phonon spectra\" \necho \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\nstart diamond-dos \n\nmemory 1950 mb \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 2.500d0 \n lat_b 2.500d0 \n lat_c 2.500d0 \n alpha 60.0d0 \n beta 60.0d0 \n gamma 60.0d0 \n end \n C 0.00000d0 0.00000d0 0.00000d0 \n C 0.25000d0 0.25000d0 0.25000d0 \nend \n\nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 #The default value of 1 needs to be increased \n lmbfgs \n xc pbe96 \n\n monkhorst-pack 9 9 9 \nend \n\ntask band energy \ntask band freq\n\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-6-optimizing-the-unit-cell-of-nickel-with-fractional-occupation","title":"NWPW Tutorial 6: optimizing the unit cell of nickel with fractional occupation","text":"(input:Media:Ni-band.nw output:Media:Ni-band.nwout) The following example demonstrates how to uses the BAND module to optimize the unit cell and geometry for FCC cell of Nickel metal
title \"Ni FCC metal, monkhorst-pack=3x3x3, 5x5x5, and 7x7x7, fermi smearing, xc=pbe96\" \necho \n\nstart Ni-band \n\nmemory 1900 mb \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\ngeometry units angstroms center noautosym noautoz print \n system crystal \n lat_a 3.5451d0 \n lat_b 3.5451d0 \n lat_c 3.5454d0 \n alpha 90.0d0 \n beta 90.0d0 \n gamma 90.0d0 \n end \n\nNi 0.000000 0.000000 0.000000 \nNi 0.000000 0.500000 0.500000 \nNi 0.500000 0.000000 0.500000 \nNi 0.500000 0.500000 0.000000 \nend \nset nwpw:cif_filename Ni-band \nset nwpw:zero_forces .true. \nset includestress .true. \n\n#turn on pseudopotential filtering \nset nwpw:kbpp_ray .true. \nset nwpw:kbpp_filter .true. \n\nnwpw \n #fractional occupation \n smear fermi \n\n #scf option used with smear \n scf anderson outer_iterations 0 kerker 2.0 \n\n ewald_ncut 8 \n ewald_rcut 3.0 \n xc pbe96 \n monkhorst-pack 3 3 3 \n np_dimensions -1 -1 4 \nend \n\n#generate initial wavefunctions w/ low cutoff energy \nnwpw \n loop 10 10 \n cutoff 10.0 \nend \ntask band energy \n\n#increase cutoff energy and number of iterations \nnwpw \n cutoff 50.0 \n loop 10 100 \nend\n\n#3x3x3 k-point mesh \nnwpw \n monkhorst-pack 3 3 3 \nend \nset nwpw:cif_filename nickel333.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#5x5x5 k-point mesh \nnwpw \n monkhorst-pack 5 5 5 \nend \nset nwpw:cif_filename nickel555.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n\n#7x7x7 k-point mesh \nnwpw \n monkhorst-pack 7 7 7 \nend \nset nwpw:cif_filename nickel777.opt \ndriver; clear; maxiter 40; end; task band optimize ignore\n
The following figure shows a plot of the cohesive energy and Ni-Ni bond distance versus the Brillouin zone sampling. As can be seen in this figure the cohesive energy (w/o zero-point correction) and Ni-Ni bond distance agree very well with the experimental values of 4.44 eV (including zero-point correction) and 2.49 Angs.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-7-optimizing-the-unit-cells-with-symmetry-diamond-with-fd-3m-symmetry-and-brucite-with-p-3m1-symmetry","title":"NWPW Tutorial 7: Optimizing the unit cells with symmetry: Diamond with Fd-3m symmetry and Brucite with P-3m1 symmetry","text":"(Diamond example, input:Media:diamond-symmetry.nw, output:Media:diamond-symmetry.nwout)
(Brucite example, input:Media:brucite-symmetry.nw, output:Media:brucite-symmetry.nwout)
The following example uses the BAND module to optimize the unit cell and geometry for a Diamond crystal with Fd-3m symmetry. The fractional coordinates, unit cell, and symmetry are defined in the geometry block.
title \"Diamond 8 atom cubic cell generated using Fd-3m symmetry - geometry and unit cell optimization\" \necho \n\nmemory 1500 mb\n\npermanent_dir ./perm\nscratch_dir ./scratch\n\nstart diamond-symmetry \n\n\ngeometry nocenter noautosym noautoz print \n system crystal \n lat_a 3.58 \n lat_b 3.58 \n lat_c 3.58 \n alpha 90.0 \n beta 90.0 \n gamma 90.0 \n end\nsymmetry Fd-3m\nC 0.0 0.0 0.0\nend \nset nwpw:cif_filename diamond-symmetry\n\n#turn on pseudopotential filtering \nset nwpw:kbpp_ray .true.\nset nwpw:kbpp_filter .true.\n\n#***** setup the nwpw Band code - 3x3x3 k-point mesh **** \nnwpw\n ewald_rcut 3.0\n ewald_ncut 8\n xc pbe96 \n lmbfgs\n monkhorst-pack 3 3 3\n np_dimensions -1 -1 4\nend \n\nset includestress .true. # tell driver to optimize unit cell\nset includelattice .true. # tell driver to optimize with a,b,c,alpha,beta,gamma\ntask band optimize ignore\n
The optimized geometry will also contain the information about the symmetry being used
.... \n ---------------------- \n Optimization converged \n ---------------------- \n\n\n Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n ---- ---------------- -------- -------- -------- -------- -------- -------- \n@ 7 -45.62102901 -4.1D-07 0.00010 0.00003 0.00019 0.00060 287.1 \n ok ok ok ok \n\n\n\n Geometry \"geometry\" -> \"geometry\" \n --------------------------------- \n\nOutput coordinates in angstroms (scale by 1.889725989 to convert to a.u.) \n\n No. Tag Charge X Y Z \n---- ---------------- ---------- -------------- -------------- -------------- \n 1 C 6.0000 0.00000000 0.00000000 0.00000000 \n 2 C 6.0000 0.00000000 1.76715074 1.76715074 \n 3 C 6.0000 1.76715074 1.76715074 0.00000000 \n 4 C 6.0000 1.76715074 0.00000000 1.76715074 \n 5 C 6.0000 2.65072611 0.88357537 2.65072611 \n 6 C 6.0000 0.88357537 0.88357537 0.88357537 \n 7 C 6.0000 0.88357537 2.65072611 2.65072611 \n 8 C 6.0000 2.65072611 2.65072611 0.88357537 \n\n Lattice Parameters \n ------------------ \n\n lattice vectors in angstroms (scale by 1.889725989 to convert to a.u.) \n\n a1=< 3.534 0.000 0.000 > \n a2=< 0.000 3.534 0.000 > \n a3=< 0.000 0.000 3.534 > \n a= 3.534 b= 3.534 c= 3.534 \n alpha= 90.000 beta= 90.000 gamma= 90.000 \n omega= 44.1 \n\n reciprocal lattice vectors in a.u. \n\n b1=< 0.941 0.000 0.000 > \n b2=< 0.000 0.941 0.000 > \n b3=< 0.000 0.000 0.941 > \n\n Atomic Mass \n ----------- \n\n C 12.000000 \n\n\n Symmetry information \n -------------------- \n\nGroup name Fd-3m \nGroup number 227 \nGroup order 192 \nNo. of unique centers 1 \nSetting number 1 \n\n Symmetry unique atoms \n\n 1 \n\n============================================================================== \n internuclear distances \n------------------------------------------------------------------------------ \n center one | center two | atomic units | angstroms \n------------------------------------------------------------------------------ \n 5 C | 4 C | 2.89203 | 1.53040 \n 6 C | 1 C | 2.89203 | 1.53040 \n 6 C | 2 C | 2.89203 | 1.53040 \n 6 C | 3 C | 2.89203 | 1.53040 \n 6 C | 4 C | 2.89203 | 1.53040 \n 7 C | 2 C | 2.89203 | 1.53040 \n 8 C | 3 C | 2.89203 | 1.53040 \n------------------------------------------------------------------------------ \n number of included internuclear distances: 7 \n============================================================================== \n\n\n\n============================================================================== \n internuclear angles \n------------------------------------------------------------------------------ \n center 1 | center 2 | center 3 | degrees \n------------------------------------------------------------------------------ \n 6 C | 2 C | 7 C | 109.47 \n 6 C | 3 C | 8 C | 109.47 \n 5 C | 4 C | 6 C | 109.47 \n 1 C | 6 C | 2 C | 109.47 \n 1 C | 6 C | 3 C | 109.47 \n 1 C | 6 C | 4 C | 109.47 \n 2 C | 6 C | 3 C | 109.47 \n 2 C | 6 C | 4 C | 109.47 \n 3 C | 6 C | 4 C | 109.47 \n------------------------------------------------------------------------------ \n number of included internuclear angles: 9 \n==============================================================================\n
The following example uses the BAND module to optimize the unit cell and geometry for a Brucite crystal (Mg(OH)2 with P-3m1 symmetry.
title \"brucite testing - using P-3m1 symmetry\" \necho \n\nmemory 1500 mb \n\npermanent_dir ./perm \nscratch_dir ./scratch \n\ngeometry nocenter noautosym noautoz print \n system crystal \n lat_a 3.14979 \n lat_b 3.14979 \n lat_c 4.7702 \n alpha 90.0 \n beta 90.0 \n gamma 120.0 \n end \nsymmetry P-3m1 \nMg 0.00000 0.00000 0.00000 \nO 0.33333 0.66667 0.22030 \nH 0.33333 0.66667 0.41300 \nend \nset nwpw:cif_filename brucite \n\n#turn on pseudopotential filtering \nset nwpw:kbpp_ray .true. \nset nwpw:kbpp_filter .true. \n\n#***** setup the nwpw gamma point code **** \nnwpw \n ewald_rcut 3.0 \n ewald_ncut 8 \n xc pbe96 \n lmbfgs \n monkhorst-pack 3 3 2 \n #np_dimensions -1 -1 4 \nend \n\ndriver \n clear \n maxiter 31 \nend \n\nset includestress .true. # tell driver to optimize unit cell \nset includelattice .true. \n\ntask band optimize ignore\n
Optimizing Brucite, which is a soft layered material (2.5-3 Mohs scale), is more difficult to optimize than a hard material such as Diamond. For these types of materials using symmetry can often result in a faster optimization. For example, with symmetry the optimization converges within 20 to 30 geometry optimization steps,
@ Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n@ ---- ---------------- -------- -------- -------- -------- -------- -------- \n@ 0 -34.39207476 0.0D+00 0.24673 0.10223 0.00000 0.00000 172.7 \n@ 1 -34.39340208 -1.3D-03 0.00872 0.00302 0.00198 0.00485 328.5 \n.... \n@ 20 -34.39042736 -1.2D-05 0.00195 0.00083 0.00440 0.01964 3019.2 \n@ 21 -34.39043463 -7.3D-06 0.00028 0.00011 0.00493 0.02042 3150.6 \n@ 22 -34.39043484 -2.1D-07 0.00043 0.00014 0.00002 0.00008 3278.5 \n@ 22 -34.39043484 -2.1D-07 0.00043 0.00014 0.00002 0.00008 3278.5\n
whereas, without symmetry the optimization may not be converged even at 100 geometry steps (input:Media:brucite-nosymmetry.nw, output:Media:brucite-nosymmetry.nwout).
@ Step Energy Delta E Gmax Grms Xrms Xmax Walltime \n@ ---- ---------------- -------- -------- -------- -------- -------- -------- \n@ 0 -34.39207476 0.0D+00 0.24673 0.10250 0.00000 0.00000 18.4 \n@ 1 -34.39340765 -1.3D-03 0.02963 0.00715 0.00202 0.00500 30.7 \n... \n@ 49 -34.39027641 -2.1D-06 0.01870 0.00646 0.00074 0.00202 595.7 \n@ 50 -34.39027503 1.4D-06 0.01962 0.00669 0.00069 0.00197 608.4 \n... \n@ 100 -34.39034236 -3.8D-07 0.00380 0.00150 0.00036 0.00132 1155.3 \n@ 101 -34.39034431 -1.9D-06 0.00305 0.00118 0.00012 0.00045 1166.8 \n@ 102 -34.39034449 -1.8D-07 0.00370 0.00144 0.00006 0.00020 1177.9 \n...\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-8-nvt-metropolis-monte-carlo-simulations","title":"NWPW Tutorial 8: NVT Metropolis Monte-Carlo Simulations","text":"In this example the PSPW module is used to run an NVT simulation for a diamond crystal using the a Metropolis Monte-Carlo algorithm.
title \"Metropolis NVT simulation of diamond - this input is used to put the system in equilibrium\" \necho \n\nstart diamond-nvt \n\n#permanent_dir ./perm \n#scratch_dir ./perm \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \nsystem crystal \n lat_a 3.56d0 \n lat_b 3.56d0 \n lat_c 3.56d0 \n alpha 90.0d0 \n beta 90.0d0 \n gamma 90.0d0 \nend \nC -0.50000d0 -0.50000d0 -0.50000d0 \nC 0.00000d0 0.00000d0 -0.50000d0 \nC 0.00000d0 -0.50000d0 0.00000d0 \nC -0.50000d0 0.00000d0 0.00000d0 \nC -0.25000d0 -0.25000d0 -0.25000d0 \nC 0.25000d0 0.25000d0 -0.25000d0 \nC 0.25000d0 -0.25000d0 0.25000d0 \nC -0.25000d0 0.25000d0 0.25000d0 \nend \nset nwpw:cif_filename diamond_nvt_234 \n\n###### setup the nwpw gamma point code ###### \nset nwpw:kbpp_ray .true. \nset nwpw:kbpp_filter .true. \nset nwpw:frozen_lattice:thresh 999.0 \nnwpw \n lmbfgs \n ewald_rcut 3.0 \n ewald_ncut 8 \n xc pbe \nend \ntask pspw energy \n\n##### optimize the unit cell ##### \nset includestress .true. #this option tells driver to optimize the unit cell \nset includelattice .true. #this option tells driver to optimize cell using a,b,c,alpha,beta,gamma \ndriver \n clear \n maxiter 51 \nend \ntask pspw optimize ignore \n\n#################################################################################### \n###### setup Metropolis NVT code - input will change in a forthcoming release ###### \n#################################################################################### \nset nwpw:mc_seed 234 # Seed for random number generator \nset nwpw:mc_algorithm 1 # 1-NVT; 2-NPT \nset nwpw:mc_aratio 0.234 # targeted acceptance ratio \nset nwpw:mc_ddx 0.1 # parameter used to adjust geometry dispacement to have sampling with targeted acceptance \nset nwpw:mc_temperature 300.0 # Temperature in K \nset nwpw:mc_step_size 0.250 # initial geometry displacement step size \n\nnwpw \n mc_steps 10 100 #total number of iterations = 10*100, number of iterations between step size adjustments = 10 \n cpmd_properties on \nend \ntask pspw Metropolis\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-9-npt-metropolis-monte-carlo-simulations","title":"NWPW Tutorial 9: NPT Metropolis Monte-Carlo Simulations","text":"In this example the PSPW module is used to run an NPT simulation for a diamond crystal using the a Metropolis Monte-Carlo algorithm.
