How to calculate the band gap using PBE and PBE0 methods

In this tutorial we will calculate the band gap of the Si compound using the PBE functional and the PBE0 functional.

We need the the 4 input files: POSCAR     INCAR    KPOINTS  POTCAR

 

PBE Calculation

POSCAR

fcc Si:
 3.9
 0.5 0.5 0.0
 0.0 0.5 0.5
 0.5 0.0 0.5
   1
cartesian
0 0 0

     Fcc Si lattice constant of 3.9  .
    1 atom per unit cell.

 

INCAR

SYSTEM = cd Si PBE

GGA    = PE

ISMEAR = -5
LORBIT = 11

    Initial charge density form overlapping atoms.
    Energy cutoff of 240 eV from POTCAR file.
 

KPOINTS

k-points
 0
Monkhorst Pack
 11 11 11
 0  0  0

 

POTCAR

Download the pseudopotential file from this link POTCAR

The POTCAR contain the PBE functional as follows:

PAW_PBE Si 05Jan2001
 4.00000000000000000
 parameters from PSCTR are:
   VRHFIN =Si: s2p2
   LEXCH  = PE
   EATOM  =   103.0669 eV,    7.5752 Ry

   TITEL  = PAW_PBE Si 05Jan2001

 

NB: you can download the input files from fccSi.tgz

 

Execution

~/Si-gap/gap-pbe$> vasp_std    ---> for serial calculation

~/Si-gap/gap-pbe$> mpirun -np 4 vasp_std    ---> for parallel calculation

 

 PBE0 Calculation

We need to modify only the INCAR as follows:

 

SYSTEM  = cd Si PBE0

GGA     = PE
LHFCALC = T

ISMEAR  = 0
SIGMA   = 0.01

ALGO    = Damped
TIME    = 0.8

 LHFCALC means that the PBE0 functional is calculated from the PBE functional as follows:

So, we will use the same POTCAR file for PBE calculation.

 

Execution

~/Si-gap/gap-pbe0$> vasp_std    ---> for serial calculation

~/Si-gap/gap-pbe0$> mpirun -np 4 vasp_std    ---> for parallel calculation

 

Analysis

To read the band gap value from the DOSCAR file we need to script called bandgap.py from the following package:

git clone https://github.com/jeffwdoak/vasp_scripts  

We need to copy the script  bandgap.py to the folder named tools created in the vasp folder as follows:

/vasp.5.4.1$ ls

arch  bin  build  makefile  makefile.include  README  src  tools 

The folder tools is configured in the  ~/.bashrc file as follows:

VASPBIN=/home/algerien1970/abinitio/vasp.5.4.1/bin
export PATH=$PATH:$VASPBIN
VASPTOOLS=/home/algerien1970/abinitio/vasp.5.4.1/tools
export PATH=$PATH:$VASPTOOLS

Now we execute the script from the 2 folders as follows:

/Si-gap/gap-pbe$ bandgap.py

 Gap, VBM, CBm
0.748 5.522 6.27

/Si-gap/gap-pbe0$ bandgap.py

Gap, VBM, CBm
1.876 4.957 6.833 

 

Reference: https://www.vasp.at/tutorials/latest/hybrids/part1/