Fitting 2-body repulsive potentials using CCS

When we use the Curvature Constrained Splines method (CCS) to fit a repulsive potential, we fit a 2-body potential to reproduce, as closely as possible, the energy difference between DFT reference energies and the corresponding electronic energies from DFTB.

This example revolves around some of the CCS scripts to handle the various tasks involved in the fitting of a repulsive potential. The data used in this example originates from the paper Towards an efficient f-in-core/f-in-valence switchable description for DFTB calculations of Ce 4f states in ceria.

Data for the f-in-core and f-in-valence approched are located in the folders IN_CORE and IN_VAL, respectively.

Two ASE data-bases, one containing the reference DFT data (computed with VASP) and one containing the corresponding DFTB data are provided in the current example.

Tip

The script RUN can be used to automatically execute the various steps of this example. The scrips can be used as templates when using CCS to fit repulsive potentials for a new system.

0. Install required software

Before we start we need to install CCS. The code is available here . Make sure to add the CCS binary folder, CCS/bin/ , to your path.

1. Collect the DFT en DFTB electroinc energies

Using the script ccs_build_db from the CCS-package, we can build two ase data-bases containing the DFT and DFTB data. These data-bases are used in the next step. We need a list pointing to the DFT data and the corresponding DFTB data. The code assume that the we provide locations of the DFT data (e.g. OUTCAR.gz or any other ASE readable file containing a geometry and corresponding energy) in the first column and the DFTB data in the second column (should be a results.tag file).

Task

* (In this example, this step have allready been performed. The raw-data used is not provided.) *

In order create the data-bases we make a folder (TRAINING_DATA in the current example) with a file pointing to the training-data (list) and the execute the command:

ccs_build_db --mode DFTB --file_list list --DFT_DB DFT.db --DFTB_DB DFTB.db

Example of a list file:

../RAW_DATA/BULK_CeO2/5.20/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.20/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.21/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.21/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.22/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.22/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.23/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.23/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.24/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.24/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.25/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.25/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.26/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.26/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.27/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.27/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.28/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.28/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.29/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.29/DFTB/results.tag
../RAW_DATA/BULK_CeO2/5.30/VASP/OUTCAR    ../RAW_DATA/BULK_CeO2/5.30/DFTB/results.tag

Tip

You can get a quick overview of the training-data using the Atomic Simulation Environment (ASE) by issuing the command:

ase-gui DFT.db

(see figure below)

ase — With the Atomic Simulation Environment we can get an quick overview of the training-data. We can, amongst much other, browse the structures and plot the energies.

Caution

All pairs you intend to make a repulsive potential for must have a dummy spline at the bottom of the it’s skf-file when the DFTB data is generated.

2. Produce the specific training-file for CCS

We collect pair-wise distances from the structures stored in the two data-bases and create a file called structures.json that CCS use for the fitting.

Task

Go to the FITTING folder and execute:

ccs_fetch --mode DFTB --DFT_DB TRAINING_DATA/DFT.db --DFTB_DB TRAINING_DATA/DFTB.db

Caution

Never use a cut-off radius that is smaller than used in the fitting (see next step). The defualt in ccs_fetch is 6.0 Å.

3. Now we can do fitting!

We provide the setting in a file CCS_input.json where we speicify the cut-off radius the resolution of the spline and the type of constraints (rep = stricktly repulsive, sw=attractive at long distance and repulsive at short distance).

CCS_input.json:

{
"Twobody":{
    "Ce-O":{
            "Rcut":5.3,
            "Resolution":0.13,
                "Swtype":"rep",
                "const_type":"Mono"
    }
},

"Onebody":["Ce"],

"Reference":"structures.json",

"General":{
    "interface":"DFTB",
        "merging":"True"
}

}

Task

Check or modify the file CCS_input.json and execute:

ccs_fit

Caution

Rcut must be smaller than the cut-off radius in the previus step!

4. Enjoy succes!(?)

The quallity of the fit is provided in CCS_error.out and the resulting parameters in CCS_params.json.

Tip

You can use the plot_fit.py script in the FITTING folder to get an overview of the fitting quallity.

python plot_fit.py

ase — Correlation plot showing the reuslts of the fitting. The target repulsive energies are given at the x-axis and the resulting repulisive from the fitting is shown at the y-axis.

5. Convert to DFTB+ Slater-Koster format

DFTB+ have a specific format for the 2-body potential, a cubic spline-table appended at the end of the Slater-Koster file. We need to convert the CCS_params.json file to this format.

Task

Execute:

ccs_export_sktable CCS_params.json

The result are printed to files X-Y.spl where X and Y are the corresponding elements in the 2-body potential, e.g X=Ce, Y=O.

Tip

You can use the plot_rep.py script in the FITTING folder to display the resulting Ce-O spline repulsive contained in the file Ce-O.spl .

python plot_rep.py

ase — Comparative plot showing a 2-body spline repulsive for Ce-O fitted to a data-set of 75 structures.

6. Use the new parameters

Replace the dummy-spline in the .skf file contained in the folder SKF-FILES/REFITTED with the data from the .spl file generated in step 5 and you are good to go.

In the folder VALIDATION you can perform a validation of the generated parameters. Two examples are provided:

Cell optimization of bulk ceria (located in the folder: VALIDATION/CELL_OPT)

Phonon spectra of of bulk ceria (located in the folder: VALIDATION/PHONONS)

In order to run these examples you need DFTB+ and phonopy.

Cell optimization of bulk ceria

Task

Go to the folder VALIDATION/CELL_OPT and run dftb by executing the command:

dftb+

The results can be inspected by comparing the files in.gen and Optimized.gen which contains the optimized DFT geometry (the starting point of the DFTB optimization) and the DFTB optimized geometry, respectively.

Note: The dftb_in.hsd file point to the Slater-Koster files contained in the SKF-FILES/REFITTED folder.

Phonon spectra of bulk ceria

Task

Go to the folders VALIDATION/PHONONS/001 and VALIDATION/PHONONS/001 and perform a dftb+ calculation in each of them. To generate the phonon spectra we go to the folder VALIDATION/PHONONS and make use of phonopy by using the following commands:

phonopy -f {001..002}/results.tag --dftb+
phonopy -p band.conf -s --dftb

The reults can visualized using the plot_phonon_spectra.py script which produce a figure like the one shown below.

ase — Comparison of phonon spectra calculated with the parametrized DFTB+ method and VASP.