(input:Media:diamond-metropolis.nw, output:Media:diamond-metropolis.nwout.gz, datafiles:Media:diamond-metropolis.emotion.gz, Media:diamond-metropolis.ion_motion.gz, Media:diamond-metropolis.xyz.gz, Media:diamond_metropolis_1234.cif.gz)
title \"Metropolis NPT simulation of diamond - this input is used to put the system in equilibrium\" \necho \n\nstart diamond-metropolis \n\n#permanent_dir ./perm \n#scratch_dir ./perm \n\n#**** Enter the geometry using fractional coordinates **** \ngeometry center noautosym noautoz print \n system crystal \n lat_a 3.56d0 \n lat_b 3.56d0 \n lat_c 3.56d0 \n alpha 90.0d0 \n beta 90.0d0 \n gamma 90.0d0 \n end \n C -0.50000d0 -0.50000d0 -0.50000d0 \n C 0.00000d0 0.00000d0 -0.50000d0 \n C 0.00000d0 -0.50000d0 0.00000d0 \n C -0.50000d0 0.00000d0 0.00000d0 \n C -0.25000d0 -0.25000d0 -0.25000d0 \n C 0.25000d0 0.25000d0 -0.25000d0 \n C 0.25000d0 -0.25000d0 0.25000d0 \n C -0.25000d0 0.25000d0 0.25000d0 \nend \nset nwpw:cif_filename pspw_metropolis \n\n###### setup the nwpw gamma point code ###### \nset nwpw:kbpp_ray .true. \nset nwpw:kbpp_filter .true. \nset nwpw:frozen_lattice:thresh 999.0 \nnwpw \n lmbfgs \n ewald_rcut 3.0 \n ewald_ncut 8 \n xc pbe \nend \ntask pspw energy \n\n\n#################################################################################### \n###### setup Metropolis NPT code - input will change in a forthcoming release ###### \n#################################################################################### \nset nwpw:mc_seed 1234 # Seed for random number generator \nset nwpw:mc_algorithm 2 # 1-NVT; 2-NPT \nset nwpw:mc_aratio 0.234 # targeted acceptance ratio \nset nwpw:mc_ddx 0.1 # parameter used to adjust geometry dispacement to have sampling with targeted acceptance \nset nwpw:mc_ddv 0.1 # parameter used to adjust volume change to have sampling with targeted acceptance \nset nwpw:mc_temperature 300.0 # Temperature in K \nset nwpw:mc_step_size 0.250 # geometry displacement step size \nset nwpw:mc_volume_step 0.130 # volume displacement step size \n\nnwpw \n bo_steps 10 100 #total number of iterations = 10*100, number of iterations between step size adjustments = 10 \nend \ntask pspw Metropolis\n
(inputs:Media:diamond-metropolis-sampling.nw.tgz)
(python analysis program:Media:makehistogram.gz)
[WE27972:~/Projects/NWChem/Metropolis] bylaska% makehistogram -t 300 -c 2 1235/diamond-metropolis-1235.emotion 1236/diamond-metropolis-1236.emotion \n1237/diamond-metropolis-1237.emotion 1238/diamond-metropolis-1238.emotion 1239/diamond-metropolis-1239.emotion 1240/diamond-metropolis-1240.emotion \n1241/diamond-metropolis-1241.emotion 1242/diamond-metropolis-1242.emotion 1243/diamond-metropolis-1243.emotion 1244/diamond-metropolis-1244.emotion \n1245/diamond-metropolis-1245.emotion 1246/diamond-metropolis-1246.emotion 1248/diamond-metropolis-1248.emotion 1249/diamond-metropolis-1249.emotion \nmakehistogram Program \nlen(args)= 14 \n\nunitconversion = 1.0 \ntemperature (K) = 300 \nRT (au) = 0.000949482834326 ( 0.5958 kcal/mol) \n\ndata columns -1 = [1] \ndata rows (n) = 52000 \n\ndelta (au) = 0.01 \nxmin-delta (au) = -45.08080365 \nxmax+delta (au) = -45.05079515 \n\ndata averaging: \n- xbar (au) = -45.0668093497 \n- S2_{n-1} (au) = 1.08378343101e-05 \n- <exp((x-xmin)/RT)> (au) = 5293374903.39 \n- <exp((x-xbar)/RT)> (au) = 2102.44405413 \n- Free energy = -45.0595449934 \n- Free energy1 = -45.0595449934 \n\nhistogram distribution parameters: \n- number of bins (Rice k) = 75 \n- bin width = 0.00040552027027 \n- norm = 1.0 \n- xbar (au) = -45.0668107987 (error= -1.44908364064e-06 ) \n- S2_{n-1} (au) = 1.0858459744e-05 (error= 2.06254339582e-08 ) \n- <exp((x-xmin)/RT)> (au) = 5184600342.01 (error= -108774561.378 ) \n- <exp((x-xbar)/RT)> (au) = 2062.38570923 (error= -40.0583449011 ) \n- Free energy = -45.0595647078 (error= -1.9714360235e-05 ) \n- Free energy1 = -45.0595647078 (error= -1.9714360235e-05 ) \n- histogram plot file = histogram.dat \n\nnormal distribution parameters: \n- average x (input xbar) = -45.0668093497 \n- unbiased sample variance (input S2_(n-1))= 1.08378343101e-05 \n- xbar-xmin = 0.0139943003357 \n- norm = 0.99998877936 \n- xbar (au) = -45.0663035243 (error= 0.000505825397738 ) \n- S2_{n-1} (au) = 1.1091077321e-05 (error= 2.53243010936e-07 ) \n- <exp((x-xmin)/RT)> (au) = 943482808.939 (error= -4349892094.45 ) \n- <exp((x-xbar)/RT)> (au) = 219.968603653 (error= -1882.47545048 ) \n- Free energy = -45.061182503 (error= -0.00163750957643 ) \n- Free energy1 = -45.061182503 (error= -0.00163750957643 ) \n- normal distribution plot file = normdist.dat \n- number data points = 1500 \n\ngamma distribution parameters: \n- alpha0= 18.0700715921 \n- beta0 = 1291.24508969 \n- xmin + alpha0/beta0 = -45.0668093497 \n- alpha = 18.5003178357 \n- beta = 1321.98948086 \n- xmin + alpha/beta = -45.0668093497 \n- norm = 0.999923464137 0.99993569948 \n- xbar (au) = -45.0633614482 -45.0639126423 (error= 0.00344790150088 0.00289670733491 ) \n- S2_{n-1} (au) = 2.27110055327e-05 1.89632753897e-05 (error= 1.18731712226e-05 8.12544107961e-06 ) \n- <exp((x-xmin)/RT)> (au) = 7932775654.26 7060892836.07 (error= 2639400750.87 1767517932.68 ) \n- <exp((x-xbar)/RT)> (au) = 83.43400035 132.707151194 (error= -2019.01005378 -1969.73690294 ) \n- Free energy = -45.059160883 -45.0592714327 (error= 0.000384110406969 0.000273560709338 ) \n- Free energy1 = -45.059160883 -45.0592714327 (error= 0.000384110406969 0.000273560709338 ) \n- gamma distribution plot file = gammadist.dat \n- number data points = 1500 \n\nHausdorff distribution parameters: \n- xmin = -45.08080365 \n- xmax = -45.05079515 \n- number moments = 15 \n -- < x^0 > = 1.000000000000000 \n -- < x^1 > = 0.466344546904007 \n -- < x^2 > = 0.229512222180349 \n -- < x^3 > = 0.119040323347820 \n -- < x^4 > = 0.064946164109284 \n -- < x^5 > = 0.037186896798964 \n -- < x^6 > = 0.022287980659815 \n -- < x^7 > = 0.013942929105868 \n -- < x^8 > = 0.009076370636747 \n -- < x^9 > = 0.006128509645342 \n -- < x^10 > = 0.004278147917961 \n -- < x^11 > = 0.003077410986590 \n -- < x^12 > = 0.002273768533280 \n -- < x^13 > = 0.001720304299285 \n -- < x^14 > = 0.001328990330385 \n- norm = 1.0000000003 \n- xbar (au) = -45.066809363 (error= -1.33426993898e-08 ) \n- S2_{n-1} (au) = 1.08376258908e-05 (error= -2.08419282206e-10 ) \n- <exp((x-xmin)/RT)> (au) = 5423305875.35 (error= 129930971.958 ) \n- <exp((x-xbar)/RT)> (au) = 2154.08083332 (error= 51.6367791881 ) \n- Free energy = -45.0595219689 (error= 2.30245307122e-05 ) \n- Free energy1 = -45.0595219689 (error= 2.30245307122e-05 ) \n- Hausdorff moment history file = moment_hist.dat \n- Hausdorff distribution plot file = hausdorff.dat \n- number data points = 1500\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-tutorial-9-free-energy-simulations","title":"NWPW Tutorial 9: Free Energy Simulations","text":"A description of using the WHAM method for generating free energy of the gas-phase dissociation reaction CHCl CH+Cl can be found in the attached pdf (nwchem-new-pmf.pdf)
"},{"location":"Plane-Wave-Density-Functional-Theory.html#paw-tutorial","title":"PAW Tutorial","text":""},{"location":"Plane-Wave-Density-Functional-Theory.html#optimizing-a-water-molecule","title":"Optimizing a water molecule","text":"The following input deck performs for a water molecule a PSPW energy calculation followed by a PAW energy calculation and a PAW geometry optimization calculation. The default unit cell parameters are used (SC=20.0, ngrid 32 32 32). In this simulation, the first PAW run optimizes the wavefunction and the second PAW run optimizes the wavefunction and geometry in tandem.
title \"paw steepest descent test\" \nstart paw_test \ncharge 0 \ngeometry units au nocenter noautoz noautosym \nO 0.00000 0.00000 0.01390 \nH -1.49490 0.00000 -1.18710 \nH 1.49490 0.00000 -1.18710 \nend \nnwpw \n time_step 15.8 \n ewald_rcut 1.50 \n tolerances 1.0d-8 1.0d-8 \nend \nset nwpw:lcao_iterations 1 \nset nwpw:minimizer 2 \ntask pspw energy \ntask paw energy \nnwpw \n time_step 5.8 \n geometry_optimize \n ewald_rcut 1.50 \n tolerances 1.0d-7 1.0d-7 1.0d-4 \nend\ntask paw steepest_descent \ntask paw optimize\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#optimizing-a-unit-cell-and-geometry-for-silicon-carbide","title":"Optimizing a unit cell and geometry for Silicon-Carbide","text":"The following example demonstrates how to uses the PAW module to optimize the unit cell and geometry for a silicon-carbide crystal.
title \"SiC 8 atom cubic cell - geometry and unit cell optimization\" \nstart SiC\n#**** Enter the geometry using fractional coordinates **** \ngeometry units au center noautosym noautoz print\n system crystal\n lat_a 8.277d0\n lat_b 8.277d0 \n lat_c 8.277d0 \n alpha 90.0d0 \n beta 90.0d0\n gamma 90.0d0\n end \nSi -0.50000d0 -0.50000d0 -0.50000d0\nSi 0.00000d0 0.00000d0 -0.50000d0 \nSi 0.00000d0 -0.50000d0 0.00000d0 \nSi -0.50000d0 0.00000d0 0.00000d0\nC -0.25000d0 -0.25000d0 -0.25000d0\nC 0.25000d0 0.25000d0 -0.25000d0 \nC 0.25000d0 -0.25000d0 0.25000d0\nC -0.25000d0 0.25000d0 0.25000d0 \nend \n#***** setup the nwpw gamma point code **** \nnwpw\n simulation_cell \n ngrid 16 16 16\n end\n ewald_ncut 8 \nend \nset nwpw:minimizer 2\nset nwpw:psi_nolattice .true. # turns of unit cell checking for wavefunctions \ndriver\n clear \n maxiter 40 \nend\nset includestress .true. # this option tells driver to optimize the unit cell\nset nwpw:stress_numerical .true. #currently only numerical stresses implemented in paw\ntask paw optimize\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#running-a-car-parrinello-simulation","title":"Running a Car-Parrinello Simulation","text":"In this section we show how use the PAW module to perform a Car-Parrinello molecular dynamic simulation for a C2 molecule at the LDA level. Before running a PAW Car-Parrinello simulation the system should be on the Born-Oppenheimer surface, i.e. the one-electron orbitals should be minimized with respect to the total energy (i.e. task pspw energy). The input needed is basically the same as for optimizing the geometry of a C2 molecule at the LDA level,except that and additional Car-Parrinello sub-block is added.
In the following example we show the input needed to run a Car-Parrinello simulation for a C2 molecule at the LDA level. In this example, default pseudopotentials from the pseudopotential library are used for C, the boundary condition is free-space, the exchange correlation functional is LDA, The boundary condition is free-space, and the simulation cell cell is aperiodic and cubic with a side length of 10.0 Angstroms and has 40 grid points in each direction (cutoff energy is 44 Ry). The time step and fake mass for the Car-Parrinello run are specified to be 5.0 au and 600.0 au, respectively.
start c2_paw_lda_md \ntitle \"C2 restricted singlet dimer, LDA/44Ry - constant energy Car-Parrinello simulation\"\ngeometry \n C -0.62 0.0 0.0 \n C 0.62 0.0 0.0 \nend\npspw \n simulation_cell units angstroms \n boundary_conditions aperiodic \n lattice \n lat_a 10.00d0 \n lat_b 10.00d0\n lat_c 10.00d0\n end \n ngrid 40 40 40\n end \n Car-Parrinello \n fake_mass 600.0\n time_step 5.0 \n loop 10 10 \n end \nend \nset nwpw:minimizer 2\ntask paw energy\ntask paw Car-Parrinello\n
"},{"location":"Plane-Wave-Density-Functional-Theory.html#nwpw-capabilities-and-limitations","title":"NWPW Capabilities and Limitations","text":" - Hybrid Functionals (e.g. PBE0, LDA-SIC) only work in PSPW.
- Wannier orbital task only works in PSPW.
- AIMD/MM simulation only works with PSPW.
