This code is the implementation of the DeepH-E3 method described in the paper General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian (arXiv:2210.13955).

You can find demo input files and instructions in these repositories: Dataset 1, Dataset 2 and Dataset 3. These are also the datasets used by the paper, so you can try to reproduce the results in the paper using those datasets.

The current code will be integrated into DeepH-pack in the future.

To use DeepH-E3, the following environment is required:

The python interpreter version needs to be at least 3.9. The following packages are also needed:

• Numpy
• PyTorch = 1.9.0
• PyTorch geometric = 1.7.2
• e3nn version 0.3.5
• h5py
• TensorBoard
• pathos
• pymatgen

The installation of Julia is optional. If you want to parse openmx output and convert into the format used by DeepH-E3, or do sparse matrix diagonalization to obtain the band structure from DeepH-E3 output, then Julia is needed.

First prepare the Julia interpreter version 1.5.4. Then install the following packages:

• Arpack.jl
• HDF5.jl
• ArgParse.jl
• JLD.jl
• JSON.jl
• IterativeSolvers.jl
• DelimitedFiles.jl
• StaticArrays.jl

In order to use Julia with DeepH-E3, you have to add the julia executable to PATH.

The usage of DeepH-E3 is similar to that of DeepH-pack. Although not mandatory, it is recommended that you learn the usage of DeepH-pack first.

First, you have to convert the output of DFT codes to the format that can be directly read by DeepH-E3. It is recommended that you directly use the preprocess utility of DeepH-pack. You must set local_coordinate = False in the DeepH preprocess config.

DeepH-E3 also has its own input conversion utility. You can use the command

/path/to/deephe3-preprocess.py preprocess.ini

to preprocess DFT data. The default config file for preprocess.ini can be found in DeepH-E3/deephe3/default_configs/base_default.ini. This default config also includes a description of each input variables.

Based on the data, one can train the DeepH-E3 model. Training can be done by the command

/path/to/deephe3-train.py train.ini

The default config file for train.ini can be found in DeepH-E3/deephe3/default_configs/train_default.ini. This default config also includes a description of each input variables.

Once you have a trained model, you can use that model to predict the Hamiltonian of some material structures and get hamiltonians_pred.h5. Inference can be done by the command

/path/to/deephe3-eval.py eval.ini

The default config file for eval.ini can be found in DeepH-E3/deephe3/default_configs/eval_default.ini. This default config also includes a description of each input variables.

For large structures that are impossible to calculate with DFT, one needs the modified OpenMX code that only generates the overlap matrix: Overlap-only-OpenMX. In this case, DeepH-E3 needs the processed overlaps.h5 instead of hamiltonians.h5 to generate the crystal graph. You have to set inference=True in eval.ini.