CRPA of SrVO3: Difference between revisions

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{{Template:gw}}
{{Template:GW - Tutorial}}
The following tutorial describes how to perform CRPA calculations, which is available as of VASP 6.
== Task ==  
== Task ==  
 
Calculation of the Coulomb matrix elements <math>U_{ijkl}(\omega=0)</math> in the constrained Random Phase Approximation ([[Constrained Random Phase Approximation|CRPA]]) of SrVO<sub>3</sub> between the Vanadium t<sub>2g</sub> states.
Calculation of the Coulomb matrix elements U<sub>ijkl</sub> in the constrained Random Phase Approximation ([[Constrained Random Phase Approximation|CRPA]]) of SrVO<sub>3</sub>.
----
----


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The easiest way to run this example is to execute:
The easiest way to run this example is to execute:
  ./doall.sh
  ./doall.sh
And compare the output of the different steps (DFT, GW, HSE) by:
./plotall.sh


In any case, one can consider the <tt>doall.sh</tt> script to be an overview of the steps described below.
In any case, one can consider the <tt>doall.sh</tt> script to be an overview of the steps described below.
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*{{TAG|INCAR}} (see INCAR.DFT)
*{{TAG|INCAR}} (see INCAR.DFT)
   
   
  {{TAGBL|SYSTEM}}  = SrVO3                       # system name
  {{TAGBL|SYSTEM}}  = SrVO3   # system name
  {{TAGBL|NBANDS}} = 36                           # small number  of bands
  {{TAGBL|NBANDS}} = 36       # small number  of bands
  {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
  {{TAGBL|ISMEAR}} = 0         # Gaussian smearing
  {{TAGBL|EDIFF}} = 1E-8                           # high precision for groundstate calculation
  {{TAGBL|EDIFF}} = 1E-8       # high precision for groundstate calculation
  {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
  {{TAGBL|KPAR}} = 2           # parallelization of k-points in two groups


Copy the aforementioned file to {{TAG|INCAR}}:
Copy the aforementioned file to {{TAG|INCAR}}:
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The {{TAG|KPOINTS}} file describes how the first Brillouin zone is sampled.
The {{TAG|KPOINTS}} file describes how the first Brillouin zone is sampled.
In the first step we use a uniform k-point sampling:
In the first step we use a uniform k-point sampling:
*{{TAG|KPOINTS}} (see KPOINTS.BULK)
*{{TAG|KPOINTS}}
<pre>
<pre>
Automatically generated mesh
Automatically generated mesh
      0
0
Gamma
Gamma
  4 4 4
  4 4 4
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'''Mind''': this is definitely not dense enough for a high-quality description of SrVO<sub>3</sub>, but in the interest of speed we will live with it.
'''Mind''': this is definitely not dense enough for a high-quality description of SrVO<sub>3</sub>, but in the interest of speed we will live with it.
Copy the aforementioned file to {{TAG|KPOINTS}}:
cp KPOINTS.BULK KPOINTS


and run VASP. If all went well, one should obtain a {{TAG|WAVECAR}} file containing the PBE wavefunction.
Run VASP. If all went well, one should obtain a {{TAG|WAVECAR}} file containing the PBE wavefunction.


== Obtain DFT virtual orbitals and long-wave limit ==
== Obtain DFT virtual orbitals and long-wave limit ==
Use following {{TAG|INCAR}} file to increase the number of virtual states and to determine the long-wave limit of the polarizability (stored in {{TAG|WAVEDER}}):
Use following {{TAG|INCAR}} file to increase the number of virtual states and to determine the long-wave limit of the polarizability (stored in {{TAG|WAVEDER}}):