"},{"location":"Plane-Wave-Density-Functional-Theory.html#questions-and-difficulties","title":"Questions and Difficulties","text":"Questions and encountered problems should be reported to the NWChem Community Forum or to Eric J. Bylaska, Eric.Bylaska@pnl.gov
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"},{"location":"Pmc2_1.html","title":"Pmc2 1","text":"group number = 26\n\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0Pmc2_1\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a04\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a03\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0 \n
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"},{"location":"Pnnm.html","title":"Pnnm","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a058\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pnnm\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,-z+1/2\n-x,-y,-z\n+x,+y,-z\n+x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Pnnn.html","title":"Pnnn","text":"group\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a048\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pnnn\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a01\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x,-y,+z\n-x,+y,-z\n+x,-y,-z\n-x+1/2,-y+1/2,-z+1/2\n+x+1/2,+y+1/2,-z+1/2\n+x+1/2,-y+1/2,+z+1/2\n-x+1/2,+y+1/2,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\ngroup\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a048\ngroup\u00a0name\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Pnnn\ncrystal\u00a0system\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a0Orthorhombic\nsetting\u00a0number\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\u00a02\nnumber\u00a0of\u00a0symmetry\u00a0operators\u00a0=\u00a08\n\n+x,+y,+z\n-x+1/2,-y+1/2,+z\n-x+1/2,+y,-z+1/2\n+x,-y+1/2,-z+1/2\n-x,-y,-z\n+x+1/2,+y+1/2,-z\n+x+1/2,-y,+z+1/2\n-x,+y+1/2,+z+1/2\n\n=\u00a0operator\u00a01\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a02\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.0\n\n=\u00a0operator\u00a03\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a04\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.5\n\n=\u00a0operator\u00a05\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a06\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a0-1.0\u00a00.0\n\n=\u00a0operator\u00a07\u00a0=\n\u00a01.0\u00a00.0\u00a00.0\u00a00.5\n\u00a00.0\u00a0-1.0\u00a00.0\u00a00.0\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5\n\n=\u00a0operator\u00a08\u00a0=\n\u00a0-1.0\u00a00.0\u00a00.0\u00a00.0\n\u00a00.0\u00a01.0\u00a00.0\u00a00.5\n\u00a00.0\u00a00.0\u00a01.0\u00a00.5 \n
"},{"location":"Potential-Energy-Surface-Analysis.html","title":"Potential Energy Surface Analysis","text":""},{"location":"Potential-Energy-Surface-Analysis.html#constraints-for-optimization","title":"Constraints for Optimization","text":""},{"location":"Potential-Energy-Surface-Analysis.html#geometry-optimization-minimization-transition-state-search","title":"Geometry Optimization (Minimization & Transition State Search)","text":""},{"location":"Potential-Energy-Surface-Analysis.html#hessians-vibrational-frequencies","title":"Hessians & Vibrational Frequencies","text":""},{"location":"Potential-Energy-Surface-Analysis.html#nudged-elastic-band-neb-and-zero-temperature-string-methods","title":"Nudged Elastic Band (NEB) and Zero Temperature String Methods","text":""},{"location":"Prepare.html","title":"Prepare","text":"The prepare module is used to set up the necessary files for a molecular dynamics simulation with NWChem. User supplied coordinates can be used to generate topology and restart files. The topology file contains all static information about a molecular system, such as lists of atoms, bonded interactions and force field parameters. The restart file contains all dynamic information about a molecular system, such as coordinates, velocities and properties.
Without any input, the prepare module checks the existence of a topology and restart file for the molecular systems. If these files exist, the module returns to the main task level without action. The module will generate these files when they do not exist. Without any input to the module, the generated system will be for a non-solvated isolated solute system.
To update existing files, including solvation, the module requires input directives read from an input deck,
prepare\n ...\nend\n
The prepare module performs three sub-tasks:
- sequence generation : This sub-task analyzes the supplied coordinates from a PDB-formatted file or from the input geometry, and generates a sequence file, containing the description of the system in terms of basic building blocks found as fragment or segment files in the database directories for the force field used. If these files do not exist, they are generated based on the supplied coordinates. This process constists of generating a fragment file with the list of atoms with their force field dependent atom types, partial atomic charges calculated from a Hartree Fock calculation for the fragment, followed by a restrained electrostatic potential fit, and a connectivity list. From the information on this fragment file the lists of all bonded interactions are generated, and the complete lists are written to a segment file.
- topology generation : Based on the generated or user-supplied sequence file and the force field specific segment database files, this sub-task compiles the lists of atoms, bonded interactions, excluded pairs, and substitutes the force field parameters. Special commands may be given to specify interaction parameters that will be changing in a free energy evaluation.
- restart generation : Using the user supplied coordinates and the topology file for the chemical system, this sub-task generates a restart file for the system with coordinates, velocities and other dynamic information. This step may include solvation of the chemical system and specifying periodic boundary conditions.
Files involved in the preparation phase exist in the following hierarchy:
- standards : The standard database files contain the original force field information. These files are to reside in a directory that is specified in the file $HOME/.nwchemrc. There will be such a directory for each supported force field. These directories contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par).
- extensions : These database files contain generally accepted extensions to the original force field and are to reside in a separate directory that is specified in the file $HOME/.nwchemrc. There will be such a directory for each supported force field. These directories contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par).
- contributed : These database files contain contributed definitions, also required for the quality assurance tests and are to reside in a separate directory that is specified in the file $HOME/.nwchemrc. There will be such a directory for each supported force field. These directories contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par).
- user preferences : These database files contain user preferred extensions to the original force field and are to reside in a separate directory that is specified in the file $HOME/.nwchemrc. Separate directories of this type should be defined for each supported force field. This directory may contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par).
- temporary files : Temporary database files contain user preferred extensions to the original force field and are to reside in a separate directory that is specified in the file $HOME/.nwchemrc. There may be such a directory for each supported force field. This directory may contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par).
- current files : Database files that contain user preferred extensions to the original force field and are to reside in a separate directory that is specified in the file $HOME/.nwchemrc. Typically this will be the current working directory, although it may be defined as a specific directory. This directory may contain fragment files (with extension frg), segment files (with extension sgm) and a parameter file (with the name of the force field and with extension par). If not specified, files will be taken from the current directory.
Data is taken from the database files searched in the above order. If data is specified more than once, the last found values are used. For example, if some standard segment is redefined in a temporary file, the latter one will be used. This allows the user to redefine standards or extensions without having to modify those database files, which may reside in a generally available, non-modifyable directory. If a filename is specified rather than a directory, the filename indicates the parameter file definition. All other files (frg and sgm files) will be take from the specified directory.
The most common problems with the prepare module are
- The format of the pdb file does not conform to the pdb standard. In particular, atom names need to correspond with definitions in the fragment and segment database files, and should adhere to IUPAC recommendations as adopted by the pdb standard. If this problem occurs, the pdb file will need to be corrected.
- Non-standard segments may contain atoms that could not be atom typed with the existing typing rules in the force field parameter files. When this happens, additional typing rules can be included in the parameter file, or the fragment file may be manually typed.
- Parameters for atom types or bonded interactions do not exist in the force field. When this happens, additional parameters may be defined in the parameter files, or the segment file may be edited to include explicit parameters.
"},{"location":"Prepare.html#default-database-directories","title":"Default database directories","text":"The file $HOME/.nwchemrc may contain the following entries that determine which files are used by the prepare module.
ffield <string ffname>\n
This entry specifies the default force field. Database files supplied with NWChem currently support values for ffname of amber, referring to AMBER95, and charmm, referring to the academic CHARMM22 force field.
<string ffname>_(1-9) <string ffdir>[{<string parfile>}]\n
Entries of this type specify the directory ffdir in which force field database files can be found. Optionally the parameterfile in this directory may be specified as parfile. The prepare module will only use files in directories specified here. One exception is that files in the current work directory will be used if no directory with current files is specified. The directories are read in the order 1-9 with duplicate parameters taken from the last occurrence found. Note that multiple parameter files may be specified that will be read in the order in which they are specified.
<string solvnam> <string solvfil>\n
This entry may be used to identify a pure solvent restart file solvfil by a name solvnam
An example file $HOME/.nwchemrc is:
ffield amber\n\namber_1 /soft/nwchem/share/amber/amber_s/amber99.par,spce.par\n\namber_2 /soft/nwchem/share/amber/amber_x/\n\namber_3 /usr/people/username/data/amber/amber_u/\n\nspce /soft/nwchem/share/solvents/spce.rst\n\ncharmm_1 /soft/nwchem/share/charmm/charmm_s/\n\ncharmm_2 /soft/nwchem/share/charmm/charmm_x/\n
"},{"location":"Prepare.html#system-name-and-coordinate-source","title":"System name and coordinate source","text":"system <string sys_calc>\n
The system name can be explicitly specified for the prepare module. If not specified, the system name will be taken from a specification in a previous md input block, or derived from the run time database name.
source ( pdb | rtdb )\n
The source of the coordinates can be explicitly specified to be from a PDB formatted file sys.pdb, or from a geometry object in the run time database. If not specified, a pdb file will be used when it exists in the current directory or the rtdb geometry otherwise.
model <integer modpdb default 0>\n
If a PDB formatted source file contains different MODELs, the model keyword can be used to specify which MODEL will be used to generate the topology and restart file. If not specified, the first MODEL found on the PDB file will be read.
altloc <character locpdb default ' '>\n
The altloc keyword may be used to specify the use of alternate location coordinates on a PDB file.
chain <character chnpdb default ' '>\n
The chain keyword may be used to specify the chain identifier for coordinates on a PDB file.
histidine ( hid | hie | hip )\n
specifies the default protonation state of histidine.
sscyx\n
Keyword sscyx may be used to rename cysteine residues that form sulphur bridges to CYX.
hbuild\n
Keyword hbuild may be used to add hydrogen atoms to the unknown segments of the structure found on the pdb file. Placement of hydrogen atoms is based on geometric criteria, and the resulting fragment and segment files should be carefully examined for correctness.
The database directories are used as specified in the file .nwchemrc. Specific definitions for the force field used may be changed in the input file using
directory_(1-9) <string ffdir> [<string parfile>]\n
"},{"location":"Prepare.html#sequence-file-generation","title":"Sequence file generation","text":"If no existing sequence file is present in the current directory, or if the new_seq keyword was specified in the prepare input deck, a new sequence file is generated from information from the pdb file, and the following input directives.
maxscf <integer maxscf default 20>\n
Variable maxscf specifies the maximum number of atoms in a segment for which partial atomic charges will be determined from an SCF calculation followed by RESP charge fitting. For larger segments a crude partial charge guestimation will be done.
qscale <real qscale default 1.0>\n
Variable qscale specifies the factor with which SCF/RESP determined charges will be multiplied.
modify sequence { <integer sgmnum>:<string sgmnam> }\n
This command specifies that segment sgmnam should be used for segment with number sgmnum. This command can be used to specify a particular protonation state. For example, the following command specifies that residue 114 is a hystidine protonated at the N\u03b5 site and residue 202 is a hystidine protonated at the N\u03b4 site:
modify sequence 114:HIE 202:HID\n
Links between atoms can be enforced with
link <string atomname> <string atomname>\n
For example, to link atom SG in segment 20 with atom FE in segment 55, use:
link 20:_SG 55:FE\n
The format of the sequence file is given in this table. In addition to the list of segments this file also includes links between non-standard segments or other non-standard links. These links are generated based on distances found between atoms on the pdb file. When atoms are involved in such non-standard links that have not been identified in the fragment of segment files as a non-chain link atom, the prepare module will ignore these links and report them as skipped. If one or more of these links are required, the user has to include them with explicit link directives in the sequence file, making them forced links. Alternatively, these links can be made forced-links by changing link into LINK in the sequence file.
fraction { <integer imol> }\n
Directive fraction can be used to separate solute molecules into fractions for which energies will be separately reported during molecular dynamics simulations. The listed molecules will be the last molecule in a fraction. Up to 10 molecules may be specified in this directive.
counter <integer num> <string ion>\n
Directive counter adds num counter ions of type ion to the sequence file. Up to 10 counter directives may appear in the input block.
counter <real factor>\n
This directive scales the counter ion charge by the specified factor in the determination of counter ions positions.
"},{"location":"Prepare.html#topology-file-generation","title":"Topology file generation","text":"new_top [ new_seq ]\n
Keyword new_top is used to force the generation of a new topology file. An existing topology file for the system in the current directory will be overwritten. If keyword new_seq is also specified, an existing sequence file will also be overwritten with a newly generated file.
amber | charmm\n
The prepare module generates force field specific fragment, segment and topology files. The force field may be explicitly specified in the prepare input block by specifying its name. Currently AMBER and CHARMM are the supported force fields. A default force field may be specified in the file $HOME/.nwchemrc.
standard <string dir_s>[<string par_s>]\nextensions <string dir_x>[<string par_x>]\ncontributed <string dir_q>[<string par_q>]\nuser <string dir_u>[<string par_u>]\ntemporary <string dir_t>[<string par_t>]\ncurrent <string dir_c>[<string par_c>]\n
The user can explicitly specify the directories where force field specific databases can be found. These include force field standards, extensions, quality assurance tests, user preferences, temporary , and current database files. Defaults for the directories where database files reside may be specified in the file $HOME/.nwchemrc for each of the supported force fields. Fragment, segment and sequence files generated by the prepare module are written in the temporary directory. When not specified, the current directory will be used. Topology and restart files are always created in the current directory.
The following directives control the modifications of a topology file. These directives are executed in the order in which they appear in the prepare input deck. The topology modifying commands are not stored on the run-time database and are, therefor, not persistent.
modify atom <string atomname> [set <integer mset> | initial | final] \\\n ( type <string atomtyp> | charge <real atomcharge> | \\\n polar <real atompolar> | dummy | self | quantum | quantum_high )\n
These modify commands change the atom type, partial atomic charge, atomic polarizability, specify a dummy, self-interaction and quantum atom, respectively. If mset is specified, the modification will only apply to the specified set, which has to be 1, 2 or 3. If not specified, the modification will be applied to all three sets. The quantum region in QM/MM simulations is defined by specifying atoms with the quantum or quantum_high label. For atoms defined quantum_high basis sets labeled X_H will be used. The atomnam should be specified as :, where isgm is the segment number, and name is the atom name. A leading blank in an atom name should be substituted with an underscore. The modify commands may be combined. For example, the following directive changes for the specified atom the charge and atom type in set 2 and specifies the atom to be a dummy in set 3.
modify atom 12:_C1 set 2 charge 0.12 type CA set 3 dummy\n
With the following directives modifications can be made for entire segments.
modify segment <integer isgm> \\\n [protonation <integer iprot> | set <integer mset> | initial | final] \\\n ( dummy | self | uncharged | quantum | quantum_high )\n
where protonation specifies a modification of the default protonation state of the segment as specified in the segment file. This option only applies to Q-HOP simulations.
Modifications to bonded interaction parameters can be made with the following modify commands.
modify ( bond <string atomtyp> <string atomtyp> | \\\n angle <string atomtyp> <string atomtyp> <string atomtyp> | \\ \n torsion <string atomtyp> <string atomtyp> <string atomtyp> \\\n <string atomtyp> [ multiplicity <integer multip> ] | \\\n plane <string atomtyp> <string atomtyp> <string atomtyp> \\\n <string atomtyp> ) [set <integer mset>` | initial | final] \\\n <real value> <real forcon>\n
where atomtyp and mset are defined as above, multip is the torsion ultiplicity for which the modification is to be applied, value is the reference bond, angle, torsion angle of out-of-plane angle value respectively, and forcon is the force constant for bond, angle, torsion angle of out-of-plane angle. When multip or mset are not defined the modification will be applied to all multiplicities and sets, respectively, for the identified bonded interaction.
