Unfolding the q grid in the prefix.result file

[whzhangg]

Hi,

I want to interface alamode result with code that does not treat the irreducible q grid, So I want to unfold the irreducible q point to the full BZ using the information from the SYMM_INFO_PRIM

Is this the correct way to perform this operation?
take the rotation part of sym operation in SYMM_INFO_PRIM by rot(1,1), rot(1,2), .... rot(3,2), rot(3,3)
find the set of full q grid by inv(rot(: ,:)) dot irr_xq(:) of all symmetry operation

I see in kpoint.cpp that transpose(inv(rot)) is used for the symmetry operation. Is the transpose necessary?

Thank you,
Wenhao

[ttadano]

The transpose is necessary.

The rotation matrix R in SYMM_INFO_PRIM is defined in the lattice coordinate and transforms the input fractional coordinate r into another equivalent structure r' = Rr. To transform the momentum defined in the reciprocal lattice basis into a symmetrically reducible one, we need to multiply S = (R^-1)^T as k' = Sk.

When the rotation is performed in the Cartesian coordinate or when the lattice vector is orthogonal, the rotation matrix R becomes orthogonal. In these cases, we have S = R.

[whzhangg]

I see, if I understand correctly we have (k2).T * R * r1 =(k1).T * r1 giving k2 = (R.T)^-1 k1.

Also, do you think it's convenient to rotate the group velocity in the result file? Is the group velocity of equivalent q point under #GAMMA_EACH tag also generated by rotation in the alamode code?

[ttadano]

The group velocities of symmetrically equivalent q point shown in the PREFIX.result file are generated by taking the finite-difference of the phonon frequency at each q point. This computation is quite cheap and easier to implement than rotating the group velocity. Rotating the group velocity by using the matrix S is, of course, possible and not very difficult.