Si HSE bandstructure

Description: Bandstructure for Si within DFT+HF

Bandstructure in VASP can be obtained following three different procedures. The standard procedure (procedure 1),

applicable at PBE level, is also described in Fcc Si bandstructure example.

Within Hybrid functional theory it is possible to plot bandstructure using procedure 2 or 3.

Procedure 1: Standard procedure (suitable for DFT calculations)

Only possible within DFT. Described in Fcc Si bandstructure example:

Standard self-consistent (SC) run

• POSCAR

system Si
5.430
0.5 0.5 0.0
0.0 0.5 0.5
0.5 0.0 0.5
2
cart
0.00 0.00 0.00
0.25 0.25 0.25

• INCAR (see INCAR.dft)

ISMEAR =  0
SIGMA  =  0.01
NBANDS = 8

• KPOINTS (see KPOINTS.6)

6x6x6
 0
G
 6 6 6
 0 0 0

Non-SC calculation (ICHARG=11)

Use preconverged CHGCAR file and a suitable KPOINTS file

• INCAR

ISMEAR =  0
SIGMA  =  0.01
NBANDS = 8
    
ICHARG = 11 #read charge from CHGCAR and keep fixed
LORBIT = 11

• KPOINTS (see KPOINTS_PBE_bands)

k-points for bandstructure L-G-X-U K-G
 10
line
reciprocal
  0.50000  0.50000  0.50000    1
  0.00000  0.00000  0.00000    1

  0.00000  0.00000  0.00000    1
  0.00000  0.50000  0.50000    1

  0.00000  0.50000  0.50000    1
  0.25000  0.62500  0.62500    1

  0.37500  0.7500   0.37500    1
  0.00000  0.00000  0.00000    1

Plot using p4v

P4VASP: p4v

Procedure 2: 0-weight (Fake) SC procedure (works DFT & hybrid functionals)

This procedure can be applied to compute bandstructure at hybrid functionals and DFT level (see the HSE_bandstructure.sh script).

Standard DFT run

Just as before

• INCAR (see INCAR.dft)

ISMEAR =  0
SIGMA  =  0.01
NBANDS = 8

• KPOINTS (see KPOINST.6)

6x6x6
 0
G
 6 6 6
 0 0 0

Hybrid calculation using a suitably modified KPOINTS file

• INCAR (see INCAR.hse)

ISMEAR =  0
SIGMA  =  0.01
    
LHFCALC = .TRUE. ; HFSCREEN = 0.2 ; AEXX = 0.25
ALGO = D ; TIME = 0.4 ; LDIAG = .TRUE. 
    
EDIFF = 1.E-6
    
NBANDS = 8

• KPOINTS (see KPOINTS_HSE_bands.6 and README.txt)

Automatically generated mesh
      26
Reciprocal lattice
    0.00000000000000    0.00000000000000    0.00000000000000             1
    0.16666666666667    0.00000000000000    0.00000000000000             8
    0.33333333333333    0.00000000000000    0.00000000000000             8
    0.50000000000000    0.00000000000000    0.00000000000000             4
    0.16666666666667    0.16666666666667    0.00000000000000             6
    0.33333333333333    0.16666666666667    0.00000000000000            24
    0.50000000000000    0.16666666666667    0.00000000000000            24
   -0.33333333333333    0.16666666666667    0.00000000000000            24
   -0.16666666666667    0.16666666666667    0.00000000000000            12
    0.33333333333333    0.33333333333333    0.00000000000000             6
    0.50000000000000    0.33333333333333    0.00000000000000            24
   -0.33333333333333    0.33333333333333    0.00000000000000            12
    0.50000000000000    0.50000000000000    0.00000000000000             3
    0.50000000000000    0.33333333333333    0.16666666666667            24
   -0.33333333333333    0.33333333333333    0.16666666666667            24
   -0.33333333333333    0.50000000000000    0.16666666666667            12
0.00000000 0.00000000 0.00000000 0.000
0.00000000 0.05555556 0.05555556 0.000
0.00000000 0.11111111 0.11111111 0.000
0.00000000 0.16666667 0.16666667 0.000
0.00000000 0.22222222 0.22222222 0.000
0.00000000 0.27777778 0.27777778 0.000
0.00000000 0.33333333 0.33333333 0.000
0.00000000 0.38888889 0.38888889 0.000
0.00000000 0.44444444 0.44444444 0.000
0.00000000 0.50000000 0.50000000 0.000