After modifying atoms to quantum atoms the bonded interactions in which only quantum atoms are involved are removed from the bonded lists using
update lists\n
Error messages resulting from parameters not being defined for bonded interaction in which only quantum atoms are involved are ignored using
ignore\n
To specify that a free energy calculation will be carried out using the topology file, the following keyword needs to be specified,
free\n
To specify that a Q-HOP simulation will be carried out using the topology file, the following keyword needs to be specified,
qhop\n
To specify that only the first set of parameters should be used, even if multiple sets have been defined in the fragment or segment files, the following keyword needs to be specified,
first\n
Note that keywords free, qhop and qhop are mutually exclusive.
"},{"location":"Prepare.html#appending-to-an-existing-topology-file","title":"Appending to an existing topology file","text":"noe <string atom1> <string atom3> \\\n\n <real dist1> <real dist2> <real dist3> <real forc1> <real forc2>\n
This directive specifies a distance restraint potential between atoms atom1 and atom2, with a harmonic function with force constant forc1 between dist1 and dist2, and a harmonic function with force constant forc2 between dist2 and dist3. For distances shorter than dist1 or larger than dist3, a constant force is applied such that force and energy are continuous at dist1 and dist3, respectively. Distances are given in nm, force constants in .
select <integer isel> { <string atoms> }\n
Directive select specifies a group of atoms used in the definition of potential of mean force potentials.
The selected atoms are specified by the string atoms which takes the form
[{isgm [ - jsgm ] [,]} [:] [{aname[,]}]\n
For example, all carbon and oxygen atoms in segments 3 and 6 through 12 are selected for group 1 by
3,6-12:_C????,_O????\npmf [all] [bias] zalign <integer isel> <real forcon1> <real forcon2>\npmf [combine] [bias] xyplane <integer isel> <real forcon1> <real forcon2>\npmf [constraint] [bias] (distance | zdistance) <integer isel> <integer jsel> \\\n <real dist1> <real dist2> <real forcon1> <real forcon2>\npmf [bias] angle <integer isel> <integer jsel> <integer ksel> \\\n <real angle1> <real angle2> <real forcon1> <real forcon2>\npmf [bias] torsion <integer isel> <integer jsel> <integer ksel> <integer lsel> \\\n <real angle1> <real angle2> <real forcon1> <real forcon2>\npmf [bias] basepair <integer isel> <integer jsel> \\\n <real dist1> <real dist2> <real forcon1> <real forcon2>\npmf [bias] (zaxis | zaxis-cog) <integer isel> <integer jsel> <integer ksel> \\\n <real dist1> <real dist2> <real forcon1> <real forcon2>\n
Directive pmf specifies a potential of mean force potential in terms of the specified atom selection. Option zalign specifies the atoms in the selection to be restrained to a line parallel to the z-axis. Option xyplane specifies the atoms in the selection to be restrained to a plane perpendicular to the z-axis. Options distance, angle and torsion, are defined in terms of the center of geometry of the specified atom selections. Keyword basepair is used to specify a harmonic potential between residues isel and jsel. Keywords zaxis and zaxis-cog can be used to pull atoms toward the z-axis. Option all may be specified to apply an equivalent pmf to each of the equivalent solute molecules in the system. Option combine may be specified to apply the specified pmf to the atoms in all of the equivalent solute molecules. Option constraint may be specified to a distance pmf to treat the distance as a constraint. Option bias may be specified to indicate that this function should be treated as a biasing potential. Appropriate corrections to free energy results will be evaluated.
"},{"location":"Prepare.html#generating-a-restart-file","title":"Generating a restart file","text":"new_rst\n
Keyword new_rst will cause an existing restart file to be overwritten with a new file.
The follwing directives control the manipulation of restart files, and are executed in the order in which they appear in the prepare input deck.
solvent name <string*3 slvnam default 'HOH'> \\ \n model <string slvmdl default 'spce'> \n
The solvent keyword can be used to specify the three letter solvent name as expected on the PDB formatted file, and the name of the solvent model for which solvent coordinates will be used.
solvate [ < real rshell default 1.2 > ] \\\n ( [ cube [ <real edge> ]] | \\\n [ box [ <real xedge> [ <real xedge> [ <real xedge> ]]]] | \\\n [ sphere <real radius> ] |\n [ troct <real edge> ])\n
Solvation can be specified to be in a cubic box with specified edge, rectangular box with specified edges, or in a sphere with specified radius. Solvation in a cube or rectangular box will automatically also set periodic boundary conditions. Solvation in a sphere will only allow simulations without periodic boundary conditions. The size of the cubic and rectangular boxes will be expanded by a length specified by the expand variable. If no shape is specified, solvation will be done for a cubic box with an edge that leaves rshell nm between any solute atom and a periodic image of any solute atom after the solute has been centered. An explicit write is not needed to write the restart file. The solvate will write out a file sys_calc.rst. If not specified, the dimension of the solvation cell will be as large as to have at least a distance of rshell nm between any solute atom and the edge of the cell. The experimental troct directive generates a truncated octrahedral box.
touch <real touch default 0.23>\n
The variable touch specifies the minimum distance between a solvent and solute atom for which a solvent molecule will be accepted for solvation.
envelope `<real xpndw default 0.0>\n
sets the expand vealues to be used in solvate operations.
expand <real xpndw default 0.1>\n
The variable xpndw specifies the size in nm with which the simulation volume will be increased after solvation.
read [rst | rst_old | pdb] <string filename>\nwrite [rst | [solute [<integer nsolvent>]] ( [large] pdb | xyz)] <string filename>\n
These directives read and write the file filename in the specified format. The solute option instructs to write out the coordinates for solute and all, or if specified the first nsolvent, crystal solvent molecules only. If no format is specified, it will be derived from the extension of the filename. Recognized extensions are rst, rst_old (read only), pdb, xyz (write only) and pov (write only). Reading and then writing the same restart file will cause the sub-block size information to be lost. If this information needs to be retained a shell copy command needs to be used. The large keyword allows PDB files to be written with more than 9999 residues. Since the PDB file will not conform to the PDB convention, this option should only be used if required. NWChem will be able to read the resulting PDB file, but other codes may not.
scale <real scale default -1.0>\n
This directive scales the volume and coordinates written to povray files. A negative value of scale (default) scales the coordinates to lie in [-1:1].
cpk [<real cpk default 1.0>]\n
This directive causes povray files to contain cpk model output. The optional value is used to scale the atomic radii. A neagtive value of cpk resets the rendering to stick.
center | centerx | centery | centerz\n
These directives center the solute center of geometry at the origin, in the y-z plane, in the x-z plane or in the x-y plane, respectively.
orient\n
This directive orients the solute principal axes.
translate [atom | segment | molecule] \\\n <integer itran> <integer itran> <real xtran(3)>\n
This directive translates solute atoms in the indicated range by xtran, without checking for bad contacts in the resulting structure.
rotate [atom | segment | molecule] \\\n\n <integer itran> <integer itran> <real angle> <real xrot(3)>\n
This directive rotates solute atoms in the indicated range by angle around the vector given by xrot,, without checking for bad contacts in the resulting structure.
remove solvent [inside | outside] [x <real xmin> <real xmax>] \\\n[y <real ymin> <real ymax>] [z <real zmin> <real zmax>]\n
This directive removes solvent molecules inside or outside the specified coordinate range.
periodic\n
This directive enables periodic boundary conditions.
vacuo\n
This directive disables periodic boundary conditions.
grid <integer mgrid default 24> <real rgrid default 0.2>\n
This directive specifies the grid size of trial counter-ion positions and minimum distance between an atom in the system and a counter-ion.
crop\n
prints minimum and maximum solute coordinates.
boxsize\n
specifies to redetermine the box size.
cube\n
specifies to redetermine the smallest cubic box size.
box <real xsize> <real ysize>` <real zsize>\n
The box directive resets the box size.
align <string atomi> <string atomj> <string atomk>\n
The align directive orients the system such that atomi and atomj are on the z-axis, and atomk in the x=y plane.
repeat [randomx | randomy | randomz] [chains | molecules | fractions ] \\\n <integer nx> <integer ny> <integer nz> [<real dist>] [<real zdist>]\n
The repeat directive causes a subsequent write pdb directive to write out multiple copies of the system, with nx copies in the x, ny copies in the y, and nz copies in the z-direction, with a minimum distance of dist between any pair of atoms from different copies. If nz is -2, an inverted copy is placed in the z direction, with a separation of zdist nm. If dist is negative, the box dimensions will be used. For systems with solvent, this directive should be used with a negative dist. Optional keywords chains, molecules and fractions specify to write each repeating solute unit as a chain, to repeat each solute molecule, or each solute fraction separately. Optional keywords randomx, randomy, and randomz can be used to apply random rotations for each repeat unit around a vector through the center of geometry of the solute in the x, y or z direction.
skip <integer ix> <integer iy> <integer iz>\n
The skip directive can be used to skip single repeat unit from the repeat directive. Up to 100 skip directives may be specified, and will only apply to the previously specified repeat directive.
(collapsexy | collapsez) [ <integer nmoves>]\n
specifies to move all solute molecules toward the z-axis or x=y-plane, respectively, to within a distance of touch nm between any pair of atoms from different solute molecules. Parameter nmoves specifies the number of collapse moves that will be made. Monatomic ions will move with the nearest multi-atom molecule.
collapse_group <integer imol> <integer jmol>\n
specifies that molecule jmol will move together with molecule imol in collapse operations.
merge <real xtran(3)> <string pdbfile>\n
specifies to merge the coordinates found on the specified pdb file into the current structure after translation by xtran(3).
"},{"location":"Print_Noprint.html","title":"Print Noprint","text":"The PRINT and NOPRINT directives allow the user to control how much output NWChem generates. These two directives are special in that the compound directives for all modules are supposed to recognize them. Each module can control both the overall print level (general verbosity) and the printing of individual items which are identified by name (see below). The standard form of the PRINT directive is as follows:
PRINT [(none || low || medium || high || debug) default medium] [<string list_of_names ... >]\nNOPRINT <string list_of_names ... >\n
The default print level is medium.
Every output that is printed by NWChem has a print threshold associated with it. If this threshold is equal to or lower than the print level requested by the user, then the output is generated. For example, the threshold for printing the SCF energy at convergence is low. This means that if the user-specified print level on the PRINT directive is low, medium, high, or debug, then the SCF energy will be printed at convergence.
The overall print level specified using the PRINT directive is a convenient tool for controlling the verbosity of NWChem. Setting the print level to high might be helpful in diagnosing convergence problems. The print level of debug might also be of use in evaluating problem cases, but the user should be aware that this can generate a huge amount of output. Setting the print level to low might be the preferable choice for geometry optimizations that will perform many steps which are in themselves of little interest to the user.
In addition, it is possible to enable the printing of specific items by naming them in the PRINT directive in the . Items identified in this way will be printed, regardless of the overall print level specified. Similarly, the NOPRINT directive can be used to suppress the printing of specific items by naming them in its . These items will not be printed, regardless of the overall print level, or the specific print level of the individual items.
The list of items that can be printed for each module is documented as part of the input instructions for that module. The items recognized by the top level of the code, and their thresholds, are:
Name Print Level Description \u201ctotal time\u201d medium Print cpu and wall time at job end \u201ctask time\u201d high Print cpu and wall time for each task \u201crtdb\u201d high Print names of RTDB entries \u201crtdbvalues\u201d high Print name and values of RTDB entries \u201cga summary\u201d medium Summarize GA allocations at job end \u201cga stats\u201d high Print GA usage statistics at job end \u201cma summary\u201d medium Summarize MA allocations at job end \u201cma stats\u201d high Print MA usage statistics at job end \u201cversion\u201d debug Print version number of all compiled routines \u201ctcgmsg\u201d never Print TCGMSG debug information"},{"location":"Print_Noprint.html#top-level-print-control-specifications","title":"Top Level Print Control Specifications","text":"The following example shows how a PRINT directive for the top level process can be used to limit printout to only essential information. The directive is
print none \"ma stats\" rtdb\n
This directive instructs the NWChem main program to print nothing, except for the memory usage statistics (ma stats) and the names of all items stored in the database at the end of the job.
The print level within a module is inherited from the calling layer. For instance, by specifying the print to be low within the MP2 module will cause the SCF, CPHF and gradient modules when invoked from the MP2 to default to low print. Explicit user input of print thresholds overrides the inherited value.
"},{"location":"Properties.html","title":"Properties","text":""},{"location":"Properties.html#overview","title":"Overview","text":"Properties can be calculated for both the Hartree-Fock and DFT wave functions. The properties that are available are:
- Natural bond analysis
- Dipole, quadrupole, and octupole moment
- Mulliken population analysis and bond order analysis
- Electrostatic potential (diamagnetic shielding) at nuclei
- Electric field and field gradient at nuclei
- Electric field gradients with relativistic effects
- Electron and spin density at nuclei
- NMR shielding (GIAO method)
- NMR hyperfine coupling (Fermi-Contact and Spin-Dipole expectation values)
- NMR indirect spin-spin coupling
- Gshift
- Response to electric and magnetic fields (static and dynamic)
- Raman
The properties module is started when the task directive TASK property is defined in the user input file. The input format has the form:
PROPERTY \n [property keyword] \n [CENTER ((com || coc || origin || arb <real x y z>) default coc)] \n END\n
Most of the properties can be computed for Hartree-Fock (closed-shell RHF, open-shell ROHF, and open-shell UHF), and DFT (closed-shell and open-shell spin unrestricted) wavefunctions. The NMR hyperfine and indirect spin-spin coupling require a UHF or ODFT wave function.
"},{"location":"Properties.html#vectors-keyword","title":"Vectors keyword","text":" VECTORS [ (<string input_movecs >)]\n
The VECTORS directive allows the user to specify the input molecular orbital vectors for the property calculation
"},{"location":"Properties.html#property-keywords","title":"Property keywords","text":"Each property can be requested by defining one of the following keywords:
NBOFILE \n DIPOLE \n QUADRUPOLE \n OCTUPOLE \n MULLIKEN \n ESP \n EFIELD \n EFIELDGRAD \n EFIELDGRADZ4 \n GSHIFT \n ELECTRONDENSITY \n HYPERFINE [<integer> number_of_atoms <integer> atom_list] \n SHIELDING [<integer> number_of_atoms <integer> atom_list] \n SPINSPIN [<integer> number_of_pairs <integer> pair_list] \n RESPONSE [<integer> response_order <real> frequency] \n AIMFILE \n MOLDENFILE \n ALL\n
The ALL keyword generates all currently available properties.
"},{"location":"Properties.html#nmr-and-epr","title":"NMR and EPR","text":"Both the NMR shielding and spin-spin coupling have additional optional parameters that can be defined in the input. For the shielding the user can define the number of atoms for which the shielding tensor should be calculated, followed by the list of specific atom centers. In the case of spin-spin coupling the number of atom pairs, followed by the atom pairs, can be defined (i.e., spinspin 1 1 2 will calculate the coupling for one pair, and the coupling will be between atoms 1 and 2).
For both the NMR spin-spin and hyperfine coupling the isotope that has the highest abundance and has spin, will be chosen for each atom under consideration.