*{{TAG|INCAR}} (see INCAR.DIAG)
*{{TAG|INCAR}} (see INCAR.PBE)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                         # system name
  {{TAGBL|SYSTEM}} = SrVO3     # system name
  {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
  {{TAGBL|ISMEAR}} = 0         # Gaussian smearing
  {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
  {{TAGBL|KPAR}} = 2           # parallelization of k-points in two groups
  {{TAGBL|ALGO}} = Exact                           # exact diagonalization
  {{TAGBL|ALGO}} = Exact       # exact diagonalization
  {{TAGBL|NELM}} = 1                               # one electronic step suffices, since WAVECAR from previous step is present
  {{TAGBL|NELM}} = 1           # one electronic step suffices, since WAVECAR from previous step is present
  {{TAGBL|NBANDS}} = 96                           # need for a lot of bands in GW
  {{TAGBL|NBANDS}} = 96       # need for a lot of bands in GW
  {{TAGBL|LOPTICS}} = .TRUE.                       # we need d phi/ d k  for GW calculations for long-wave limit
  {{TAGBL|LOPTICS}} = .TRUE.   # we need d phi/ d k  for GW calculations for long-wave limit


Restart VASP.
Restart VASP.
At this stage it is a good idea to make a safety copy of the {{TAG|WAVECAR}} and {{TAG|WAVEDER}} files since we will repeatedly need them in the calculations that follow:  
At this stage it is a good idea to make a safety copy of the {{TAG|WAVECAR}} and {{TAG|WAVEDER}} files since we will repeatedly need them in the calculations that follow:  
  cp {{TAGBL|WAVECAR}} WAVECAR.DIAG
  cp {{TAGBL|WAVECAR}} WAVECAR.PBE
  cp {{TAGBL|WAVEDER}} WAVEDER.DIAG
  cp {{TAGBL|WAVEDER}} WAVEDER.PBE
Also make a backup of the charge density for later:
cp {{TAGBL|CHGCAR}} CHGCAR.DIAG


=== The dielectric function ===  
== CRPA Calculation ==
Calculate the CRPA interaction parameters for the t2g states by using the PBE wavefunction as input
cp WAVECAR.PBE {{TAGBL|WAVECAR}}
cp WAVEDER.PBE {{TAGBL|WAVEDER}}


As a bonus, VASP determines the frequency dependent dielectric function in the independent-particle (IP) picture and writes the result to the {{FILE|OUTCAR}} and {{FILE|vasprun.xml}} files.
And use following input file as
In the {{FILE|OUTCAR}} you should search for
*{{TAG|INCAR}} (see INCAR.CRPA) and run vasp
 
  frequency dependent IMAGINARY DIELECTRIC FUNCTION (independent particle, no local field effects)
 
and
 
  frequency dependent      REAL DIELECTRIC FUNCTION (independent particle, no local field effects)
 
To visualize the real and imaginary parts of the frequency dependent dielectric function (from the {{FILE|vasprun.xml}}) you may execute
 
./plotoptics2
 
== GW Step ==
The actual GW calculation requires a set of one-electron energies and eigenstates. In this case we use the PBE solution obtained from previous step:
cp WAVECAR.DIAG {{TAGBL|WAVECAR}}
cp WAVEDER.DIAG {{TAGBL|WAVEDER}}
 
The following {{TAG|INCAR}} file selects the 'single shot' GW calculation also known as G<sub>0</sub>W<sub>0</sub>:
*{{TAG|INCAR}} (see INCAR.GW0)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                         # system name
  {{TAGBL|SYSTEM}} = SrVO3           # system name
  {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
  {{TAGBL|ISMEAR}} = 0               # Gaussian smearing
  {{TAGBL|KPAR}} = 2                              # parallelization of k-points in two groups
  {{TAGBL|NCSHMEM}} = 1              # switch off shared memory for chi
  {{TAGBL|ALGO}} = GW0                            # GW with iteration in G, W kept on DFT level
  {{TAGBL|ALGO}} = CRPA              # Switch on CRPA
{{TAGBL|NELM}} = 1                              # one electronic step suffices, since WAVECAR from previous step is present
  {{TAGBL|NBANDS}} = 96               # CRPA needs many empty states
  {{TAGBL|NBANDS}} = 96                           # need for a lot of bands in GW
  {{TAGBL|PRECFOCK}} = Fast           # fast mode for FFTs
  {{TAGBL|PRECFOCK}} = Fast                       # fast mode for FFTs
  {{TAGBL|NTARGET_STATES}} = 1 2 3    # exclude wannier states 1 - 3 in screening
  {{TAGBL|ENCUTGW}} = 100                          # small energy cutoff for response function suffices for this tutorial
  {{TAGBL|LWRITE_WANPROJ}} = .TRUE.  # write wannier projection file
  {{TAGBL|NOMEGA}} = 200                          # large number of real frequency points for Hilbert transforms of W and self-energy
{{NB|warning|As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR.}}