Please note that step two requires a WAVECAR obtained from a standard DFT run (not an HSE calculation), otherwise the resulting conduction bands often have a zig-zag structure.

Plot using p4v

P4VASP: p4v

Mind: Zoom in on the right-side part of the bandstructure plot.

Procedure 3: VASP2WANNIER90 (works for DFT, hybrid functionals, and GW)

Wannier function interpolation using the VASP2WANNIER90 interface: this procedure is applicable to DFT, hybrid functionals, and GW bandstructure calculations. Here we apply it for a hybrid functional. For GW see the Bandstructure of Si in GW (VASP2WANNIER90) and bandstructure of SrVO3 in GW examples.

To see a summary of the workflow below, have a look at the HSE_bandstructure_with_wannier90.sh.

Standard DFT run

Just as before

• INCAR (see INCAR.dft)

ISMEAR =  0
SIGMA  =  0.01
NBANDS = 8

• KPOINTS (see KPOINST.6)

6x6x6
 0
G
 6 6 6
 0 0 0

Increase the number of states to 24

This step is optional.

• INCAR (see INCAR.diag)

ISMEAR =  0
SIGMA  =  0.01
     
ALGO = Exact
NELM = 1
     
NBANDS = 24

HSE + LWANNIER90 run

Run the hybrid functional calculation and call wannier90 (see LWANNIER90_RUN). .

• INCAR (see INCAR.hse_with_wannier90)

ISMEAR =  0
SIGMA  =  0.01
     
LHFCALC = .TRUE. ; HFSCREEN = 0.2 ; AEXX = 0.25
ALGO = D ; TIME = 0.4 ; LDIAG = .TRUE. 
NKRED = 2
    
EDIFF = 1.E-6
    
NBANDS = 24
    
LWANNIER90_RUN = .TRUE.

You will have to provide some instructions for wannier90 as well:

• wannier90.win (see wannier90.win_start)

num_wann=18
num_bands=24

Begin Projections
Si:s ; p ; d
End Projections

#dis_froz_max=9
dis_num_iter=100

#guiding_centres=true

bands_plot      =  true
begin kpoint_path
L 0.50000  0.50000 0.5000 G 0.00000  0.00000 0.0000
G 0.00000  0.00000 0.0000 X 0.50000  0.00000 0.5000
X 0.50000  0.00000 0.5000 K 0.37500 -0.37500 0.0000
K 0.37500 -0.37500 0.0000 G 0.00000  0.00000 0.0000
end kpoint_path
bands_num_points 40
bands_plot_format gnuplot xmgrace

Mind: If the wannier90.win file does not exist VASP will create a default wannier90.win compatible with the POSCAR and INCAR files, which needs to be suitably modified by including the proper instruction required to generate the maximally localized wannier functions (refer to the WANNIER90 manual).

Plot bandstructure (Wannier interpolation) using XMGRACE or GNUPLOT

If all went well, wannier90 will have generated the following bandstructure files which can be visualized using xmgrace or gnuplot:

• wannier90_band.agr

xmgrace ./wannier90_band.agr

• wannier90_band.dat

• wannier90_band.gnu

gnuplot -persist ./wannier90_band.gnu

N.B.: Most modern versions of gnuplot will respond with an error message unless you remove the first line of wannier90_band.gnu (some deprecated syntax issue).

Download

Si_HSE_band.tgz

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