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# Bandgap of Si using different DFT+HF methods

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## Contents

Calculation of the band gap in Si using different DFT+HF schemes (PBE, B3LYP, PBE0, HSE06, and HF).

## Input

### POSCAR

System: Si
5.430
0.5 0.5 0.0
0.0 0.5 0.5
0.5 0.0 0.5
1
Cartesian
0    0    0
0.25 0.25 0.25


### INCAR

## Better preconverge with PBE first
## and use the WAVECAR file as inout for the DFT+HF calculation

## Selects the B3LYP hybrid function
#LHFCALC = .TRUE. ; GGA = B3 ; AEXX = 0.2 ; AGGAX = 0.72
#AGGAC = 0.81 ; ALDAC = 0.19
#ALGO = D ; TIME = 0.4

## Selects the PBE0  hybrid function
#LHFCALC = .TRUE. ;
#ALGO = D ; TIME = 0.4

## Selects the HSE06 hybrid function
#LHFCALC = .TRUE. ; HFSCREEN = 0.2 ;
#ALGO = D ; TIME = 0.4

## Selects HF
#LHFCALC = .TRUE. ; AEXX = 1.0 ; ALDAC = 0.0 ; AGGAC = 0
#ALGO = D ; TIME = 0.4

## Leave this in
ISMEAR =  0
SIGMA  =  0.01
GGA    = PE



### KPOINTS

k-points
0
Gamma
6  6  6
0  0  0


### Calculation

• script to extract eigenvalues and calculate the bandgap
homo=awk '/NELECT/ {print $3/2}'$1
lumo=awk '/NELECT/ {print $3/2+1}'$1
nkpt=awk '/NKPTS/ {print $4}'$1

e1=grep "     $homo "$1 | head -$nkpt | sort -n -k 2 | tail -1 | awk '{print$2}'
e2=grep "     $lumo "$1 | head -$nkpt | sort -n -k 2 | head -1 | awk '{print$2}'

echo "HOMO: band:" $homo " E="$e1
echo "LUMO: band:" $lumo " E="$e2

type
./gap.sh OUTCAR


For each HF+DFT method (B3LYP, PBE0, HSE06, and HF) compute the bandgap of Si
adopting the following procedure:

i) Perform a standard PBE calculation
ii) Perform a HF+DFT run (VASP reads in the WAVECAR from run (i)
iii) Calculate the value of the bandgap by running the script 'gap':
bandgap = min(cband) - max(vband)