Restarting VASP will overwrite the present {{TAGBL|WAVECAR}} and {{TAGBL|vasprun.xml}} file. Make a copy them for later.
  {{TAGBL|NUM_WANN}} = 3
  cp {{TAGBL|WAVECAR}} WAVECAR.GW0
  {{TAGBL|WANNIER90_WIN}} = "
  cp {{TAGBL|vasprun.xml}} vasprun.GW0.xml
  num_bands=   96
 
=== The dielectric function ===
 
To extract the frequency dependent dielectric constant, both in the independent-particle picture as well as including local field effects (either in DFT or in the RPA) and plot the real and imaginary components using ''gnuplot'', execute
 
  ./plotchi
 
== HSE hybrid functional ==
 
To illustrate the kind of results one would obtain for SrVO<sub>3</sub> using the [[Hartree-Fock_and_HF/DFT_hybrid_functionals#range_separated|DFT/Hartree-Fock hybrid functional HSE]], without actually doing a full selfconsistent calculation, we will recalculate the one-electron energies and DOS ({{TAG|ALGO}}=Eigenval) using the HSE functional with DFT orbitals as input
cp WAVECAR.DIAG {{TAGBL|WAVECAR}}
 
Use the following {{TAG|INCAR}} file:
*{{TAG|INCAR}} (see INCAR.HSE)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                        # system name
  # because bands 21, 22, 23 do not cross with other bands
  {{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
  # one can exclude all other bands in wannierization
  {{TAGBL|KPAR}} = 2                              # parallelization of k-points in two groups
  # and omit the definition of an energy window like so
  {{TAGBL|ALGO}} = Eigenval                        # calulate eigenvalues
  exclude_bands = 1-20, 24-96
{{TAGBL|NELM}} = 1                               # one electronic step suffices, since WAVECAR from previous step is present
{{TAGBL|NBANDS}} = 48                            # small number of bands suffice
{{TAGBL|PRECFOCK}} = Fast                        # fast mode for FFTs
{{TAGBL|LHFCALC}} = .TRUE.                      # switch on Hartree-Fock routines to calculate exact exchange
{{TAGBL|HFSCREEN}} = 0.2                        # HSE06 screening parameter


Restart VASP and make a copy of the wavefunction for post-processing
  begin projections
  cp {{TAGBL|WAVECAR}} WAVECAR.HSE
  V:dxy;dxz;dyz
 
end projections
== Post-processing: Density of states and Band structure for PBE, GW and HSE ==
  "
 
The CRPA interaction values for <math>\omega=0</math> can be found in the {{TAG|OUTCAR}}:
=== Density of States ===
spin components:  1  1, frequency:    0.0000    0.0000
The DOS of the PBE, GW and HSE solution can be calculated in a post-processing step with
*{{TAG|INCAR}} (see INCAR.DOS)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                        # system name
  screened Coulomb repulsion U_iijj between MLWFs:
{{TAGBL|ISMEAR}} = -5                            # Bloechl's tetrahedron method (requires at least 3x3x3 k-points)
        1         2        3
{{TAGBL|ALGO}} = NONE                            # no electronic changes required
    1   3.3746    2.3385    2.3385
{{TAGBL|NELM}} = 1                               # one electronic step suffices, since WAVECAR from previous step is present
    2    2.3385    3.3746    2.3385
{{TAGBL|NBANDS}} = 48                            # number of bands used
    3    2.3385    2.3385    3.3746
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20                # smallest/largest energy included in calculation
{{TAGBL|NEDOS}} = 1000                          # sampling points for DOS
{{TAGBL|LORBIT}} = 11                            # calculate l-m decomposed DOS
{{TAGBL|LWAVE}} = .FALSE.                        # do not overwrite WAVECAR
{{TAGBL|LCHARG}} = .FALSE.                      # do not overwrite CHGCAR
 
