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@ -2,8 +2,6 @@
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# Force constants calculation using pypolymlp (machine learning potential)
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**This is an experimental feature.**
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With the `--pypolymlp` option, phono3py can interface with the polynomial
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machine learning potential (MLP) code,
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[pypolymlp](https://github.com/sekocha/pypolymlp), to perform training and
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@ -20,8 +18,8 @@ For further details on combining phono3py calculations with pypolymlp, refer to
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[[doi](https://doi.org/10.1063/5.0211296)]
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[[arxiv](https://arxiv.org/abs/2401.17531)].
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An example of its usage can be found in the `example/NaCl-pypolymlp` directory
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in the distribution from GitHub or PyPI.
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Examples of its usage can be found in the `example/NaCl-pypolymlp` and
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`example/AlN-rd` directories in the distribution from GitHub or PyPI.
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## Citation of pypolymlp
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@ -42,15 +40,12 @@ in the distribution from GitHub or PyPI.
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## Requirements
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- [pypolymlp](https://github.com/sekocha/pypolymlp) < 0.9
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- [pypolymlp](https://github.com/sekocha/pypolymlp)
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For linux (x86-64), a compiled package of pypolymlp can be installed via
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conda-forge (recommended). Otherwise, pypolymlp can be installed from
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source-code.
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From pypolymlp 0.9, its file format was changed. This will be taken care of
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by the future version of phonopy and phono3py.
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## How to calculate
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### Workflow
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@ -156,28 +151,28 @@ obtained by
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```
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``````
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### Step 4: Development of MLPs
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The `phono3py_params.yaml` file contains the training data required for
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developing polynomial MLPs when running with the `--pypolymlp` option.
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```
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% phono3py-load --pypolymlp phono3py_params.yaml
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phono3py-load --pypolymlp phono3py_params.yaml
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.11.3
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3.18.0
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-------------------------[time 2025-01-19 18:02:40]-------------------------
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-------------------------[time 2025-07-26 13:59:10]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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Python version 3.13.3
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Spglib version 2.6.1
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----------------------------- General settings -----------------------------
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Run mode: pypolymlp
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py_params.yaml".
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Supercell (dim): [2 2 2]
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@ -190,6 +185,7 @@ Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py_params.yaml".
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Displacement dataset for fc3 was read from "phono3py_params.yaml".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp version 0.12.9
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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@ -202,26 +198,11 @@ Parameters:
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gaussian_params1: (1.0, 1.0, 1)
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gaussian_params2: (0.0, 7.0, 10)
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Developing MLPs by pypolymlp...
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Regression: cholesky decomposition ...
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- alpha: 0.001
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- alpha: 0.01
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- alpha: 0.1
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- alpha: 1.0
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- alpha: 10.0
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Clear training X.T @ X
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Calculate X.T @ X for test data
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Clear test X.T @ X
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Regression: model selection ...
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- alpha = 1.000e-03 : rmse (train, test) = 1.12211e+15 1.12211e+15
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- alpha = 1.000e-02 : rmse (train, test) = 1.12211e+15 1.12211e+15
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- alpha = 1.000e-01 : rmse (train, test) = 0.00002 0.00002
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- alpha = 1.000e+00 : rmse (train, test) = 0.00002 0.00002
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- alpha = 1.000e+01 : rmse (train, test) = 0.00002 0.00002
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MLPs were written into "polymlp.yaml"
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------------------------------ pypolymlp end -------------------------------
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Generate displacements (--rd or -d) for proceeding to phonon calculations.
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2025-01-19 18:03:44]-------------------------
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-------------------------[time 2025-07-26 14:00:12]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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@ -252,14 +233,15 @@ structure file.
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.11.3
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3.18.0
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-------------------------[time 2025-01-19 18:06:46]-------------------------
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-------------------------[time 2025-07-26 14:00:49]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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Python version 3.13.3
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Spglib version 2.6.1
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----------------------------- General settings -----------------------------
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Run mode: pypolymlp + force constants
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py.yaml".
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Supercell (dim): [2 2 2]
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@ -271,6 +253,7 @@ Spacegroup: Fm-3m (225)
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Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py.yaml".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp version 0.12.9
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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@ -279,6 +262,7 @@ Load MLPs from "polymlp.yaml".
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Generate displacements
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Displacement distance: 0.01
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Evaluate forces in 292 supercells by pypolymlp
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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----------------------------- Force constants ------------------------------
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Computing fc3[ 1, x, x ] using numpy.linalg.pinv.
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Displacements (in Angstrom):
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@ -289,16 +273,26 @@ Displacements (in Angstrom):
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[ 0.0100 0.0000 0.0000]
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[-0.0100 0.0000 0.0000]
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Expanding fc3.
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fc3 was symmetrized.