"},{"location":"Properties.html#calculating-epr-and-paramagnetic-nmr-parameters","title":"Calculating EPR and paramagnetic NMR parameters","text":"The following tutorial illustrates how to combine the hyperfine, gshift and shielding to calculate the EPR and paramagnetic NMR parameters of an open-shell system. All calculations are compatible with the ZORA model potential approach.
For theoretical and computational details, please refer to references123.
"},{"location":"Properties.html#nmr-input-example","title":"NMR: Input Example","text":"geometry nocenter\n C 0.00000000 0.00000000 0.00000000\n O 1.18337200 0.00000000 0.00000000\n H -.63151821 0.94387462 0.00000000\nend\n\nbasis\n \"*\" library 6-311G**\nend\nproperty\n efieldgradz4 1 3\n shielding 2 1 2\n hyperfine 2 1 3\n gshift\nend\n\nrelativistic\n zora on\n zora:cutoff_NMR 1d-8\n zora:cutoff 1d-30\nend\n\ndft\nmult 2\nxc becke88 perdew86\nend\n\ntask dft property\n
"},{"location":"Properties.html#center-center-of-expansion-for-multipole-calculations","title":"CENTER: Center of expansion for multipole calculations","text":"The user also has the option to choose the center of expansion for the dipole, quadrupole, and octupole calculations.
[CENTER ((com || coc || origin || arb <real x y z>) default coc)]\n
com is the center of mass, coc is the center of charge, origin is (0.0, 0.0, 0.0) and arb is any arbitrary point which must be accompanied by the coordinated to be used. Currently the x, y, and z coordinates must be given in the same units as UNITS in GEOMETRY.
"},{"location":"Properties.html#response-calculations","title":"Response Calculations","text":"Response calculations can be calculated as follows:
property\n response 1 7.73178E-2 # response order and frequency in Hartree energy units \n velocity # use modified velocity gauge for electric dipole \n orbeta # calculate optical rotation 'beta' directly [^4] \n giao # GIAO optical rotation [^5][^6][^7], forces orbeta \n bdtensor # calculates B-tilde of Refs. [^5][^7] \n analysis # analyze response in terms of MOs [^7] \n damping 0.007 # complex response functions with damping, Ref [^8] \n convergence 1e-4 # set CPKS convergence criterion (default 1e-4) \nend\n
Response calculations are currently supported only for
- order 1 (linear response),
- single frequency,
- electric field,
- mixed electric-magnetic field perturbations.
The output consists of the electric polarizability and optical rotation tensors (alpha, beta for optical rotation) in atomic units. The response keyword requires two arguments: response order and frequency in Hartree energy units (the aoresponse keyword can be used with same effect as the response keyword). If the velocity or giao keywords are absent, the dipole-length form will be used for the dipole integrals. This is a bit faster. The isotropic optical rotation is origin independent when using the velocity gauge (by means of velocity keyword) or with GIAOs 5 (by means of the giao keyword). With the keyword bdtensor, a fully origin-invariant optical rotation tensor is calculated 57. Note that velocity and orbeta are incompatible. The input line
set prop:newaoresp 0\n
outside of the properties block forces the use of an older version of the response code, which has fewer features (in particular, no working GIAO optical rotation) but which has been tested more thoroughly. In the default newer version you may encounter undocumented features (bugs). The keyword analysis triggers an analysis of the response tensors in terms of molecular orbitals. If the property input block also contains the keyword pmlocalization, then the analysis is performed in terms of Pipek-Mezey localized MOs, otherwise the canonical set is used (this feature may currently not work, please check the sum of the analysis carefully). See Ref. [6] for an example. Works with HF and density functionals for which linear response kernels are implemented in NWChem.
Please refer to papers546987 for further details:
"},{"location":"Properties.html#raman","title":"Raman","text":"Raman calculations can be performed by specifying the Raman block. These calculations are performed in conjunction with polarizability calculations. Detailed description of input parameters at https://pubs.acs.org/doi/10.1021/jp411039m#notes-1
RAMAN \n [ (NORMAL | | RESONANCE) default NORMAL ] \n [ (LORENTZIAN | | GAUSSIAN) default LORENTZIAN ] \n [ LOW <double low default 0.0> ] \n [ HIGH <double high default highest normal mode> ] \n [ FIRST <integer first default 7> ] \n [ LAST < integer last default number of normal modes > ] \n [ WIDTH <double width default 20.0> ] \n [ DQ <double dq default 0.01> ] \nEND \ntask dft raman\n
or
task dft raman numerical\n
Sample input block:
property\n response 1 8.8559E-2 \n damping 0.007 \nend \nraman \n normal \n lorentzian \nend\n
"},{"location":"Properties.html#raman-keywords","title":"Raman Keywords","text":" NORMAL and RESONANCE: Type of Raman plot to make.LORENTZIAN and GAUSSIAN: Generation of smoothed spectra (rather than sticks) using either a Lorentzian function or a Gaussian function. The default is LORENTZIAN.LOW and HIGH: The default range in which to generate the Raman spectrum plot is (0.0, highest wavenumber normal mode) cm-1. The LOW and HIGH keywords modify the frequency range.FIRST and LAST: The default range of indices of normal modes used in the plot is (7, number of normal modes). The FIRST and LAST keywords modify the range of indices.WIDTH: Controls the width in the smoothed peaks, using Lorentzians or Gaussians, in the plot. The default value for WIDTH is 20.0.DQ: Size of the steps along the normal modes. The default value for DQ is 0.01. It is related to the step size dR used in numerical evaluation of polarizability derivative
"},{"location":"Properties.html#raman-output","title":"Raman Output","text":"Raman spectrum in stick format and smoothed using Lorentzians or Gaussians stored in a filename with format [fname].normal. The number of points is 1000 by default. This value can be changed by adding the following SET directive to the input file
set raman:numpts <integer>\n
"},{"location":"Properties.html#raman-references","title":"Raman References","text":"Please refer to papers1011 for further details:
"},{"location":"Properties.html#polarizability-computed-with-the-sum-over-orbitals-method","title":"Polarizability computed with the Sum over Orbitals method","text":"As an alternative to the linear response method, the Sum over Orbitals (SOO) method is available to compute polarizabilities. Results of these method are much less accurate than linear response calculations, with values off by a factor of 2-4x. However, the qualitative nature of this results can be used to compute Raman frequencies when coupled with QMD, as described in references 1213.
Sample input computing polarizability both with the SOO method and the linear response method:
property\n polfromsos\nend\n\ntask dft property\n\nproperty\n response 1 0\nend\ntask dft property\n
"},{"location":"Properties.html#nbofile","title":"Nbofile","text":"The keyword NBOFILE does not execute the Natural Bond Analysis code, but simply creates an input file to be used as input to the stand-alone NBO code. All other properties are calculated upon request.
Following the successful completion of an electronic structure calculation, a Natural Bond Orbital (NBO) analysis may be carried out by providing the keyword NBOFILE in the PROPERTY directive. NWChem will query the rtdb and construct an ASCII file, file_prefix.gen, that may be used as input to the stand alone version of the NBO program, GenNBO. file_prefix is equal to string following the START directive. The input deck may be edited to provide additional options to the NBO calculation, (see the NBO user\u2019s manual for details.)
Users that have their own NBO version can compile and link the code into the NWChem software. See the INSTALL file in the source for details.
"},{"location":"Properties.html#gaussian-cube-files","title":"Gaussian Cube Files","text":"Electrostatic potential (keyword esp) and the magnitude of the electric field (keyword efield) on the grid can be generated in the form of the Gaussian Cube File. This behavior is triggered by the inclusion of grid keyword as shown below
grid [pad dx [dy dz]] [rmax x y z] [rmin x y z] [ngrid nx [ny nz]] [output filename]\n
where
-
pad dx [dy dz] - specifies amount of padding (in angstroms) in x,y, and z dimensions that will be applied in the automatic construction of the rectangular grid volume based on the geometry of the system. If only one number is provided then the same amount of padding will be applied in all dimensions. The default setting is 4 angstrom padding in all dimensions.
-
rmin x y z - specifies the coordinates (in angstroms) of the minimum corner of the rectangular grid volume. This will override any padding in this direction.
-
rmax x y z - specifies the coordinates (in angstroms) of the maximum corner of the rectangular grid volume. This will override any padding in this direction.
-
ngrid nx [ny nz] - specifies number of grid points along each dimension. If only one number is provided then the same number of grid points are assumed all dimensions. In the absence of this directive the number of grid points would be computed such that grid spacing will be close to 0.2 angstrom, but not exceeding 50 grid points in either dimension.
-
output filename - specifies name of the output cube file. The default behavior is to use prefix-elp.cube or prefix-elf.cube file names for electrostatic potential or electric field respectively. Here prefix denotes the system name as specified in start directive. Note that Gaussian cube files will be written in the run directory (where the input file resides).
Example input file
echo \n start nacl \n\n\n geometry nocenter noautoz noautosym \n Na -0.00000000 0.00000000 -0.70428494 \n Cl 0.00000000 -0.00000000 1.70428494 \n end \n\n\n basis \n * library 6-31g* \n end \n\n #electric field would be written out to nacl.elf.cube file \n #with \n #ngrid : 20 20 20 \n #rmax : 4.000 4.000 5.704 \n #rmin :-4.000 -4.000 -4.704 \n\n property \n efield \n grid pad 4.0 ngrid 20 \n end \n\n task dft property \n\n #electrostatic potential would be written to esp-pad.cube file \n # with the same parameters as above \n\n property \n esp \n grid pad 4.0 ngrid 20 output esp-pad.cube \n end \n\n task dft property \n\n #illustrating explicit specification of minumum box coordinates \n\n property \n esp \n grid pad 4.0 rmax 4.000 4.000 5.704 ngrid 20 \n end \n\n task dft property\n
"},{"location":"Properties.html#aimfile","title":"Aimfile","text":"This keyword generates AIM Wavefunction files. The resulting AIM wavefunction file (.wfn/.wfx) can be post-processed with a variety of codes, e.g.
- XAIM
- NCIPLOT
- Multiwfn
- Postg
WARNING: Since we have discovered issues in generating .WFN files with this module (e.g. systems with ECPs), the recommended method for generating .WFN file is to first generate a Molden file with the Moldenfile option, then convert the Molden file into a WFN file by using the Molden2AIM program.
"},{"location":"Properties.html#moldenfile","title":"Moldenfile","text":"MOLDENFILE\nMOLDEN_NORM (JANPA | | NWCHEM || NONE)\n
This keyword generates files using the Molden format. The resulting Molden file (.molden) should compatible with a variety of codes that can input Molden files, e.g.
- Molden
- JANPA (the nwchem2molden step is no longer required when using .molden files and the
MOLDEN_NORM JANPA keyword) - orbkit
- Molden2qmc
- Molden2AIM
- Multiwfn
the MOLDEN_NORM option allows the renormalization of the basis set coefficients. By default, the coefficient values from input are not modified. Using the JANPA value coefficients are normalized following JANPA\u2018s convention (where basis coefficients are normalized to unity), while the NWCHEM will produce coefficients normalized according to NWChem\u2019s convention. Using MOLDEN_NORM equal NONE will leave the input coefficients unmodified. It is strongly recommended to use spherical basis set when using the NWChem Molden output for JANPA analysis
Example input file for a scf calculation. The resulting Molden file will be named h2o.molden
start heat\n\n geometry; he 0. 0. 0.; end \n\n basis spherical; * library 6-31g ; end \n\n task scf \n\n property \n vectors heat.movecs \n moldenfile \n molden_norm janpa \n end\n\n task scf property\n
Then, the resulting h2o.molden file can be post processed by Janpa with the following command
java -jar janpa.jar h2o.molden > h2o.janpa.txt\n
"},{"location":"Properties.html#localization","title":"Localization","text":"Localized molecular orbitals can be computed with the localization keyword.
property localization (( pm || boys || ibo) default pm) end
The following methods are available:
- Pipek-Mezey14,
pm keyword (default) - Foster-Boys15,
boys keyword - IAO/IBO1617,
ibo keyword
"},{"location":"Properties.html#references","title":"References","text":" -
Autschbach, J.; Patchkovskii, S.; Pritchard, B. Calculation of Hyperfine Tensors and Paramagnetic NMR Shifts Using the Relativistic Zeroth-Order Regular Approximation and Density Functional Theory. Journal of Chemical Theory and Computation 2011, 7 (7), 2175\u20132188. https://doi.org/10.1021/ct200143w.\u00a0\u21a9
-
Aquino, F.; Pritchard, B.; Autschbach, J. Scalar Relativistic Computations and Localized Orbital Analyses of Nuclear Hyperfine Coupling and Paramagnetic NMR Chemical Shifts. Journal of Chemical Theory and Computation 2012, 8 (2), 598\u2013609. https://doi.org/10.1021/ct2008507.\u00a0\u21a9
-
Aquino, F.; Govind, N.; Autschbach, J. Scalar Relativistic Computations of Nuclear Magnetic Shielding and <i>g</i>-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals. Journal of Chemical Theory and Computation 2011, 7 (10), 3278\u20133292. https://doi.org/10.1021/ct200408j.\u00a0\u21a9
-
Autschbach. Computation of Optical Rotation Using Timedependent Density Functional Theory. Computing Letters 2007, 3 (2), 131\u2013150. https://doi.org/10.1163/157404007782913327.\u00a0\u21a9
-
Autschbach, J. Time-Dependent Density Functional Theory for Calculating Origin-Independent Optical Rotation and Rotatory Strength Tensors. ChemPhysChem 2011, 12 (17), 3224\u20133235. https://doi.org/10.1002/cphc.201100225.\u00a0\u21a9\u21a9\u21a9
-
Krykunov, M.; Autschbach, J. Calculation of Optical Rotation with Time-Periodic Magnetic-Field-Dependent Basis Functions in Approximate Time-Dependent Density-Functional Theory. The Journal of Chemical Physics 2005, 123 (11), 114103. https://doi.org/10.1063/1.2032428.\u00a0\u21a9
-
Moore, B.; Srebro, M.; Autschbach, J. Analysis of Optical Activity in Terms of Bonds and Lone-Pairs: The Exceptionally Large Optical Rotation of Norbornenone. Journal of Chemical Theory and Computation 2012, 8 (11), 4336\u20134346. https://doi.org/10.1021/ct300839y.\u00a0\u21a9\u21a9
-
Krykunov, M.; Kundrat, M. D.; Autschbach, J. Calculation of Circular Dichroism Spectra from Optical Rotatory Dispersion, and Vice Versa, as Complementary Tools for Theoretical Studies of Optical Activity Using Time-Dependent Density Functional Theory. The Journal of Chemical Physics 2006, 125 (19), 194110. https://doi.org/10.1063/1.2363372.\u00a0\u21a9
-
Hammond, J. R.; Govind, N.; Kowalski, K.; Autschbach, J.; Xantheas, S. S. Accurate Dipole Polarizabilities for Water Clusters n=212 at the Coupled-Cluster Level of Theory and Benchmarking of Various Density Functionals. The Journal of Chemical Physics 2009, 131 (21), 214103. https://doi.org/10.1063/1.3263604.\u00a0\u21a9
-
Mullin, J. M.; Autschbach, J.; Schatz, G. C. Time-Dependent Density Functional Methods for Surface Enhanced Raman Scattering (SERS) Studies. Computational and Theoretical Chemistry 2012, 987, 32\u201341. https://doi.org/10.1016/j.comptc.2011.08.027.\u00a0\u21a9
-
Aquino, F. W.; Schatz, G. C. Time-Dependent Density Functional Methods for Raman Spectra in Open-Shell Systems. The Journal of Physical Chemistry A 2014, 118 (2), 517\u2013525. https://doi.org/10.1021/jp411039m.\u00a0\u21a9
-
Fischer, S. A.; Ueltschi, T. W.; El-Khoury, P. Z.; Mifflin, A. L.; Hess, W. P.; Wang, H.-F.; Cramer, C. J.; Govind, N. Infrared and Raman Spectroscopy from Ab Initio Molecular Dynamics and Static Normal Mode Analysis: The C-H Region of DMSO as a Case Study. The Journal of Physical Chemistry B 2015, 120 (8), 1429\u20131436. https://doi.org/10.1021/acs.jpcb.5b03323.\u00a0\u21a9
-
Apr\u00e0, E.; Bhattarai, A.; Baxter, E.; Wang, S.; Johnson, G. E.; Govind, N.; El-Khoury, P. Z. Simplified Ab Initio Molecular Dynamics-Based Raman Spectral Simulations. Applied Spectroscopy 2020, 74 (11), 1350\u20131357. https://doi.org/10.1177/0003702820923392.\u00a0\u21a9
-
Pipek, J.; Mezey, P. G. A Fast Intrinsic Localization Procedure Applicable for Ab Initio and Semiempirical Linear Combination of Atomic Orbital Wave Functions. The Journal of Chemical Physics 1989, 90 (9), 4916\u20134926. https://doi.org/10.1063/1.456588.\u00a0\u21a9
-
Foster, J. M.; Boys, S. F. Canonical Configurational Interaction Procedure. Reviews of Modern Physics 1960, 32 (2), 300\u2013302. https://doi.org/10.1103/revmodphys.32.300.\u00a0\u21a9
-
Knizia, G. Intrinsic Atomic Orbitals: An Unbiased Bridge Between Quantum Theory and Chemical Concepts. Journal of Chemical Theory and Computation 2013, 9 (11), 4834\u20134843. https://doi.org/10.1021/ct400687b.\u00a0\u21a9
-
Knizia, G.; Klein, J. E. M. N. Electron Flow in Reaction Mechanisms-Revealed from First Principles. Angewandte Chemie International Edition 2015, 54 (18), 5518\u20135522. https://doi.org/10.1002/anie.201410637.\u00a0\u21a9
"},{"location":"Python.html","title":"Controlling NWChem with Python","text":""},{"location":"Python.html#overview","title":"Overview","text":"Python programs may be embedded into the NWChem input and used to control the execution of NWChem. Python is a very powerful and widely used scripting language that provides useful things such as variables, conditional branches and loops, and is also readily extended. Example applications include scanning potential energy surfaces, computing properties in a variety of basis sets, optimizing the energy w.r.t. parameters in the basis set, computing polarizabilities with finite field, and simple molecular dynamics.
