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 NaCl. We need the input files, the pseudopotentials and a script

NaCl.in

 &control
    calculation = 'scf'
    tprnfor = .true.
    tstress = .true.
    pseudo_dir = '/home/togo/espresso/pseudo/'
 /
 &system
    ibrav = 0
    nat = 8
    ntyp = 2
    ecutwfc = 70.0
 /
 &electrons
    diagonalization = 'david'
    conv_thr = 1.0d-9
 /
ATOMIC_SPECIES
 Na  22.98976928 Na.pbe-spn-kjpaw_psl.1.0.0.UPF
 Cl  35.453      Cl.pbe-n-rrkjus_psl.0.1.UPF
ATOMIC_POSITIONS crystal
 Na   0.0000000000000000  0.0000000000000000  0.0000000000000000
 Na   0.0000000000000000  0.5000000000000000  0.5000000000000000
 Na   0.5000000000000000  0.0000000000000000  0.5000000000000000
 Na   0.5000000000000000  0.5000000000000000  0.0000000000000000
 Cl   0.5000000000000000  0.5000000000000000  0.5000000000000000
 Cl   0.5000000000000000  0.0000000000000000  0.0000000000000000
 Cl   0.0000000000000000  0.5000000000000000  0.0000000000000000
 Cl   0.0000000000000000  0.0000000000000000  0.5000000000000000
CELL_PARAMETERS angstrom
 5.6903014761756712 0 0
 0 5.6903014761756712 0
 0 0 5.6903014761756712
K_POINTS automatic
 8 8 8 1 1 1

Pseudopotentials

Na.pbe-spn-kjpaw_psl.1.0.0.UPF

Cl.pbe-n-rrkjus_psl.0.1.UPF

To download the PP click on the right of the mouse and choose Save Page As

Script ph.sh

#!/bin/bash

# Creating different directories for different displacements

N=$(ls NaCl-*.in | wc -l)
echo $N

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

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

(
     cd disp-$d
     
     cp ../NaCl-$d.in NaCl-$d.in
     cp ../Na.pbe-spn-kjpaw_psl.1.0.0.UPF Na.pbe-spn-kjpaw_psl.1.0.0.UPF
     cp ../Cl.pbe-n-rrkjus_psl.0.1.UPF Cl.pbe-n-rrkjus_psl.0.1.UPF
     
#mpirun -np 4 pw.x -i NaCl-$d.in |& tee NaCl-$d.out  # for parallel calculation
pw.x -i NaCl-$d.in |& tee NaCl-$d.out  # for serial calculation
      
      cd ..
)

done

Calculation

1- Creation of displacement Struct files

% conda activate phonopy

(phonopy) % phonopy --qe -c NaCl.in -d --dim="2 2 2"

In this example, 2x2x2 supercells are created. supercell.in and supercell-xxx.in (xxx are numbers) give the perfect supercell and supercells with displacements, respectively. In the case of the NaCl example, two files supercell-001.in and supercell-002.in are created. In these supercell files, lines only relevant to crystal structures are given. phonopy_disp.yaml is also generated, which contains information about supercell and displacements.

To make QE-PW input files, necessary setting information is added to supercell-xxx.in files, e.g., by:

(phonopy) % for i in {001,002};do cat header.in supercell-$i.in >| NaCl-$i.in; done

where header.in is specially made for this NaCl 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.in

 &control
    calculation = 'scf'
    tprnfor = .true.
    tstress = .true.
    pseudo_dir = '/home/togo/espresso/pseudo/'
    disk_io = 'none'
 /
 &system
    ibrav = 0
    nat = 64
    ntyp = 2
    ecutwfc = 70.0
 /
 &electrons
    diagonalization = 'david'
    conv_thr = 1.0d-9
 /
K_POINTS automatic
 2 2 2  1 1 1

2- Phonon calculations

chmod +x ph.sh

./ph.sh

3- Calculation of sets of forces

(phonopy) % phonopy --qe -f disp-001/NaCl-001.out disp-002/NaCl-002.out

Here .out files are the output of the PW calculations and are supposed to contain the forces on atoms calculated by PW. The disp.yaml file has to be put in the current directory.

Post-process

In the post-process,

Force constants are calculated from the sets of forces
A part of dynamical matrix is built from the force constants
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:

DIM = 2 2 2
PRIMITIVE_AXIS = 0.0 0.5 0.5  0.5 0.0 0.5  0.5 0.5 0.0
BAND = 0.0 0.0 0.0  0.5 0.0 0.0  0.5 0.5 0.0  0.0 0.0 0.0  0.5 0.5 0.5

The band structure is plotted by:

(phonopy) % phonopy --qe -c NaCl.in -p band.conf

Non-analytical term correction (Optional)

To activate non-analytical term correction, BORN (optional) is required. This file contains the information of Born effective charge and dielectric constant.

BORN

default value
2.472958201 0 0 0 2.472958201 0 0 0 2.472958201
1.105385 0 0 0 1.105385 0 0 0 1.105385
-1.105385 0 0 0 -1.105385 0 0 0 -1.105385

Non-analytical term correction can be applied using --nac option by

% phonopy --qe --nac -c NaCl.in -p band.conf

BORN file is created running DFPT calculation using ph.x (phonon) code in the quantum espresso package. The details of howto are found in the phonopy documentation. The input and output files of the ph.x DFPT calculation are NaCl.ph.in and NaCl.ph.out.