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fc2 was symmetrized.
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Max drift of fc3: 0.000000 (zzz) 0.000000 (zzz) 0.000000 (zzz)
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Max drift of fc2: 0.000000 (zz) 0.000000 (zz)
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Symmetrizing fc3 by symfc projector.
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Symfc version 1.5.3 (https://github.com/symfc/symfc)
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Citation: A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024)
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Symmetrizing fc2 by symfc projector.
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Symfc version 1.5.3 (https://github.com/symfc/symfc)
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Citation: A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024)
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Max drift of fc3: 0.00000000 (zyz) 0.00000000 (yzz) 0.00000000 (yzz)
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Max drift of fc2: -0.00000000 (yy) -0.00000000 (yy)
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fc3 was written into "fc3.hdf5".
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fc2 was written into "fc2.hdf5".
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--------------------------- Calculation settings ---------------------------
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Non-analytical term correction (NAC): True
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NAC unit conversion factor: 14.39965
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BZ integration: Tetrahedron-method
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Temperatures: 0.0 300.0
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Cutoff frequency: 0.01
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Frequency conversion factor to THz: 15.63330
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----------- None of ph-ph interaction calculation was performed. -----------
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2025-01-19 18:06:55]-------------------------
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-------------------------[time 2025-07-26 14:00:58]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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@ -315,29 +309,28 @@ corresponding forces are stored in the `phono3py_mlp_eval_dataset.yaml` file.
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### Steps 5-7: Force constants calculation (random displacements in step 5)
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Random displacements are generated by specifying {ref}`--rd
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<random_displacements_option>` option. To compute force constants with random
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displacements, an external force constants calculator is necessary. By default,
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symfc is used unless another force constants solver is explicitly specified.
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When running with the `--pypolymlp` option, MLPs are read from `polymlp.yaml`
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if the file exists. In this case, training data is no longer required, and files
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such as `phono3py.yaml` can be used as the input structure file.
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<random_displacements_option>` option. When running with the `--pypolymlp`
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option, MLPs are read from `polymlp.yaml` if the file exists. In this case,
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training data is no longer required, and files such as `phono3py.yaml` can be
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used as the input structure file.
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```
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% phono3py-load --pypolymlp --rd 200 phono3py.yaml
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% phono3py-load --pypolymlp --rd auto phono3py.yaml
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.11.3
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3.18.0
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-------------------------[time 2025-01-19 18:13:21]-------------------------
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-------------------------[time 2025-07-26 14:02:24]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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Python version 3.13.3
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Spglib version 2.6.1
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----------------------------- General settings -----------------------------
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Run mode: pypolymlp + force constants
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py.yaml".
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Supercell (dim): [2 2 2]
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@ -349,6 +342,7 @@ Spacegroup: Fm-3m (225)
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Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py.yaml".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp version 0.12.9
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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@ -357,31 +351,34 @@ Load MLPs from "polymlp.yaml".
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Generate random displacements
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Twice of number of snapshots will be generated for plus-minus displacements.
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Displacement distance: 0.01
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Evaluate forces in 400 supercells by pypolymlp
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Evaluate forces in 32 supercells by pypolymlp
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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----------------------------- Force constants ------------------------------
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Symfc will be used to handle general (or random) displacements.
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Type-II dataset for displacements and forces was provided,
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but the selected force constants calculator cannot process it.
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Use another force constants calculator, e.g., symfc,
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to generate force constants.
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Try symfc to handle general (or random) displacements.
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-------------------------------- Symfc start -------------------------------
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Symfc is a force constants calculator. See the following paper:
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A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024).
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Symfc is developed at https://github.com/symfc/symfc.
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Symfc version 1.5.3 (https://github.com/symfc/symfc)
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Citation: A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024)
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Computing [2, 3] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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-------------------------------- Symfc start -------------------------------
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Symfc is a force constants calculator. See the following paper:
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A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024).
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Symfc is developed at https://github.com/symfc/symfc.
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Computing [2] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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Max drift of fc3: -0.000000 (zxz) -0.000000 (xzz) -0.000000 (xzz)
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Max drift of fc2: -0.000000 (yy) -0.000000 (yy)
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Max drift of fc3: -0.00000000 (xyx) -0.00000000 (yxx) -0.00000000 (yxx)
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Max drift of fc2: -0.00000000 (yy) -0.00000000 (yy)
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fc3 was written into "fc3.hdf5".
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fc2 was written into "fc2.hdf5".
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--------------------------- Calculation settings ---------------------------
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Non-analytical term correction (NAC): True
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NAC unit conversion factor: 14.39965
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BZ integration: Tetrahedron-method
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Temperatures: 0.0 300.0
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Cutoff frequency: 0.01
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Frequency conversion factor to THz: 15.63330
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----------- None of ph-ph interaction calculation was performed. -----------
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2025-01-19 18:13:34]-------------------------
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-------------------------[time 2025-07-26 14:02:29]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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@ -389,88 +386,121 @@ Summary of calculation was written in "phono3py.yaml".