and requires the apropriate {{TAG|WAVECAR}} file from one of the previous steps. Copy
cp WAVECAR.DIAG WAVECAR
or
cp WAVECAR.GW0 WAVECAR
or
cp WAVECAR.HSE WAVECAR
and restart VASP. The density of states is written to {{TAG|DOSCAR}}, make a copy of this file
cp {{TAGBL|DOSCAR}} DOSCAR.XXX
where XXX is either PBE, GW0 or HSE. Visualize the projected DOS for the V-t2g, V-eg and O-p states with the scriptfile
./plotdos.sh DOSCAR.*
This requires gnuplot to be installed.
 
===  Band structure with <tt>wannier90</tt>===
The band structure can be calculated via Wannier interpolation using <tt>wannier90</tt> in the library mode
*{{TAG|INCAR}} (see INCAR.WAN)
{{TAGBL|SYSTEM}} = SrVO3                        # system name
{{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
{{TAGBL|ALGO}} = NONE                            # no electronic changes required
{{TAGBL|NELM}} = 1                               # one electronic step suffices, since WAVECAR from previous step is present
{{TAGBL|NBANDS}} = 48                            # number of bands used
{{TAGBL|LWAVE}} = .FALSE.                       # do not overwrite WAVECAR
{{TAGBL|LCHARG}} = .FALSE.                       # do not overwrite CHGCAR
{{TAGBL|LWANNIER90_RUN}} = .TRUE.               # run wannier90 in library mode
Use the corresponding wannier90.win.XXX file as input for <tt>wannier90</tt>
cp wannier90.win.XXX wannier90.win
where XXX=PBE, GW0 or HSE and looks similar to
bands_plot = true
   
   
  begin kpoint_path
  screened Coulomb repulsion U_ijji between MLWFs:
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000
        1        2        3
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000
    1    3.3746    0.4429    0.4429
X  0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000
    2    0.4429    3.3746    0.4429
M  0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000
    3    0.4429    0.4429    3.3746
end kpoint_path
   
   
  # number of wannier states
  screened Coulomb repulsion U_ijij between MLWFs:
num_wann =   3
        1        2        3
    1    3.3746    0.4429    0.4429
    2    0.4429    3.3746    0.4429
    3    0.4429    0.4429   3.3746
   
   
  # number of bloch bands
  averaged interaction parameter
  num_bands=  96
  screened Hubbard U =   3.3746   -0.0000
   
  screened Hubbard u =   2.3385    0.0000
# GW energy window for t2g states
  screened Hubbard J =   0.4429  -0.0000
dis_win_min = 7.4
  dis_win_max = 9.95
begin projections
V:dxy;dxz;dyz
end projections


Use the corresponding WAVECAR.XXX file as input
:'''N.B.:''' The frequency point <math>\omega</math> can be set by {{TAG|OMEGAMAX}} in the INCAR. For instance to evaluate the CRPA interaction matrix at <math>\omega=10</math> eV, add
cp WAVECAR.XXX {{TAGBL|WAVECAR}}
  {{TAGBL|OMEGAMAX}} = 10
and restart VASP. If all went well, the Vanadium t2g band dispersion thus obtained, may conveniently be visualized with gnuplot:
to the INCAR and restart VASP. In contrast, adding following two lines to the {{TAG|INCAR}}
gnuplot -persist ./wannier90_band.gnu
  {{TAGBL|OMEGAMAX}} = 10
  {{TAGBL|NOMEGAR}} = 0
tells VASP to calculate the interaction on the imaginary frequency axis at <math>\omega=i 10</math>. This can be used to evaluate <math>U</math> at a specific Matsubara frequency point.  