Look in the NWChem contrib directory for useful scripts and examples. Visit the Python web-site https://www.python.org for a full manual and lots of useful code and resources.
"},{"location":"Python.html#how-to-input-and-run-a-python-program-inside-nwchem","title":"How to input and run a Python program inside NWChem","text":"A Python program is input into NWChem inside a Python compound directive.
python [print|noprint]\n ...\n end\n
The END directive must be flush against the left margin (see the Troubleshooting section for the reason why).
The program is by default printed to standard output when read, but this may be disabled with the noprint keyword. Python uses indentation to indicate scope (and the initial level of indentation must be zero), whereas NWChem uses optional indentation only to make the input more readable. For example, in Python, the contents of a loop, or conditionally-executed block of code must be indented further than the surrounding code. Also, Python attaches special meaning to several symbols also used by NWChem. For these reasons, the input inside a PYTHON compound directive is read verbatim except that if the first line of the Python program is indented, the same amount of indentation is removed from all subsequent lines. This is so that a program may be indented inside the PYTHON input block for improved readability of the NWChem input, while satisfying the constraint that when given to Python the first line has zero indentation.
E.g., the following two sets of input specify the same Python program.
python \n print (\"Hello\")\n print (\"Goodbye\")\nend\n\npython \nprint (\"Hello\")\nprint (\"Goodbye\")\nend\n
whereas this program is in error since the indentation of the second line is less than that of the first.
python \n print (\"Hello\")\nprint (\"Goodbye\")\nend\n
The Python program is not executed until the following directive is encountered
task python\n
which is to maintain consistency with the behavior of NWChem in general. The program is executed by all nodes. This enables the full functionality and speed of NWChem to be accessible from Python, but there are some gotchas
- Print statements and other output will be executed by all nodes so you will get a lot more output than probably desired unless the output is restricted to just one node (by convention node zero).
- The calls to NWChem functions are all collective (i.e., all nodes must execute them). If these calls are not made collectively your program may deadlock (i.e., cease to make progress).
- When writing to the database (
rtdb_put()) it is the data from node zero that is written. - NWChem overrides certain default signal handlers so care must be taken when creating processes (see Section describing a scanning example).
"},{"location":"Python.html#nwchem-extensions","title":"NWChem extensions","text":"Since we have little experience using Python, the NWChem-Python interface might change in a non-backwardly compatible fashion as we discover better ways of providing useful functionality. We would appreciate suggestions about useful things that can be added to the NWChem-Python interface. In principle, nearly any Fortran or C routine within NWChem can be extended to Python, but we are also interested in ideas that will enable users to build completely new things. For instance, how about being able to define your own energy functions that can be used with the existing optimizers or dynamics package?
Python has been extended with a module named \u201cnwchem\u201d which is automatically imported and contains the following NWChem-specific commands. They all handle NWChem-related errors by raising the exception \u201cNWChemError\u201d, which may be handled in the standard Python manner (see Section describing handling exception).
input_parse(string) \u2013 invokes the standard NWChem input parser with the data in string as input. Note that the usual behavior of NWChem will apply \u2013 the parser only reads input up to either end of input or until a TASK directive is encountered (the task directive is not executed by the parser).task_energy(theory) \u2013 returns the energy as if computed with the NWChem directive TASK ENERGY <THEORY>.task_gradient(theory) \u2013 returns a tuple (energy,gradient) as if computed with the NWChem directive TASK GRADIENT <THEORY>.task_optimize(theory) \u2013 returns a tuple (energy,gradient) as if computed with the NWChem directive TASK OPTIMIZE <THEORY>. The energy and gradient will be those at the last point in the optimization and consistent with the current geometry in the database.ga_nodeid() \u2013 returns the number of the parallel process.rtdb_print(print_values) \u2013 prints the contents of the RTDB. If print_values is 0, only the keys are printed, if it is 1 then the values are also printed.rtdb_put(name, values) or rtdb_put(name, values, type) \u2013 puts the values into the database with the given name. In the first form, the type is inferred from the first value, and in the second form the type is specified using the last argument as one of INT, DBL, LOGICAL, or CHAR.rtdb_get(name) \u2013 returns the data from the database associated with the given name.
An example below explains, in lieu of a Python wrapper for the geometry object, how to obtain the Cartesian molecular coordinates directly from the database.
"},{"location":"Python.html#examples","title":"Examples","text":"Several examples will provide the best explanation of how the extensions are used, and how Python might prove useful.
"},{"location":"Python.html#hello-world","title":"Hello world","text":"python\n print ('Hello world from process %i' % ga_nodeid())\nend\n\ntask python\n
This input prints the traditional greeting from each parallel process.
"},{"location":"Python.html#scanning-a-basis-exponent","title":"Scanning a basis exponent","text":"geometry units au\n O 0 0 0; H 0 1.430 -1.107; H 0 -1.430 -1.107\nend\n\npython\nexponent = 0.1\nwhile (exponent <= 2.01):\n input_parse(''' \n basis noprint \n H library 3-21g; O library 3-21g; O d; %f 1.0 \n end \n ''' % (exponent))\n print (' exponent = %5.4f,' % exponent, ', energy = %16.10f' % task_energy('scf'))\n exponent = exponent + 0.1\nend\n\nprint none\n\ntask python\n
This program augments a 3-21g basis for water with a d-function on oxygen and varies the exponent from 0.1 to 2.0 in steps of 0.1, printing the exponent and energy at each step.
The geometry is input as usual, but the basis set input is embedded inside a call to input_parse() in the Python program. The standard Python string substitution is used to put the current value of the exponent into the basis set (replacing the %f) before being parsed by NWChem. The energy is returned by task_energy('scf') and printed out. The print none in the NWChem input switches off all NWChem output so all you will see is the output from your Python program.
Note that execution in parallel may produce unwanted output since all process execute the print statement inside the Python program.
Look in the NWChem contrib directory for a routine that makes the above task easier.
"},{"location":"Python.html#scanning-a-basis-exponent-revisited","title":"Scanning a basis exponent revisited","text":"geometry units au\nO 0 0 0; H 0 1.430 -1.107; H 0 -1.430 -1.107\nend\n\n\npython\n if (ga_nodeid() == 0): plotdata = open(\"plotdata\",'w')\n\n def energy_at_exponent(exponent):\n input_parse(''' \n basis noprint \n H library 3-21g; O library 3-21g; O d; %f 1.0 \n end \n ''' % (exponent))\n return task_energy('scf')\n\n exponent = 0.1\n while exponent <= 2.01:\n energy = energy_at_exponent(exponent)\n if (ga_nodeid() == 0):\n print (' exponent = %5.4f,' % exponent, ', energy = %16.10f' % energy)\n plotdata.write('%f %f\\n' % (exponent , energy))\n exponent = exponent + 0.1\n\n if (ga_nodeid() == 0): plotdata.close()\nend\n\nprint none\ntask python\n
This input performs exactly the same calculation as the previous one, but uses a slightly more sophisticated Python program, also writes the data out to a file for easy visualization with a package such as gnuplot, and protects write statements to prevent duplicate output in a parallel job. The only significant differences are in the Python program. A file called \u201cplotdata\u201d is opened, and then a procedure is defined which given an exponent returns the energy. Next comes the main loop that scans the exponent through the desired range and prints the results to standard output and to the file. When the loop is finished the additional output file is closed.
"},{"location":"Python.html#scanning-a-geometric-variable","title":"Scanning a geometric variable","text":"python\n geometry = '''\n geometry noprint; symmetry d2h\n C 0 0 %f; H 0 0.916 1.224\n end\n '''\n x = 0.6\n while (x < 0.721):\n input_parse(geometry % x)\n energy = task_energy('scf')\n print (' x = %5.2f energy = %10.6f' % (x, energy))\n x = x + 0.01\nend\n\nbasis; C library 6-31g*; H library 6-31g*; end\n\nprint none\n\ntask python\n
This scans the bond length in ethene from 1.2 to 1.44 in steps of 0.2 computing the energy at each geometry. Since it is using D2h symmetry the program actually uses a variable (x) that is half the bond length.
Look in the NWChem contrib directory for a routine that makes the above task easier.
"},{"location":"Python.html#scan-using-the-bsse-counterpoise-corrected-energy","title":"Scan using the BSSE counterpoise corrected energy","text":"basis spherical\n Ne library cc-pvdz; BqNe library Ne cc-pvdz\n He library cc-pvdz; BqHe library He cc-pvdz\nend\n\nmp2; tight; freeze core atomic; end\n\nprint none\n\npython\n supermolecule = 'geometry noprint; Ne 0 0 0; He 0 0 %f; end\\n'\n fragment1 = 'geometry noprint; Ne 0 0 0; BqHe 0 0 %f; end\\n'\n fragment2 = 'geometry noprint; BqNe 0 0 0; He 0 0 %f; end\\n'\n\n def energy(geometry):\n input_parse(geometry + 'scf; vectors atomic; end\\n')\n return task_energy('mp2')\n\n def bsse_energy(z):\n return energy(supermolecule % z) - \\\n energy(fragment1 % z) - \\\n energy(fragment2 % z)\n z = 3.3\n while (z < 4.301):\n e = bsse_energy(z)\n if (ga_nodeid() == 0): print (' z = %5.2f energy = %10.7f ' % (z, e))\n z = z + 0.1\nend\n\ntask python\n
This example scans the He\u2013Ne bond-length from 3.3 to 4.3 and prints out the BSSE counterpoise corrected MP2 energy.
The basis set is specified as usual, noting that we will need functions on ghost centers to do the counterpoise correction. The Python program commences by defining strings containing the geometry of the super-molecule and two fragments, each having one variable to be substituted. Next, a function is defined to compute the energy given a geometry, and then a function is defined to compute the counterpoise corrected energy at a given bond length. Finally, the bond length is scanned and the energy printed. When computing the energy, the atomic guess has to be forced in the SCF since by default it will attempt to use orbitals from the previous calculation which is not appropriate here.
Since the counterpoise corrected energy is a linear combination of other standard energies, it is possible to compute the analytic derivatives term by term. Thus, combining this example and the next could yield the foundation of a BSSE corrected geometry optimization package.
"},{"location":"Python.html#scan-the-geometry-and-compute-the-energy-and-gradient","title":"Scan the geometry and compute the energy and gradient","text":" basis noprint; H library sto-3g; O library sto-3g; end\n\n python\n print (' y z energy gradient')\n print (' ----- ----- ---------- ------------------------------------')\n y = 1.2\n while y <= 1.61:\n z = 1.0\n while z <= 1.21:\n input_parse('''\n geometry noprint units atomic\n O 0 0 0\n H 0 %f -%f\n H 0 -%f -%f\n end\n ''' % (y, z, y, z))\n\n (energy,gradient) = task_gradient('scf')\n\n print (' %5.2f %5.2f %9.6f' % (y, z, energy)),\n i = 0\n while (i < len(gradient)):\n print ('%5.2f' % gradient[i]),\n i = i + 1\n print ('')\n z = z + 0.1\n y = y + 0.1\nend\n\nprint none\n\ntask python\n
This program illustrates evaluating the energy and gradient by calling task_gradient(). A water molecule is scanned through several C2v geometries by varying the y and z coordinates of the two hydrogen atoms. At each geometry the coordinates, energy and gradient are printed.
The basis set (sto-3g) is input as usual. The two while loops vary the y and z coordinates. These are then substituted into a geometry which is parsed by NWChem using input_parse(). The energy and gradient are then evaluated by calling task_gradient() which returns a tuple containing the energy (a scalar) and the gradient (a vector or list). These are printed out exploiting the Python convention that a print statement ending in a comma does not print end-of-line.