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\___|_| |_|\__,_|
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```
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After the MLPs are read, 200 supercells with random directional displacements
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are generated. These displacements are then inverted (such as $\Delta
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\mathbf{u}_i$ and $-\Delta \mathbf{u}_i$ of all atoms $i$ in each supercell),
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resulting in an additional 200 supercells. In total, 400 supercells are created.
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The forces for these supercells are then evaluated. Finally, the force constants
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are calculated using symfc.
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After the MLPs are read, 16 supercells with random directional displacements are
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generated by the option `--rd auto`. These displacements are then inverted (such
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as $\Delta \mathbf{u}_i$ and $-\Delta \mathbf{u}_i$ of all atoms $i$ in each
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supercell), resulting in an additional 16 supercells. In total, 32 supercells
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are created. The forces for these supercells are then evaluated. Finally, the
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force constants are calculated using symfc. The `--rd-auto-factor` option can
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change the number of supercells generated.
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### Command options for force constants calculation
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## Command options for force constants calculation
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After obtaining the MLPs, displacements are generated using those MLPs, and the
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resulting forces are computed accordingly. The displacement distance is set by
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the `--amplitude` option, whose default value is 0.01 Angstrom. When the `--rd`
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option is used, it specifies the number of supercells with random directional
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displacements. Note that to achieve accurate force constants, the actual number
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of generated supercells is twice the specified number. If `--rd` is omitted,
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systematic displacements are introduced.
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After obtaining the MLPs, displacements are generated using these MLPs, and the
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resulting forces are computed. The displacement distance is controlled by the
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`--amplitude` option, with a default value of 0.01 Angstrom. When `-d` is
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specified, systematic displacements are introduced. When the `--rd` option is
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used, it specifies the number of supercells with random directional
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displacements. To ensure accurate force constants, the actual number of
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generated supercells is twice the specified value.
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Once the file `polymlp.yaml` is obtained, force constants can be calculated
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using MLPs from `polymlp.yaml`. After removing the `fc3.hdf5` and `fc2.hdf5`
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files, `phono3py-load` will detect `polymlp.yaml` and then compute the force
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constants by loading the MLPs from `polymlp.yaml` as follows:
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When atoms in the unit cell have positional degrees of freedom within the
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crystal symmetry, the `--relax-atomic-positions` option can relax their
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positions using MLPs. In the `example/AlN-rd` case, the following command
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develops polynomial MLPs and then relaxes atomic positions using these MLPs. The
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force constants are calculated using supercells with 0.005 Angstrom systematic
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displacements.
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```
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% phono3py-load --pypolymlp --rd 100 --amplitude 0.005 phono3py.yaml
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% phono3py-load phonopy_params_mp-661.yaml.xz --pypolymlp --relax-atomic-positions -d
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_ _____
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_ __ | |__ ___ _ __ ___|___ / _ __ _ _
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| '_ \| '_ \ / _ \| '_ \ / _ \ |_ \| '_ \| | | |
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| |_) | | | | (_) | | | | (_) |__) | |_) | |_| |
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| .__/|_| |_|\___/|_| |_|\___/____/| .__/ \__, |
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|_| |_| |___/
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3.11.3
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3.18.0-dev21+ge26f3ecb
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-------------------------[time 2025-01-19 18:19:02]-------------------------
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-------------------------[time 2025-07-26 14:29:16]-------------------------
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Compiled with OpenMP support (max 10 threads).
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Running in phono3py.load mode.
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Python version 3.12.6
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Spglib version 2.5.0
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Python version 3.13.3
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Spglib version 2.6.1
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----------------------------- General settings -----------------------------
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Run mode: pypolymlp + force constants
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HDF5 data compression filter: gzip
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Crystal structure was read from "phono3py.yaml".
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Supercell (dim): [2 2 2]
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Crystal structure was read from "phonopy_params_mp-661.yaml.xz".
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Supercell (dim): [4 4 2]
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Primitive matrix:
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[0. 0.5 0.5]
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[0.5 0. 0.5]
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[0.5 0.5 0. ]
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Spacegroup: Fm-3m (225)
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[1. 0. 0.]
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[0. 1. 0.]
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[0. 0. 1.]
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Spacegroup: P6_3mc (186)
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Use -v option to watch primitive cell, unit cell, and supercell structures.
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NAC parameters were read from "phono3py.yaml".
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NAC parameters were read from "phonopy_params_mp-661.yaml.xz".
