Equilibrium volume of Si in the RPA

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Task

Calculation of the equilibrium lattice constant of Si in the RPA (ACFDT).

Input

POSCAR

system Si
  5.8
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

Calculation

The workflow of RPA total energy calculations consists of five consecutive steps:

• Step 1: a “standard” DFT groundstate calculation with a “dense” mesh of k-points.
• Step 2: compute the Hartree-Fock energy using the orbitals of Step 1. Needs WAVECAR file from step 1.
• Step 3: a “standard” DFT groundstate calculation with “coarse” mesh of k-points.
• Step 4: obtain DFT “virtual” orbitals (empty states). Needs WAVECAR file from step 3.
• Step 5: the RPA correlation energy (ACFDT) calculation. Needs WAVECAR and WAVEDER files from step 4.

In case of metallic systems there is an additional step between Steps 4 and 5, that is beyond the scope of this example.

All of the calculation steps are prepared in the script doall.sh.

Step 1

• DFT groundstate calculation with a “dense” mesh of k-points
• The following INCAR file is used (INCAR.DFT):

ISMEAR = 0 ; SIGMA = 0.05
EDIFF = 1E-8

• The following KPOINTS file is used (KPOINTS.12):

12x12x12
 0
G
 12 12 12
  0  0  0

Step 2

• Compute the Hartree-Fock energy using the DFT orbitals (WAVECAR) of Step 1.
• The INCAR file INCAR.EXX is used in this step:

ALGO = EIGENVAL ; NELM = 1
LWAVE = .FALSE.
LHFCALC = .TRUE.
AEXX = 1.0 ; ALDAC = 0.0 ; AGGAC = 0.0
NKRED = 2
ISMEAR = 0 ; SIGMA = 0.05
KPAR = 8
NBANDS = 4

• NKRED=2 is used for the downsample the k-space representation of the Fock-potential to save time.
• Using NBANDS=4 only occupied states are considered to save time.

Step 3

• DFT groundstate calculation with a “coarse” mesh of k-points.
• The following INCAR file is used (INCAR.DFT):

ISMEAR = 0 ; SIGMA = 0.05
EDIFF = 1E-8

• The following coarse KPOINTS file is used (KPOINTS.12):

6x6x6
 0
G
  6  6  6
  0  0  0

Step 4

• Obtain DFT "virtual" orbitals (empty states).
• The following INCAR file is used in this step (INCAR.DIAG):

ALGO = Exact
NBANDS = 64
NELM = 1
LOPTICS = .TRUE.
ISMEAR = 0 ; SIGMA = 0.05 

• In this step one needs to set LOPTICS=.TRUE. to have VASP calculate the derivative of the orbitals w.r.t. the Bloch wavevector (stored in the WAVEDER file). These are needed to correctly describe the long-wavelength limit of the dielectric screening.
• We use exact diagonalization (ALGO=Exact) and keep 64 bands after diagonalization (NBANDS=64).
• This calculations needs the orbitals (WAVECAR file) written in Step 3.

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Used INCAR Tags

AEXX, AGGAC, ALDAC, ALGO, EDIFF, ISMEAR, KPAR, LHFCALC, LOPTICS, LWAVE, NBANDS, NELM, NKRED, NOMEGA, SIGMA, SYSTEM

Download

Si_ACFDT_vol.tgz

Overview > bandgap of Si in GW > bandstructure of Si in GW (VASP2WANNIER90) > bandstructure of SrVO3 in GW  > CRPA of SrVO3  > Equilibrium volume of Si in the RPA > List of tutorials

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