phonopy/example/KCl-SSCHA

Example of KCl SSCHA calculation

How to run

The displacements for the training data used in polynomial machine learning potentials (MLPs) are generated with a command like the following:

% phonopy --pa auto --rd 1000 -c POSCAR-unitcell --dim 2 2 2 --amin 0.03 --amax 1.5

After calculating forces using the VASP code, the phonopy_params.yaml file, which contains displacements, forces, and supercell energies, is created with the following command:

% phonopy --sp -f vasprun-{001..120}.xml

In this example, the file phonopy_mlpsscha_params_KCl-120.yaml.xz in the example directory serves as precomputed data for KCl. To develop the MLPs using this file, run:

% phonopy-load phonopy_mlpsscha_params_KCl-120.yaml.xz --pypolymlp --mlp-params="ntrain=100, ntest=20"

This command generates the phonopy.pmlp file, which contains the developed MLPs. This file under current directory is read when running phonopy with the --pypolymlp option. To perform the SSCHA calculation, execute:

% phonopy-load phonopy_mlpsscha_params_KCl-120.yaml.xz --pypolymlp --sscha 10 --rd-temperature 300 --rd 1000

The calculated SSCHA force constants are stored in phonopy_sscha_fc_10.yaml.xz, where 10 indicates the final iteration number. These SSCHA force constants can be compared with phonopy_fc_JPCM2022.yaml.xz, which is explained in the next section. The phonon band structures corresponding to these force constants can be plotted and compared using the following command:

% phonopy-load phonopy_sscha_fc_JPCM2022.yaml.xz --band auto
% mv band.yaml band-JPCM2022.yaml
% phonopy-load phonopy_sscha_fc_10.yaml.xz --band auto
% phonopy-bandplot band.yaml band-JPCM2022.yaml

Comparison with the reported result

The file phonopy_fc_JPCM2022.yaml.xz contains the full ab initio SSCHA force constants for a 2×2×2 supercell of the conventional unit cell, as calculated in the study by A. Togo et al., J. Phys.: Condens. Matter 34, 365401 (2022). The SSCHA force constants from the final iteration are expected to closely resemble these force constants if the MLPs are good.

The files phonopy_fc222_JPCM2022.yaml.xz and phonopy_fc444_JPCM2022.yaml.xz provide the harmonic force constants for 2×2×2 and 4×4×4 supercells, respectively, as calculated in the same study. To compute a temperature-dependent phonon band structure for a 4×4×4 supercell, an approximation was employed where the SSCHA force constants for the 2×2×2 supercell were embedded into the harmonic force constants of the 4×4×4 supercell.

This embedding process involved first interpolating the SSCHA and harmonic force constants of the 2×2×2 supercell to match those of the 4×4×4 supercell. The difference between the interpolated SSCHA and harmonic force constants was then added to the harmonic force constants for the 4x4x4 supercell. The detailed procedure is described in A. Togo et al., J. Phys.: Condens. Matter 35, 353001 (2023). The Python script embed_sscha_fc.py automates this embedding process.

Finally, for KCl, the difference in the phonon band structure between the 2×2×2 and 4×4×4 supercells was negligible. Consequently, this technique was not particularly necessary.