:'''N.B.:''' Most modern versions of <tt>gnuplot</tt> will respond with an error message unless you remove the first line of <tt>wannier90_band.gnu</tt> (some deprecated syntax issue).
In addition, the bare Coulomb interaction matrix is calculated for a high {{TAG|VCUTOFF}} and low energy cutoff {{TAG|ENCUTGW}} and written in that order to the {{TAG|OUTCAR}} file. Look for the lines similar to:


=== Alternative way to calculate the PBE band structure ===
spin components:  1 1
VASP allows to interpolate the PBE band structure from the PBE charge density
  cp CHGCAR.DIAG CHGCAR
  cp WAVECAR.DIAG WAVECAR
by adapting the {{TAG|KPOINTS}} file as follows:
*{{TAG|KPOINTS}} (see KPOINTS.BSTR)
Auto
15
Linemode
reciprocal
0.50000000  0.50000000  0.50000000  !R
0.00000000  0.00000000  0.00000000  !G
0.00000000  0.00000000  0.00000000  !G
0.50000000  0.00000000  0.00000000  !X
0.50000000  0.00000000  0.00000000  !X
0.50000000 0.50000000 0.00000000  !M
   
   
  0.50000000  0.50000000  0.00000000  !M
  bare Coulomb repulsion V_iijj between MLWFs:
0.00000000  0.00000000  0.00000000  !G
        1        2        3
The following {{TAGBL|INCAR}} file tells VASP to interpolate the band structure:
    1  16.3485  15.0984  15.0984
*{{TAG|INCAR}} (see INCAR.BSTR)
    2  15.0984  16.3485  15.0984
{{TAGBL|SYSTEM}} = SrVO3                        # system name
    3  15.0984  15.0984  16.3485
{{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
{{TAGBL|EDIFF}} = 1E-7                          # tight convergence criterion
{{TAGBL|NBANDS}} = 36                            # 36 bands are sufficient
{{TAGBL|LWAVE}} = .FALSE.                       # do not overwrite WAVECAR
{{TAGBL|LCHARG}} = .FALSE.                      # do not overwrite CHGCAR
{{TAGBL|ICHARG}} = 11                            # use CHGCAR file for interpolation
{{TAGBL|LORBIT}} = 11                            # compute lm-decomposed states
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20                # smallest/largest energy included in calculation
{{TAGBL|NEDOS}} = 1000                          # sampling points for DOS
This PBE band structure and the Wannier-interpolated structures of the PBE, HSE and GW calculation can be compared via
./plotbands.sh
:'''N.B.:''' Mind that this approach works only for DFT wavefunctions, like PBE or LDA.
 
== CRPA Calculation ==
Calculate the CRPA interaction parameters for the t2g states by using the PBE wavefunction as input
cp WAVECAR.DIAG {{TAGBL|WAVECAR}}
cp WAVEDER.DIAG {{TAGBL|WAVEDER}}
Use following Wannier projection for the basis:
 
*{{TAG|wannier90.win}} (see wannier90.win.CRPA)
num_wann =    3
num_bands=  96
   
   
  # PBE energy window of t2g states (band 21-23)
  bare Coulomb repulsion V_ijji between MLWFs:
dis_win_min = 6.4
        1        2        3
dis_win_max = 9.0
    1  16.3485    0.5351    0.5351
    2    0.5351  16.3485    0.5351
    3    0.5351    0.5351  16.3485
   
   
  begin projections
  bare Coulomb repulsion V_ijij between MLWFs:
  V:dxy;dxz;dyz
        1        2        3
end projections
    1  16.3485    0.5351    0.5351
 
    2    0.5351  16.3485    0.5351
Copy this file to wannier90.win
    3    0.5351    0.5351  16.3485
cp wannier90.win.CRPA wannier90.win
 
