Folder contents

• oep-wy: codes for OEP and dataset generation
• nn-train: codes to train and test a NN model
• xcnn: codes to perform KS-DFT/NN using trained NN model as an xc function

Example

An example is provided in folder example. 11 $\rm H_2$ and 11 $\rm HeH^+$ molecules are used.

• OEP: python run_oep.py
• Generate dataset: python gen_dataset.py
• Training: python run_train.py
• Testing: python run_test.py (only to check training progress, different from KS-SCF/NN)
• KS-SCF/NN: python run_xcnn.py

The model obtained from training can be used in KS-DFT/NN. A pre-trained model is also provided in example/xcnn/saved_model/H2-HeH+_CNN_GGA_1_0.504-0.896-0.008_HFX_ll_0.9_9.dat.

Configuration

OEP and Dataset

[OEP]

Key	Value	Note
InputDensity	none	Density matrix in ndarray format. Will compute a CCSD 1-rdm if none is given.
Structure	structure/H2/d0500.str
OrbitalBasis	aug-cc-pvqz
PotentialBasis	aug-cc-pvqz
ReferencePotential	hfx	Coulomb matrix and Hartree-Fock Exchange matrix
PotentialCoefficientInit	zeros	Can use a txt or ndarray file
CheckPointPath	oep-wy/chk/H2/d0500
ConvergenceCriterion	1.e-12	Stop criterion of Newton optimization procedure.
SVDCutoff	5.e-6	Cutoff for truncated SVD
LambdaRegulation	0	Lambda value for regulation to get smooth potential. Used for multiple electrons system.
ZeroForceConstrain	false	It seems not a good choice to use zero force constrain during optimization
RealSpaceAnalysis	true	Output density difference between input and output density in real space

[DATASET]

Key	Value	Note
MeshLevel	3
CubeLength	0.9	in Bohr
CubePoint	9	number of discrete points
OutputPath	oep-wy/dataset/H2
OutputName	d0500
Symmetric	xz	Transform $(x, y, z)$ to $(\sqrt{x^2 + y^2}, 0, z)$ and keep only unique points

Training and Testing

Training

[OPTIONS]

Key	Value	Note
prefix	nn-train
log_path	%(prefix)s/train/train.log
verbose	False
data_path	%(prefix)s/dataset/H2-HeH+_0.9_9.npy
model	CNN_GGA_1_zsym	The models with and without _zsym suffix have same architecture and only differ in output. See nn-train/model.py and nn-train/const_list.py.
model_save_path	%(prefix)s/train/model_chk/H2-HeH+_0.9_0_CNN_GGA_1.dat
batch_size	200
max_epoch	200000
learning_rate	5e-3
loss_function	MSELoss_zsym
optimiser	SGD
train_set_size	78800
validate_set_size	19600
enable_cuda	True
constrain	zsym	Needs to be zsym to use model and loss function with _zsym suffix

Testing

[OPTIONS]

Key	Value	Note
prefix	nn-train
log_path	%(prefix)s/test/H2/d0500/test.log
verbose	False
data_path	%(prefix)s/dataset/H2/d0500.npy
model	CNN_GGA_1
restart	%(prefix)s/train/model_chk/H2-HeH+_0.9_0_CNN_GGA_1.dat.restart10000
batch_size	1
loss_function	MSELoss
optimiser	SGD
test_set_size	4920
enable_cuda	True
output_path	%(prefix)s/test/H2/d0500
constrain	none

KS-SCF/NN

[XCNN]

Key	Value	Note
Verbose	True
CheckPointPath	xcnn/chk/H2/d0500
EnableCuda	True
Structure	structure/H2/d0500.str
OrbitalBasis	aug-cc-pVQZ
ReferencePotential	hfx	Should be same as the one used in OEP
Model	cnn_gga_1
ModelPath	xcnn/saved_model/H2-HeH+_0.9_0_CNN_GGA_1.dat.restart10000
MeshLevel	3	Should be same as the one used in training
CubeLength	0.9	Should be same as the one used in training
CubePoint	9	Should be same as the one used in training
Symmetric	xz+	Similar to xz but keep only $z>0$ part. Only for $\rm H_2$
InitDensityMatrix	rks	Used in combination with next row to setup initial density matrix for KS-SCF/NN
xcFunctional	b3lypg	Follow PySCF's convention. In PySCF, b3lyp is different from b3lypg and the latter refers to conventional B3LYP functional.
ConvergenceCriterion	1.e-6	For SCF procedure
MaxIteration	99
ZeroForceConstrain	True	Typically enabled to keep zero force condition.

Dependencies

• numpy
• scipy
• tqdm
• ConfigParser/configparser
• PyTorch with CUDA support
• PySCF > 1.5

Note on PySCF

A customised version of libcint is used to support extra Gaussian integrals. Therefore PySCF installed using pip/conda/docker will fail and you may have to compile it from source code. A straight workaround is described below (maybe not that efficient):

1. Download PySCF source code and follow its procedure to compile core module.
2. Go to pyscf/lib/build/deps/src/libcint, where the source code of libcint is placed.
3. Open scripts/auto_intor.cl and add the following two lines to the last gen-cint block:

  '("int3c1e_ovlp"              ( \, \, ))
  '("int3c1e_ipovlp"            (nabla \, \, ))

4. Follow the instructions at Generating integrals in README of libcint library to generate new codes and place them accordingly. I choose to NOT update libcint here.
5. Go back to pyscf/lib/build where the command to compile PySCF core module is executed. Run make again and the libcint library will be updated.
6. Open pyscf/gto/moleintor.py and add the following two lines to _INTOR_FUNCTIONS

    'int3c1e_ovlp'              : (1, 1),
    'int3c1e_ipovlp'            : (3, 3),

7. Done