"},{"location":"Python.html#reaction-energies-varying-the-basis-set","title":"Reaction energies varying the basis set","text":"mp2; freeze atomic; end\n\nprint none\n\npython\n energies = {}\n c2h4 = 'geometry noprint; symmetry d2h; \\\n C 0 0 0.672; H 0 0.935 1.238; end\\n'\n ch4 = 'geometry noprint; symmetry td; \\\n C 0 0 0; H 0.634 0.634 0.634; end\\n'\n h2 = 'geometry noprint; H 0 0 0.378; H 0 0 -0.378; end\\n'\n\n def energy(basis, geometry):\n input_parse('''\n basis spherical noprint\n c library %s ; h library %s \n end\n ''' % (basis, basis))\n input_parse(geometry)\n return task_energy('mp2')\n\n for basis in ('sto-3g', '6-31g', '6-31g*', 'cc-pvdz', 'cc-pvtz'):\n energies[basis] = 2*energy(basis, ch4) \\\n - 2*energy(basis, h2) - energy(basis, c2h4)\n if (ga_nodeid() == 0): print (basis, ' %8.6f' % energies[basis])\nend \n\ntask python\n
In this example the reaction energy for 2H2 + C2H4 \u2192 2CH4 is evaluated using MP2 in several basis sets. The geometries are fixed, but could be re-optimized in each basis. To illustrate the useful associative arrays in Python, the reaction energies are put into the associative array energies \u2013 note its declaration at the top of the program.
"},{"location":"Python.html#using-the-database","title":"Using the database","text":" python \n rtdb_put(\"test_int2\", 22) \n rtdb_put(\"test_int\", [22, 10, 3], INT) \n rtdb_put(\"test_dbl\", [22.9, 12.4, 23.908], DBL) \n rtdb_put(\"test_str\", \"hello\", CHAR) \n rtdb_put(\"test_logic\", [0,1,0,1,0,1], LOGICAL) \n rtdb_put(\"test_logic2\", 0, LOGICAL) \n\n rtdb_print(1) \n\n print \"test_str = \", rtdb_get(\"test_str\") \n print \"test_int = \", rtdb_get(\"test_int\") \n print \"test_in2 = \", rtdb_get(\"test_int2\") \n print \"test_dbl = \", rtdb_get(\"test_dbl\") \n print \"test_logic = \", rtdb_get(\"test_logic\") \n print \"test_logic2 = \", rtdb_get(\"test_logic2\") \n end \n\n task python\n
This example illustrates how to access the database from Python.
"},{"location":"Python.html#handling-exceptions-from-nwchem","title":"Handling exceptions from NWChem","text":" geometry; he 0 0 0; he 0 0 2; end \n basis; he library 3-21g; end \n scf; maxiter 1; end \n\n python \n try: \n task_energy('scf') \n except NWChemError, message: \n print 'Error from NWChem ... ', message \n end \n\n task python\n
The above test program shows how to handle exceptions generated by NWChem by forcing an SCF calculation on He2<\\sub> to fail due to insufficient iterations.
If an NWChem command fails it will raise the exception \u201cNWChemError\u201d (case sensitive) unless the error was fatal. If the exception is not caught, then it will cause the entire Python program to terminate with an error. This Python program catches the exception, prints out the message, and then continues as if all was well since the exception has been handled.
If your Python program detects an error, raise an unhandled exception. Do not call exit(1) since this may circumvent necessary clean-up of the NWChem execution environment.
"},{"location":"Python.html#accessing-geometry-information-a-temporary-hack","title":"Accessing geometry information: a temporary hack","text":"In an ideal world the geometry and basis set objects would have full Python wrappers, but until then a back-door solution will have to suffice. We\u2019ve already seen how to use input_parse() to put geometry (and basis) data into NWChem, so it only remains to get the geometry data back after it has been updated by a geometry optimzation or some other operation.
The following Python procedure retrieves the coordinates in the same units as initially input for a geometry of a given name. Its full source is included in the NWChem contrib directory.
def geom_get_coords(name): \n try: \n actualname = rtdb_get(name) \n except NWChemError: \n actualname = name \n coords = rtdb_get('geometry:' + actualname + ':coords') \n units = rtdb_get('geometry:' + actualname + ':user units') \n if (units == 'a.u.'): \n factor = 1.0 \n elif (units == 'angstroms'): \n factor = rtdb_get('geometry:'+actualname+':angstrom_to_au') \n else: \n raise NWChemError,'unknown units' \n i = 0 \n while (i < len(coords)): \n coords[i] = coords[i] / factor \n i = i + 1 \n return coords\n
A geometry with name NAME has its coordinates (in atomic units) stored in the database entry geometry:NAME:coords. A minor wrinkle here is that indirection is possible (and used by the optimizers) so that we must first check if NAME actually points to another name. In the program this is done in the first try\u2026except sequence. With the actual name of the geometry, we can get the coordinates. Any exceptions are passed up to the caller. The rest of the code is just to convert back into the initial input units \u2013 only atomic units or Angstr\u00f8ms are handled in this simple example. Returned is a list of the atomic coordinates in the same units as your initial input.
The routine is used as follows
coords = geom_get_coords('geometry')\n
or, if you want better error handling
try: \n coords = geom_get_coords('geometry') \n except NWChemError,message: \n print 'Coordinates for geometry not found ', message \n else: \n print coords\n
This is very dirty and definitely not supported from one release to another, but, browsing the output of rtdb_print() at the end of a calculation is a good way to find stuff. To be on safer ground, look in the programmers manual since some of the high-level routines do pass data via the database in a well-defined and supported manner. Be warned \u2013 you must be very careful if you try to modify data in the database. The input parser does many important things that are not immediately apparent (e.g., ensure the geometry is consistent with the point group, mark the SCF as not converged if the SCF options are changed, \u2026). Where at all possible your Python program should generate standard NWChem input and pass it to input_parse() rather than setting parameters directly in the database.
"},{"location":"Python.html#scaning-a-basis-exponent-yet-again-plotting-and-handling-child-processes","title":"Scaning a basis exponent yet again: plotting and handling child processes","text":" geometry units au \n O 0 0 0; H 0 1.430 -1.107; H 0 -1.430 -1.107 \n end \n\n print none \n\n python \n import Gnuplot, time, signal \n\n def energy_at_exponent(exponent): \n input_parse(''' \n basis noprint \n H library 3-21g; O library 3-21g; O d; %f 1.0 \n end \n ''' % (exponent)) \n return task_energy('scf') \n\n data = [] \n exponent = 0.5 \n while exponent <= 0.6: \n energy = energy_at_exponent(exponent) \n print ' exponent = ', exponent, ' energy = ', energy \n data = data + [exponent,energy](exponent,energy.md) \n exponent = exponent + 0.02 \n\n if (ga_nodeid() == 0): \n signal.signal(signal.SIGCHLD, signal.SIG_DFL) \n g = Gnuplot.Gnuplot() \n g('set data style linespoints') \n g.plot(data) \n time.sleep(30) # 30s to look at the plot \n\n end \n\n task python\n
This illustrates how to handle signals from terminating child processes and how to generate simple plots on UNIX systems. The scanning example is modified so that instead of writing the data to a file for subsequent visualization, it is saved for subsequent visualization with Gnuplot (you\u2019ll need both Gnuplot and the corresponding package for Python in your PYTHONPATH. Look at https://web.archive.org/web/20010717060625/http://monsoon.harvard.edu/~mhagger/download/).
The issue is that NWChem traps various signals from the O/S that usually indicate bad news in order to provide better error handling and reliable clean-up of shared, parallel resources. One of these signals is SIGCHLD which is generated whenever a child process terminates. If you want to create child processes within Python, then the NWChem handler for SIGCHLD must be replaced with the default handler. There seems to be no easy way to restore the NWChem handler after the child has completed, but this should have no serious side effect.
"},{"location":"Python.html#troubleshooting","title":"Troubleshooting","text":"Common problems with Python programs inside NWChem.
- You get the message
0:python_input: indentation must be >= that of first line: 4 \n
This indicates that NWChem thinks that a line is less indented than\nthe first line. If this is not the case then perhaps there is a tab\nin your input which NWChem treats as a single space character but\nappears to you as more spaces. Try running untabify in Emacs. The\nproblem could also be the END directive that terminates the PYTHON\ncompound directive -- since Python also has an end statement. To\navoid confusion the END directive for NWChem must be at the start of\nthe line.\n
- Your program hangs or deadlocks \u2013 most likely you have a piece of code that is restricted to executing on a subset of the processors (perhaps just node 0) but is calling (perhaps indirectly) a function that must execute on all nodes.
"},{"location":"QMMM.html","title":"QMMM Simulations","text":" - Introduction
- Topology and Restart Files
- Prerequisites
- QM region definition
- Solvation
- Permanent Constraints
- Input File
- QM Parameters
- MM Parameters
- QM/MM Parameters
- Single Point Calculations
- Ground State Energy and Gradient
- Excited State Energy
- Properties
- ESP Charge Analysis
- Potential Energy Surface Analysis
- Optimization
- Transition States
- Hessians and Frequency
- Reaction Pathway Calculations with NEB
- Dynamics
- Free Energy Calculations
- Appendix
- Format of NWChem parameter file
- Conversion from AMBER program parameter files to NWChem
- References
"},{"location":"QMMM_Appendix.html","title":"QMMM Apppendix","text":""},{"location":"QMMM_Appendix.html#preparing-qmmm-calculations-from-scratch","title":"Preparing QM/MM calculations from scratch","text":"Setting up QM/MM calculations for a new system for which classical force analog is not readily available would typically involve the following steps
- Generation of the proper PDB file
- Construction the fragment file(s)
- Creation of parameter file if new atom types were defined
"},{"location":"QMMM_Appendix.html#generation-of-the-proper-pdb-file","title":"Generation of the proper PDB file","text":"It is often the case that the input structure for the system comes in the form of the xyz file. Let us take a concrete example of N3O3- molecule, which we would like to embed in classical solvent and perform QM/MM calculations. Here is the structure of just N3O3- in xyz format (generated in course of gas phase optimizations)
6 \n geometry \n N 1.31562667 0.93574165 -0.42424728 \n O 1.56161766 0.18015298 -1.36827899 \n N 2.36373381 1.02559495 0.48834956 \n O 3.47240000 0.42852552 0.42137570 \n N 1.95804013 1.90608355 1.48799418 \n O 2.81393172 2.06788134 2.36142683\n
We cannot use this file as is in the QM/MM simulations, and it has to be converted into PDB format. This is needed even if we plan to treat this molecule quantum mechanically. There is more than way to do it. For example, we could use Babel http://openbabel.org/wiki/Main_Page, which will generate the PDB file as
COMPND geometry \nAUTHOR GENERATED BY OPEN BABEL 2.3.0 \nHETATM 1 O LIG 1 1.562 0.180 -1.368 1.00 0.00 O \nHETATM 2 N LIG 1 1.316 0.936 -0.424 1.00 0.00 N \nHETATM 3 N LIG 1 2.364 1.026 0.488 1.00 0.00 N \nHETATM 4 O LIG 1 3.472 0.429 0.421 1.00 0.00 O \nHETATM 5 N LIG 1 1.958 1.906 1.488 1.00 0.00 N \nHETATM 6 O LIG 1 2.814 2.068 2.361 1.00 0.00 O \nCONECT 1 2 \nCONECT 2 1 3 \nCONECT 3 2 4 5 \nCONECT 4 3 \nCONECT 5 3 6 \nCONECT 6 5 \nMASTER 0 0 0 0 0 0 0 0 6 0 6 0 \nEND\n
which after stripping nonessential information becomes
HETATM 1 O LIG 1 1.562 0.180 -1.368 1.00 0.00 O \n HETATM 2 N LIG 1 1.316 0.936 -0.424 1.00 0.00 N \n HETATM 3 N LIG 1 2.364 1.026 0.488 1.00 0.00 N \n HETATM 4 O LIG 1 3.472 0.429 0.421 1.00 0.00 O \n HETATM 5 N LIG 1 1.958 1.906 1.488 1.00 0.00 N \n HETATM 6 O LIG 1 2.814 2.068 2.361 1.00 0.00 O \n END\n
This is not yet the format we want. So what we need to do is
- replace HETATM field by ATOM preserving the format (column locations) of the rest of the file:
I would typically use sed for this purpose
sed 's/HETATM/ATOM /' n3o3-bad.pdb > n3o3-step1.pdb\n
where n3o3-bad.pdb is the original pdb file from Babel and n3o3-step1.pdb is the converted one as shown below
ATOM 1 O LIG 1 1.562 0.180 -1.368 1.00 0.00 O \nATOM 2 N LIG 1 1.316 0.936 -0.424 1.00 0.00 N \nATOM 3 N LIG 1 2.364 1.026 0.488 1.00 0.00 N \nATOM 4 O LIG 1 3.472 0.429 0.421 1.00 0.00 O \nATOM 5 N LIG 1 1.958 1.906 1.488 1.00 0.00 N \nATOM 6 O LIG 1 2.814 2.068 2.361 1.00 0.00 O \nEND\n
- define residues (aka molecules):
In our case Babel did this for us and the entire system is defined as one residue with the name LIG (see columns 4 and 5). We can leave it as, but I will redefine residue name to NN3 (keep it to 3 characters !). Again running sed 's/LIG/NN3/' n3o3-step1.pdb > n3o3-step2.pdb
ATOM 1 O NN3 1 1.562 0.180 -1.368 1.00 0.00 O \nATOM 2 N NN3 1 1.316 0.936 -0.424 1.00 0.00 N \nATOM 3 N NN3 1 2.364 1.026 0.488 1.00 0.00 N \nATOM 4 O NN3 1 3.472 0.429 0.421 1.00 0.00 O \nATOM 5 N NN3 1 1.958 1.906 1.488 1.00 0.00 N \nATOM 6 O NN3 1 2.814 2.068 2.361 1.00 0.00 O \nEND\n
You could have also broken it up into several residues as
ATOM 1 O NN2 1 1.562 0.180 -1.368 1.00 0.00 O \nATOM 2 N NN2 1 1.316 0.936 -0.424 1.00 0.00 N \nATOM 3 N NN2 1 2.364 1.026 0.488 1.00 0.00 N \nATOM 4 O NN2 1 3.472 0.429 0.421 1.00 0.00 O \nATOM 5 N NN1 2 1.958 1.906 1.488 1.00 0.00 N \nATOM 6 O NN1 2 2.814 2.068 2.361 1.00 0.00 O \nEND\n
where I defined two residues NN2 and NN1 (note changes in columns 4 and 5). To keep things simple I will stay with one residue version for now
- make unique atom names:
This has to do with the requirement that all atoms names have to be unique within a given residue. So if we take our one residue version it could be modified as (notice column 3)
ATOM 1 O1 NN3 1 1.562 0.180 -1.368 1.00 0.00 O \nATOM 2 N1 NN3 1 1.316 0.936 -0.424 1.00 0.00 N \nATOM 3 N2 NN3 1 2.364 1.026 0.488 1.00 0.00 N \nATOM 4 O2 NN3 1 3.472 0.429 0.421 1.00 0.00 O \nATOM 5 N3 NN3 2 1.958 1.906 1.488 1.00 0.00 N \nATOM 6 O3 NN3 2 2.814 2.068 2.361 1.00 0.00 O \nEND\n
Now we have a PDB file for our system in \u201cproper\u201d PDB format. Before we move to next step, I should mention that the last 3 columns are not necessary and could have been removed at any point leading to n3o3.pdb
ATOM 1 O1 NN3 1 1.562 0.180 -1.368 \nATOM 2 N1 NN3 1 1.316 0.936 -0.424 \nATOM 3 N2 NN3 1 2.364 1.026 0.488 \nATOM 4 O2 NN3 1 3.472 0.429 0.421 \nATOM 5 N3 NN3 2 1.958 1.906 1.488 \nATOM 6 O3 NN3 2 2.814 2.068 2.361 \nEND\n
"},{"location":"QMMM_Appendix.html#generation-of-new-fragment-files","title":"Generation of new fragment files","text":"While setting up QM/MM calculations is often necessary to generate new fragment files for the molecules that are not available as part of standard set. The IMPORTANT assumption here is that these new molecules/residues will be part of OQM region, and as a result only minimum information needs to be provided to include them in QM/MM calculations.