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Displacement dataset for fc3 was read from "phonopy_params_mp-661.yaml.xz".
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----------------------------- pypolymlp start ------------------------------
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Pypolymlp version 0.12.9.post0
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Pypolymlp is a generator of polynomial machine learning potentials.
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Please cite the paper: A. Seko, J. Appl. Phys. 133, 011101 (2023).
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Pypolymlp is developed at https://github.com/sekocha/pypolymlp.
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Load MLPs from "polymlp.yaml".
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Parameters:
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cutoff: 8.0
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model_type: 3
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max_p: 2
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gtinv_order: 3
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gtinv_maxl: (8, 8)
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gaussian_params1: (1.0, 1.0, 1)
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gaussian_params2: (0.0, 7.0, 10)
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Developing MLPs by pypolymlp...
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MLPs were written into "polymlp.yaml"
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------------------------------ pypolymlp end -------------------------------
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Generate random displacements
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Twice of number of snapshots will be generated for plus-minus displacements.
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Relaxing atomic positions using polynomial MLPs...
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Change in fractional position and in distance:
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1 N : 0.00000000 0.00000000 -0.00000021 (|d|=0.00000105)
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2 N : 0.00000000 0.00000000 -0.00000021 (|d|=0.00000105)
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3 Al: 0.00000000 0.00000000 0.00000021 (|d|=0.00000105)
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4 Al: 0.00000000 0.00000000 0.00000021 (|d|=0.00000105)
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----------------------------------------------------------------------------
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Generate displacements
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Displacement distance: 0.005
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Evaluate forces in 200 supercells by pypolymlp
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Evaluate forces in 3720 supercells by pypolymlp
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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----------------------------- Force constants ------------------------------
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Symfc will be used to handle general (or random) displacements.
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-------------------------------- Symfc start -------------------------------
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Symfc is a force constants calculator. See the following paper:
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A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024).
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Symfc is developed at https://github.com/symfc/symfc.
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Computing [2, 3] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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-------------------------------- Symfc start -------------------------------
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Symfc is a force constants calculator. See the following paper:
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A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024).
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Symfc is developed at https://github.com/symfc/symfc.
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Computing [2] order force constants.
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Increase log-level to watch detailed symfc log.
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--------------------------------- Symfc end --------------------------------
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Max drift of fc3: -0.000000 (zxz) -0.000000 (xzz) -0.000000 (xzz)
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Max drift of fc2: -0.000000 (yy) -0.000000 (yy)
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Computing fc3[ 1, x, x ] using numpy.linalg.pinv.
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Displacements (in Angstrom):
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[ 0.0050 0.0000 0.0000]
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[-0.0050 0.0000 0.0000]
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[ 0.0000 0.0000 0.0050]
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[ 0.0000 0.0000 -0.0050]
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Computing fc3[ 65, x, x ] using numpy.linalg.pinv.
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Displacements (in Angstrom):
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[ 0.0050 0.0000 0.0000]
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[-0.0050 0.0000 0.0000]
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[ 0.0000 0.0000 0.0050]
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[ 0.0000 0.0000 -0.0050]
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Expanding fc3.
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Symmetrizing fc3 by symfc projector.
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Symfc version 1.5.3 (https://github.com/symfc/symfc)
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Citation: A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024)
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Symmetrizing fc2 by symfc projector.
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Symfc version 1.5.3 (https://github.com/symfc/symfc)
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Citation: A. Seko and A. Togo, Phys. Rev. B, 110, 214302 (2024)
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Max drift of fc3: -0.00000000 (xxz) -0.00000000 (xxz) -0.00000000 (xzx)
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Max drift of fc2: -0.00000000 (xx) -0.00000000 (xx)
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fc3 was written into "fc3.hdf5".
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fc2 was written into "fc2.hdf5".
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--------------------------- Calculation settings ---------------------------
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Non-analytical term correction (NAC): True
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NAC unit conversion factor: 14.39965
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BZ integration: Tetrahedron-method
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Temperatures: 0.0 300.0
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Cutoff frequency: 0.01
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Frequency conversion factor to THz: 15.63330
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----------- None of ph-ph interaction calculation was performed. -----------
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Dataset generated using MLPs was written in "phono3py_mlp_eval_dataset.yaml".
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Summary of calculation was written in "phono3py.yaml".
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-------------------------[time 2025-01-19 18:19:09]-------------------------
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-------------------------[time 2025-07-26 14:39:11]-------------------------
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_
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___ _ __ __| |
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/ _ \ '_ \ / _` |
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@ -478,7 +508,6 @@ Summary of calculation was written in "phono3py.yaml".
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\___|_| |_|\__,_|
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```
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## Parameters for developing MLPs
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A few parameters can be specified using the `--mlp-params` option for the
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Atsushi Togo