Equilibrium volume of Si in the RPA: Difference between revisions
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*The {{TAG|INCAR}} file INCAR.EXX is used in this step: | *The {{TAG|INCAR}} file INCAR.EXX is used in this step: | ||
{{TAGBL|ALGO}} = EIGENVAL ; {{TAGBL|NELM}} = 1 | {{TAGBL|ALGO}} = EIGENVAL ; {{TAGBL|NELM}} = 1 | ||
{{TAGBL|LWAVE}} = .FALSE. | {{TAGBL|LWAVE}} = .FALSE. | ||
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{{TAGBL|KPAR}} = 8 | {{TAGBL|KPAR}} = 8 | ||
{{TAGBL|NBANDS}} = 4 | {{TAGBL|NBANDS}} = 4 | ||
*{{TAG|NKRED}}=2 is used for the downsample the k-space representation of the Fock-potential to save time. | *{{TAG|NKRED}}=2 is used for the downsample the k-space representation of the Fock-potential to save time. | ||
*Using {{TAG|NBANDS}}=4 only occupied states are considered to save time. | *Using {{TAG|NBANDS}}=4 only occupied states are considered to save time. | ||
=== Step 3: DFT groundstate calculation with a “coarse” mesh of k-points === | === Step 3: DFT groundstate calculation with a “coarse” mesh of k-points === |
Revision as of 17:13, 24 June 2019
Task
In this example you will calculate the equilibrium lattice constant of Si in the RPA (ACFDT).
The workflow of a 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 DFT 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.
N.B.:To compute the equilibrium lattice constant of Si we need to calculate the RPA total energy for a range of different lattice constants. All of the calculation steps are prepared automatically performed by the script doall.sh (see below):
./doall.sh
This script will perform the following calculations for a range of different lattice constants:
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
- Perform a 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.6):
6x6x6 0 G 6 6 6 0 0 0
Step 4: Obtain DFT "virtual" orbitals (empty states)
- 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. so that VASP calculates 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: calculate the RPA correlation energy (ACFDT)
- 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, the sum of the RPA correlation energy of step 5 EC(RPA) and the Hartree fock energy EXX of step 2.
- To get the Hartree fock energy
grep “free energy”
in the OUTCAR.EXX.* file (there are two spaces between free and energy).
Running this example
The following bash-script doall.sh
will run through all of the aforementioned calculational steps (step 1-5) for a range of different lattice constants (a=5.1-5.8Å in steps of 0.1Å)
# # To run VASP this script calls $vasp_std # (or posibly $vasp_gam and/or $vasp_ncl). # These variables can be defined by sourcing vaspcmd . vaspcmd 2> /dev/null # # When vaspcmd is not available and $vasp_std, # $vasp_gam, and/or $vasp_ncl are not set as environment # variables, you can specify them here [ -z "`echo $vasp_std`" ] && vasp_std="mpirun -np 8 /path-to-your-vasp/vasp_std" [ -z "`echo $vasp_gam`" ] && vasp_gam="mpirun -np 8 /path-to-your-vasp/vasp_gam" [ -z "`echo $vasp_ncl`" ] && vasp_ncl="mpirun -np 8 /path-to-your-vasp/vasp_ncl" # # The real work starts here # for i in 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 ; do cat >POSCAR <<! system Si $i 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 ! # start with a PBE calculation with a lot of k-points (needed for EXX) rm WAVECAR WAVEDER cp KPOINTS.12 KPOINTS cp INCAR.DFT INCAR $vasp_std cp OUTCAR OUTCAR.DFT.$i e1=`awk '/free energy/ {print $5}' OUTCAR` # get the HF energy with PBE orbitals cp INCAR.EXX INCAR $vasp_std e2=`awk '/free energy/ {print $5}' OUTCAR` cp OUTCAR OUTCAR.EXX.$i # now a PBE calculation with less k-points rm WAVECAR WAVEDER cp KPOINTS.6 KPOINTS cp INCAR.DFT INCAR $vasp_std # obtain virtual orbitals cp INCAR.DIAG INCAR $vasp_std cp OUTCAR OUTCAR.DIAG.$i cp WAVECAR WAVECAR.$i cp WAVEDER WAVEDER.$i ## for metals # cp INCAR.HFC INCAR # $vasp_std # # cp OUTCAR OUTCAR.HFC.$i # e3=`awk '/HF-correction/ {print $4}' OUTCAR` # RPA correlation cp INCAR.ACFDT INCAR $vasp_std cp OUTCAR OUTCAR.ACFDT.$i e4=`awk '/converged value/ {print $3}' OUTCAR` # echo $i $e1 $e2 $e3 $e4 >> summary echo $i $e1 $e2 $e4 >> summary done
To execute the aforementions script:
./doall.sh
- When everything is finished you can quickly visualize (with gnuplot) the total energy vs. lattice-constant curves for DFT and RPA by means of:
./plotall.sh
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