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# Bandgap of Si using different DFT+HF methods

## 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