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.

Step 5

• The RPA correlation energy (ACFDT) calculation.
• The following INCAR file is used in this step (INCAR.ACFDT):

ALGO = ACFDT
NBANDS = 64
ISMEAR = 0 ; SIGMA = 0.05

• In OUTCAR.ACFDT.X.X one finds the RPA correlation energy, e.g.:

       cutoff energy      smooth cutoff    RPA   correlation   Hartree contr. to MP2
---------------------------------------------------------------------------------
            163.563            130.851       -10.7869840331      -19.0268026572
            155.775            124.620       -10.7813600055      -19.0200457142
            148.357            118.685       -10.7744584182      -19.0118291822
            141.292            113.034       -10.7659931963      -19.0017871991
            134.564            107.651       -10.7555712745      -18.9894197881
            128.156            102.525       -10.7428704760      -18.9742991317
            122.054             97.643       -10.7273118140      -18.9556871679
            116.241             92.993       -10.7085991597      -18.9331679971

linear regression converged value -10.9079580568 -19.1711146204

• Take the “converged value”, in this case: EC(RPA) = -10.9079580568eV (an approximate “infinite basis set” limit).
• This calculations needs the orbitals (WAVECAR file) and the derivative of the orbitals w.r.t. the Bloch wavevectors (WAVEDER file) written in Step 4.
• The RPA total energy is calculated as the, E(RPA)=EC(RPA)+EXX sum of the RPA correlation energy of step 5 EC(RPA) and the Hartree fock energy EXX. To get the Hartree fock energy grep “free energy” in the OUTCAR.EXX.* file (there are two spaces between free and energy).
• The sample output for the total energy vs volume curves for DFT and RPA should look like the following:

File:Fig ACFDT 1.png

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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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