And use following input file as
*{{TAG|INCAR}} (see INCAR.CRPA)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                        # system name
  averaged bare interaction
  {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
  bare Hubbard U =   16.3485  -0.0000
  {{TAGBL|NCSHMEM}} = 1                            # switch off shared memory for chi
  bare Hubbard u =   15.0984  -0.0000
{{TAGBL|ALGO}} = CRPA                            # Switch on CRPA
  bare Hubbard J =    0.5351    0.0000
{{TAGBL|NBANDS}} = 96                            # CRPA needs many empty states
{{TAGBL|PRECFOCK}} = Fast                        # fast mode for FFTs
{{TAGBL|NTARGET_STATES}} = 1 2 3                # exclude wannier states 1 - 3 in screening
{{TAGBL|LWRITE_WANPROJ}} = .TRUE.                # write wannier projection file
 
and run VASP. The CRPA interaction values can be found in the {{TAG|OUTCAR}} file after following lines
  screened Coulomb repulsion U_iijj between MLWFs:
including an averaged value:
screened Hubbard U =    3.3746  -0.0000
Make a copy of the output file
cp {{TAGBL|OUTCAR}} OUTCAR.CRPA


=== CRPA calculation on full imaginary frequency axis (optional) ===
=== CRPA calculation with spacetime Algorithm ===
To calculate the CRPA interaction for a set of imaginary frequency points use once again the PBE wavefunction as input
Note that the same frequency grid is used as for {{TAG|ALGO}}=RPA (RPA correlation energy calculation) and can not be changed directly.
  cp WAVECAR.DIAG {{TAGBL|WAVECAR}}
To calculate the CRPA interaction for a set of automatically chosen imaginary frequency points use once again the PBE wavefunction as input
  cp WAVEDER.DIAG {{TAGBL|WAVEDER}}
  cp WAVECAR.PBE {{TAGBL|WAVECAR}}
This step requires uses the WANPROJ file from previous step, no wannier90.win file is necessary.
  cp WAVEDER.PBE {{TAGBL|WAVEDER}}
Currently, this step requires the {{TAG|WANPROJ}} file from previous step, no wannier90.win file is necessary.
You can also, delete {{TAG|WANPROJ}} and define a wannier projection as in the previous step in the {{FILE|INCAR}}.  


Select the space-time CRPA algorithm with following file:
Select the space-time CRPA algorithm with following file:
*{{TAG|INCAR}} (see INCAR.CRPAR)
*{{TAG|INCAR}} (see INCAR.CRPAR)
   
   
  {{TAGBL|SYSTEM}} = SrVO3                         # system name
  {{TAGBL|SYSTEM}} = SrVO3             # system name
  {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
  {{TAGBL|ISMEAR}} = 0                 # Gaussian smearing
  {{TAGBL|NCSHMEM}} = 1                           # switch off shared memory for chi
  {{TAGBL|NCSHMEM}} = 1               # switch off shared memory for chi
  {{TAGBL|ALGO}} = CRPAR                           # Switch on CRPA on imaginary axis
  {{TAGBL|ALGO}} = CRPAR               # Switch on CRPA on imaginary axis
  {{TAGBL|NBANDS}} = 96                           # CRPA needs many empty states
  {{TAGBL|NBANDS}} = 96               # CRPA needs many empty states
  {{TAGBL|PRECFOCK}} = Fast                       # fast mode for FFTs
  {{TAGBL|PRECFOCK}} = Fast           # fast mode for FFTs
  {{TAGBL|NTARGET_STATES}} = 1 2 3                 # exclude wannier states 1 - 3 in screening
  {{TAGBL|NTARGET_STATES}} = 1 2 3     # exclude wannier states 1 - 3 in screening
  {{TAGBL|NCRPA_BANDS}} = 21 22 23                 # remove bands 21-23 in screening, currently required for space-time algo
  {{TAGBL|NCRPA_BANDS}} = 21 22 23     # remove bands 21-23 in screening, currently required for space-time algo
  {{TAGBL|NOMEGA}} = 12                           # use 12 imaginary frequency points
  {{TAGBL|NOMEGA}} = 12               # use 12 imaginary frequency points
  {{TAGBL|NTAUPAR}} = 4                           # distribute 12 time points into 4 groups
  {{TAGBL|NTAUPAR}} = 4               # distribute 12 time points into 4 groups


Run VASP and make a copy of the output file
Run VASP and make a copy of the output file
  cp {{TAGBL|OUTCAR}} OUTCAR.CRPAR
  cp {{TAGBL|OUTCAR}} OUTCAR.CRPAR
The resulting interactions are written for every imaginary frequency point to the {{TAG|OUTCAR}} file.
 
