How to calculate the Phonon Band Structure using the Phonopy code

 

Phonopy code is developped to calculate the phonon and thermal properties plus some other functionalities.

To install the code click on the following link:

How to install Phonopy Code to calculate Phonon and Thermal properties

 

 We will calculate the Band structure of Silicon. We need the input files, the pseudopotentials and a script 

 Si.fdf

SystemName          silicon
SystemLabel         Si

NumberOfSpecies     1

%block ChemicalSpeciesLabel
 1  14  Si
%endblock ChemicalSpeciesLabel

PAO.BasisSize       sz

MeshCutoff         400.0 Ry

MaxSCFIterations    50
DM.MixingWeight      0.2
DM.NumberPulay       3
DM.Tolerance         1.d-4
DM.UseSaveDM

SolutionMethod       diagon

WriteForces          .true.

ElectronicTemperature  100 K

AtomicCoordinatesFormat  Fractional


%block kgrid_Monkhorst_Pack
   8   0   0  0.0
   0   8   0  0.0
   0   0   8  0.0
%endblock Kgrid_Monkhorst_Pack


NumberOfAtoms       2
LatticeConstant     5.430 Ang
%block LatticeVectors
  0.000  0.500  0.500
  0.500  0.000  0.500
  0.500  0.500  0.000
%endblock LatticeVectors

%block AtomicCoordinatesAndAtomicSpecies
    0.00    0.00    0.00   1 #  Si  1
    0.25    0.25    0.25   1 #  Si  2
%endblock AtomicCoordinatesAndAtomicSpecies

Pseudopotential

Si.psf

Script force.sh

#!/bin/bash

# Creating different directories for different displacements

N=$(ls Si-*.fdf | wc -l)
echo $N

for s in $(eval echo "{001..$N}")

do
    d=${s%%.fdf}
    
    mkdir disp-$d

(
     cd disp-$d
     cp ../supercell-$d.fdf supercell-$d.fdf
     cat ../header-supercell > Si-$d.fdf
     echo "LatticeConstant 1.0 Bohr">> Si-$d.fdf
     echo "%include supercell-$d.fdf" >> Si-$d.fdf
     cp ../Si.psf Si.psf
     
siesta < Si-$d.fdf
      
      cd ..
)

done

 

Calculation

1- Creation of displacement Struct files

% conda activate phonopy

(phonopy) % phonopy --siesta -c Si.fdf -d --dim="3 3 3"

A perfect 3x3x3 supercell (supercell.fdf) and one 3x3x3 supercells (supercell-xxx.in) of the conventional unit cell written in Si.fdf are created. In addition, disp.yaml file is created.

To make SIESTA input files, necessary setting information is added to supercell-xxx.fdf files, e.g., by executing the script force.sh. and file header-supercell ,

where header-supercell is specially made for this Si example. This setting is of course dependent on systems and has to be written for each interested system. Note that supercells with displacements must not be relaxed in the force calculations, because atomic forces induced by a small atomic displacement are what we need for phonon calculation.

 

header-supercell

SystemName          silicon
SystemLabel         Si

NumberOfSpecies     1

%block ChemicalSpeciesLabel
 1  14  Si
%endblock ChemicalSpeciesLabel

PAO.BasisSize       sz

MeshCutoff         400.0 Ry

MaxSCFIterations    50
DM.MixingWeight      0.2
DM.NumberPulay       3
DM.Tolerance         1.d-4
DM.UseSaveDM

SolutionMethod       diagon

WriteForces          .true.

ElectronicTemperature  100 K

AtomicCoordinatesFormat  Fractional

%block kgrid_Monkhorst_Pack
   3   0   0  0.0
   0   3   0  0.0
   0   0   3  0.0
%endblock Kgrid_Monkhorst_Pack

 

2- Phonon calculations

chmod +x force.sh

./force.sh 

 

3- Calculation of sets of forces

After force calculation with the crystal structure in supercell-001.fdf, it is needed to create FORCE_SETS file by 

(phonopy) % phonopy --siesta -f disp-001/Si.FA

Here the .FA file contains the forces on atoms calculated by Siesta. The disp.yaml file has to be put in the current directory.

 

Post-process

In the post-process,

1. Force constants are calculated from the sets of forces

2. A part of dynamical matrix is built from the force constants

3. Phonon frequencies and eigenvectors are calculated from the dynamical matrices with the specified q-points.

   
   

Band structure is calculated with the following setting file named, e.g., band.conf by:

ATOM_NAME = Si O
DIM =  3 3 3
BAND_POINTS = 100
BAND = 1/2 1/2 1/2  0.0 0.0 0.0  0.0 1/2 1/2  1.0 1.0 1.0

The band structure is plotted by:

(phonopy) % phonopy --siesta -c Si.fdf -p band.conf