Force constants calculation with random displacements of atoms

Force constants calculation with random displacements of atoms#

Random displacements and corresponding forces in supercells can be employed as a displacement-force dataset for computing force constants. This requires an external force constants calculator, e.g., symfc or ALM. Here, examples are presented with using symfc that can be installed via pip or conda easily.

Generation of random directional displacements#

The option --rd NUM is used instead of -d in generating displacements as follows:

% phono3py --rd 100 --dim 2 2 2 --pa auto -c POSCAR-unitcell

NUM means the number of supercells with random directional displacements. This must be specified, and the initial guess may be from around the number of supecells generated for the systematic displacements by -d. In the case of the NaCl-rd example, 146 supercells are generated with -d, so similar number --rd 100 was chosen here.

If random directional displacements for fc2 are expected, --rd-fc2 and --dim-fc2 have to be specified:

% phono3py --rd 100 --dim 2 2 2 --rd-fc2 2 --dim-fc2 4 4 4 --pa auto -c POSCAR-unitcell

where --dim is necessary but --rd is not.

Create FORCES_FC3 and FORCES_FC2#

FORCES_FC3 and optionally FORCES_FC2, which contains forces corresponding to displacements, can be created by

% phono3py --cf3 vasprun_xmls/vasprun-00{001..100}.xml

Here it is assumed that the forces were calculated by VASP, and the output files (vasprun.xml) are stored in vasprun_xmls directory after renaming. When running this command, phono3py_disp.yaml is automatically read. For the different file name, e.g. phono3py_disp_rd.yaml, it is specified with -c option:

% phono3py -c phono3py_disp_rd.yaml --cf3 vasprun_xmls/vasprun-00{001..100}.xml

FORCES_FC2 is created similarly, e.g., from the VASP output stored as vasprun_xmls/vasprun-ph000{1,2}.xml,

% phono3py --cf2 vasprun_xmls/vasprun-ph000{1,2}.xml

Create phono3py_params.yaml#

Instead of creating FORCES_FC3 and FORCES_FC2, more convenient data file to store displacement-force dataset is created by --sp option:

% phono3py --cf3 vasprun_xmls/vasprun-00{001..100}.xml --cf2 vasprun_xmls/vasprun-ph0000{1,2}.xml --sp

The advantage to employ phono3py_params.yaml is that this file can contain all the information required to run phono3py such as crystal structure, supercell information, displacements, forces, and parameters for non-analytical term correction. This file is immediately usable for phono3py-load command (phono3py-load command).

Calculation of force constants#

If phono3py_disp.yaml is located in current directory, force constants are calculated from FORCES_FC3 (and optionally FORCES_FC2) and phono3py_disp.yaml by

% phono3py-load --symfc -v

or

% phono3py-load phono3py_params.yaml --symfc -v

Similarly, it is performed by also using phono3py command,

% phono3py --symfc -v

or with phono3py_params.yaml

% phono3py -c phono3py_params.yaml --symfc -v

Cutoff pair-distance for fc3 calculation#

The number of supercells required for calculating fc3 depends on crystal structure, crystal symmetry, and supercell size. For larger supercells, the number can be very large. In addition, the required computational time and memory space can also become large. In such case, it may be good to consider introducing cutoff distance for pairs of atoms. It is performed by --fc-calc-opt option as

% phono3py-load --symfc -v --fc-calc-opt "cutoff=8"

The shortcut of --fc-calc-opt "cutoff=8" is --cutoff-pair 8.

The convergence of fc3 has to be checked. With the same input of displacement-force dataset, calculated force constants gradually converge by increasing cutoff pair-distance. The convergence may be checked by lattice thermal conductivity, but it may depend on quantity that is expected to be calculated.