Equilibrium volume of Si in the RPA

From VASP Wiki

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

  • To Compute the Hartree-Fock energy using DFT orbitals we need the (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:

Download

Si_ACFDT_vol.tgz

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