First we must ensure that we have a proper PDB format for our as discussed in the Generation of the proper PDB file section. As a concrete example we will start with N3O3 example that was discussed there as well
ATOM 1 O1 NN3 1 1.562 0.180 -1.368 \nATOM 2 N1 NN3 1 1.316 0.936 -0.424 \nATOM 3 N2 NN3 1 2.364 1.026 0.488 \nATOM 4 O2 NN3 1 3.472 0.429 0.421 \nATOM 5 N3 NN3 1 1.958 1.906 1.488 \nATOM 6 O3 NN3 1 2.814 2.068 2.361 \nEND\n
We have residue named NN3 and therefore looking to construct fragment file NN3.frg. The best way to do it is to run a simple prepare job
start n3o3 \n\nprepare \nsource n3o3.pdb \nnew_top new_seq \nnew_rst \nmodify segment 1 quantum \nupdate lists \nignore \nwrite n3o3_ref.pdb \nwrite n3o3_ref.rst \nend \n\ntask prepare\n
This prepare job will necessarily fail because NN3.frg is not yet available:
Created fragment ./NN3.frg_TMP \n\nUnresolved atom types in fragment NN3 \n\n\n ********** \n * 0: pre_mkfrg failed 9999 \n **********\n
As part of this process skeleton fragment file (NN3.frg_TMP) will be generated that can be modified into the final correct form. Let us take a look at NN3.frg_TMP
# This is an automatically generated fragment file \n# Atom types and connectivity were derived from coordinates \n# Atomic partial charges are crude estimates \n# 00/00/00 00:00:00 \n# \n$NN3 \n 6 1 1 0 \nNN3 \n 1 O1 0 0 0 1 1 0.000000 0.000000 \n 2 N1 0 0 0 1 1 0.000000 0.000000 \n 3 N2 0 0 0 1 1 0.000000 0.000000 \n 4 O2 0 0 0 1 1 0.000000 0.000000 \n 5 N3 0 0 0 1 1 0.000000 0.000000 \n 6 O3 0 0 0 1 1 0.000000 0.000000 \n 1 2 \n 2 3 \n 3 4 \n 3 5 \n 5 6\n
The main problem with this fragment file is that there are no atom types to be found in column 12. What atom type does is to identify what classical parameters should be assigned to it. Since, as mentioned in the beginning, we are planing to treat this residue/molecule as part of QM region, the only classical information needed is VDW parameters. We will assume that all nitrogens atoms in our molecule can use the same set of parameters, and the same for oxygens. Therefore we will define two atom types NX and OX
$NN3 \n 6 1 1 0 \nNN3 \n 1 O1 OX 0 0 0 1 1 0.000000 0.000000 \n 2 N1 NX 0 0 0 1 1 0.000000 0.000000 \n 3 N2 NX 0 0 0 1 1 0.000000 0.000000 \n 4 O2 OX 0 0 0 1 1 0.000000 0.000000 \n 5 N3 NX 0 0 0 1 1 0.000000 0.000000 \n 6 O3 OX 0 0 0 1 1 0.000000 0.000000 \n 1 2 \n 2 3 \n 3 4 \n 3 5 \n 5 6\n
and rename resulting file as NN3.frg. Please note that the overall format of the fragment file was preserved and atom types were entered starting at column 12. Rerunning the same prepare job moves as a bit further this time
modify segment 1 set 0 quantum \n Parameter file /Users/marat/opt/codes/nwchem-new/src/data/amber_s/amber.par \n Parameter file /Users/marat/opt/codes/nwchem-new/src/data/amber_q/amber.par \n Parameter file /Users/marat/opt/codes/nwchem-new/src/data/amber_x/amber.par \n Parameter file /Users/marat/opt/codes/nwchem-new/src/data/amber_u/amber.par\n\n Undetermined force field parameters\n\n Parameters could not be found for atom type OX Q \n Parameters could not be found for atom type NX Q\n\n ********** \n * 0: pre_check failed 9999 \n **********\n
complaining now that atom types OX and NX are not defined. This brings us to the next step of defining new parameter file for our calculation.
"},{"location":"QMMM_Appendix.html#generation-of-new-parameter-files","title":"Generation of new parameter files","text":"Continuing with our fragment construction in Generation of new fragment files section, we now need to define VDW parameters for our new atom types NX and OX. The best way to do it is to create amber.par file in the directory where you plan to rerun final prepare
Electrostatic 1-4 scaling factor 0.833333 \nRelative dielectric constant 1.000000 \nParameters epsilon R* \n# \nAtoms \nNX 14.01000 7.11280E-01 1.82400E-01 1 1111111111 \n Q 7 3.55640E-01 1.82400E-01 \nOX 16.00000 6.35968E-01 1.76830E-01 1 1111111111 \n Q 8 3.17984E-01 1.76830E-01 \nEnd\n
The format of this file is documented in Format of NWChem parameter file. How to actually choose the appropriate values for VDW parameters is a whole new subject, which I do not think anybody yet fully addressed. The practical strategy is to copy from known atom types, which are chemically similar to the ones in your system. In the case above I copied parameters from standard AMBER atom types N and OW.
"},{"location":"QMMM_Appendix.html#format-of-nwchem-parameter-file","title":"Format of NWChem parameter file","text":"The format of NWChem parameter is illustrated on the figure below and also available as pdf file.
"},{"location":"QMMM_Appendix.html#conversion-of-standard-amber-program-parameter-files","title":"Conversion of standard AMBER program parameter files","text":"Fortran code that performs conversion from AMBER program parameter file format to NWChem can be found here. It works by parsing out free format AMBER style parameter file contained in amber.in
MASS \nC 12.01 \nCA 12.01 \nBOND \n#this is a comment \nC -CA 469.0 1.409 this is also a comment \nC - CB 447.0 1.419 \nANGLE \nC -CA-CA 63.0 120.00 another comment \nC -CB-NB 70.0 130.00 \nDIHEDRAL \nX -C -CA-X 4 14.50 180.0 2. intrpol.bsd.on C6H6 \n X - C - CB -X 4 12.00 180.0 2. intrpol.bsd.on C6H6 \nIMPROPER \nX -CT-N -CT 1.0 180. 2. JCC,7,(1986),230 \nCT -O - C -OH 10.5 180. 2. \nNONBOND \n CA 1.9080 0.0860 \nC 1.9080 0.0860\n
to fixed format NWChem style amber.par file
#Generated amber.par file \nElectrostatic 1-4 scaling factor 0.833333 \nRelative dielectric constant 1.000000 \nParameters epsilon R* \n# \nAtoms \nCA 12.01000 3.59824E-01 1.90800E-01 1 1111111111 \n 6 1.79912E-01 1.90800E-01 \nC 12.01000 3.59824E-01 1.90800E-01 1 1111111111 \n 6 1.79912E-01 1.90800E-01 \nBonds \nC -CA 0.14090 3.92459E+05 \nC -CB 0.14190 3.74050E+05 \nAngles \nC -CA -CA 2.09440 5.27184E+02 \nC -CB -NB 2.26893 5.85760E+02 \nProper dihedrals \n -C -CA - 3.14159 1.51670E+01 2 \n -C -CB - 3.14159 1.25520E+01 2 \nImproper dihedrals \n -CT -N -CT 3.14159 4.18400E+00 2 \nCT -O -C -OH 3.14159 4.39320E+01 2 \nEnd\n
"},{"location":"QMMM_Dynamics.html","title":"QMMM Dynamics","text":"Dynamical simulations within QM/MM framework can be initiated using
task\u00a0qmmm\u00a0 <qmtheory> \u00a0dynamics \n
directive. User has to specify the region for which simulation will performed. If dynamics is performed only for the classical parts of the system (QM region is fixed) then ESP point charge representation (density espfit) is recommended to speed up simulations. If this option is utilized then wavefunction file (.movecs) has to be available and present in the permanent directory (this can be most easily achieved by running energy calculation prior to dynamics)."},{"location":"QMMM_ESP.html","title":"QMMM ESP Charge Analysis","text":"
- Example QM/MM ESP Calculation:
The example below illustrates dipole property QM/MM DFT/B3LYP calculation for quantum water molecule embedded into 20 angstrom box of classical SPCE/E water molecules.
The preparation stage that involves definition of the QM region and solvation is performed as part of the calculation. Note that water fragment file wtr.frg is required in this calculation. Prepare run will generate restart file (wtr_ref.rst) and topology file (wtr.top)
In the QM/MM interface block the use of bq_zone value of 3.0 Angstrom is specified.
start wtr\n\n permanent_dir ./perm \n scratch_dir ./data\n\n prepare \n source wtr0.pdb \n new_top new_seq \n new_rst \n modify segment 1 quantum \n center \n orient \n solvate box 3.0 \n update lists \n ignore \n write wtr_ref.rst \n write wtr_ref.pdb \n end\n\n task prepare\n\n md \n system wtr_ref \n end\n\n basis \n * library \"6-31G\" \n end\n\n dft \n xc b3lyp \n end\n\n qmmm \n bq_zone 3.0 \n end\n\n property \n dipole \n end\n\n task qmmm dft property\n
"},{"location":"QMMM_Excited_States.html","title":"QMMM Excited State Energy","text":"The excited state QM/MM energy calculations can be performed with TCE
task\u00a0qmmm\u00a0tce\u00a0energy
or TDDFT
task\u00a0qmmm\u00a0tddft\u00a0energy
levels of theory. The excited state QM/MM gradient energy calculations can be performed only numerically.
"},{"location":"QMMM_FEP_Example.html","title":"Example of QM/MM solvation free energy calculation input file","text":"A total of two sampling cycles will be performed with 1000 samples per each cycle
memory total 2000 Mb\n\n start clfoh\n\n permanent_dir ./perm\n scratch_dir /scratch\n\n\n md\n #this will require topology [clfoh.top](clfoh.top) and restart [clfoh_neb.rst](clfoh_neb.rst) files \n system clfoh_neb\n cutoff 1.5 qmmm 1.5\n noshake solute\n isotherm\n end\n\n qmmm\n print low\n nsamples 1000\n ncycles 2\n end\n\n set qmmm:fep_geom [clfoh_neb-s.xyzi](clfoh_neb-s.xyzi) [clfoh_neb-e.xyzi](clfoh_neb-e.xyzi)\n set qmmm:fep_esp [clfoh_neb-s.esp](clfoh_neb-s.esp.md) [clfoh_neb-e.esp](clfoh_neb-e.esp.md)\n set qmmm:fep_lambda 0.0 0.1\n set qmmm:fep_deriv .true.\n\n task qmmm fep\n
"},{"location":"QMMM_Free_Energy.html","title":"QMMM Free Energy","text":""},{"location":"QMMM_Free_Energy.html#overview","title":"Overview","text":"Free energy capabilities of QM/MM module are at this point restricted to calculations of free energy differences between two fixed configurations of the QM region.
Users must be warned that this the least automated QM/MM functionality containing several calculation stages. Solid understanding of free energy calculations is required to achieve a meaningful calculation.
Description of the implemented methodology can be found in the following paper. In this approach the free energy difference between the two configurations of the QM region (e.g. A and B):
is approximated as a sum of internal QM contribution and solvation:
It is presumed that structures of A and B configurations are available as restart files sharing common topology file.
"},{"location":"QMMM_Free_Energy.html#internal-contribution","title":"Internal contribution","text":"The internal QM contribution is given by the differences in the internal QM energies evaluated at the optimized MM environment:
The internal QM energy is nothing more but a gas phase expression total energy but evaluated with the wavefunction obtained in the presence of the environment. To calculate internal QM contribution to free energy difference one has to
- Optimize MM environment for each configuration
- Perform total energy calculation for each configuration
- Calculate internal energy difference
Note that internal QM energy can be found in the QM/MM output file under \u201cquantum energy internal\u201d name.
"},{"location":"QMMM_Free_Energy.html#solvation-contribution","title":"Solvation contribution","text":"The solvation contribution is evaluated by averaging energy difference between A and B configurations of the QM system represented by a set of ESP charges.
where is the total energy of the system where QM region is replaced by a set of fixed point ESP charges.
In majority of cases the A and B configuration are \u201ctoo far apart\u201d and one step free energy calculation as shown above will not lead to meaningful results. One solution is to introduce intermediate points that bridge A and B configurations by linear interpolation
where
The solvation free energy difference can be then written as sum of differences for the subintervals :
To expedite the calculation it is convenient to use a double wide sampling strategy where the free energy differences for the intervals and are calculated simultaneously by sampling around point. In the simplest case where we use two subintervals (n=2)
or
The following items are necessary:
- Restart file corresponding to either A or B configuration of the QM region (sharing the same topology file)
- ESP charges for QM region in .esp format for both configurations
- Coordinates for QM regions in .xyzi format for both configurations
Both .esp and .xyzi files would be typically obtained during the calculation of internal free energy (see above). ESP charges would be generated in the perm directory during optimization of the MM region. The xyzi is basically xyz structure file with an extra column that allows to map coordinates of QM atoms to the overall system. The xyzi file can also be obtained as part of calculation of internal free energy by inserting
set qmmm:region_print .true.\n
anywhere in the input file during energy calculation. Both xyzi and esp files should be placed into the perm directory!!!
In the input file the restart file is specified in the MD block following the standard notation
md\n system < name of rst file without extension>\n ...\nend\n
while coordinates of QM region (xyzi files) and ESP charges (esp files) are set using the following directives (at the top level outside of any input blocks)
set qmmm:fep_geom xxx_A.xyzi xxx_B.xyzi\nset qmmm:fep_esp xxx_A.esp xxx_B.esp\n
The current interpolation interval for which free energy difference is calculated is defined as
set qmmm:fep_lambda lambda_i lambda_i+1\n
To enable double wide sampling use the following directive
set qmmm:fep_deriv .true.\n
If set, the above directive will perform both and calculations, where
The calculation proceeds in cycles, each cycle consisting of two phases. First phase is generation of classical MD trajectory around point. Second phase is processing of the generated trajectory to calculate averages of relevant energy differences. The number of MD steps in the first phase is controlled by the QM/MM directive
Are you just
diff --git a/print_page.html b/print_page.html
index 419a30eaeb..91166803b2 100644
--- a/print_page.html
+++ b/print_page.html
@@ -2862,7 +2862,8 @@