For instance, to extract the averaged on-site U interaction for each point enter following command
After a successful run, the interaction values are written to the {{TAG|OUTCAR}} file. Here is the result for the first frequency point:
  grep "screened Hubbard U" OUTCAR
spin components:  1  1, frequency:    0.0000    0.2248
resulting in following output
  screened Coulomb repulsion U_iijj between MLWFs:
        1        2        3
    1    3.3798    2.3436    2.3436
    2    2.3436    3.3798    2.3436
    3    2.3436    2.3436    3.3798
screened Coulomb repulsion U_ijji between MLWFs:
        1        2        3
    1    3.3798    0.4433    0.4433
    2    0.4433    3.3798    0.4433
    3    0.4433    0.4433    3.3798
screened Coulomb repulsion U_ijij between MLWFs:
        1        2        3
    1    3.3798    0.4433    0.4433
    2    0.4433    3.3798    0.4433
    3    0.4433    0.4433    3.3798
averaged interaction parameter
  screened Hubbard U =    3.3798  -0.0000
  screened Hubbard U =    3.3798  -0.0000
  screened Hubbard U =    3.4172  -0.0000
  screened Hubbard u =    2.3436   0.0000
screened Hubbard U =   3.5169  -0.0000
  screened Hubbard J =    0.4433   -0.0000
  screened Hubbard U =    3.7418  -0.0000
 
screened Hubbard U =    4.2069   -0.0000
:'''N.B.:''' The number of frequency points should be large enough to guarantee for an accurate Fourier transformation of the CRPA polarizability matrix from the imaginary time to imaginary frequency domain. See [[ACFDT/RPA calculations#Low_scaling_ACFDT.2FRPA_algorithm|ACFDT/RPA calculations]] for more information.
screened Hubbard U =    5.0802  -0.0000
screened Hubbard U =    6.5456  -0.0000
screened Hubbard U =    8.6426  -0.0000
screened Hubbard U =  11.0815  -0.0000
screened Hubbard U =  13.3615  -0.0000
screened Hubbard U =  15.0636  -0.0000
screened Hubbard U =  16.0412  -0.0000
Here each line corresponds to an (increasing) imaginary frequency point.
The first line is the CRPA interaction at the lowest frequency point and is roughly the same as the value at 0 calculated in previous step.  
The last line (interaction at the highest frequency point) approaches the bare Coulomb interaction in this basis, which is also written to the {{TAG|OUTCAR}}:
bare Hubbard U =  16.3485    0.0000


== Downloads ==
[[Media:CRPA of SrVO3.zip| CRPA_of_SrVO3.zip]]


{{Template:gw}}
{{Template:GW - Tutorial}}


Back to the [[The_VASP_Manual|main page]].
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[[Category:Examples]]
[[Category:Examples]][[Category:Constrained-random-phase approximation]]

Latest revision as of 08:50, 13 June 2024

The following tutorial describes how to perform CRPA calculations, which is available as of VASP 6.

Task

Calculation of the Coulomb matrix elements in the constrained Random Phase Approximation (CRPA) of SrVO3 between the Vanadium t2g states.

Performing a CRPA calculation with VASP is a 3-step procedure: a DFT groundstate calculation, a calculation to obtain a number of virtual orbitals, and the actual CRPA calculation itself.

N.B.: This example involves quite a number of individual calculations. The easiest way to run this example is to execute: 

./doall.sh

In any case, one can consider the doall.sh script to be an overview of the steps described below.

DFT groundstate calculation

The first step is a conventional DFT (in this case PBE) groundstate calculation. 

SYSTEM  = SrVO3    # system name
NBANDS = 36        # small number  of bands
ISMEAR = 0         # Gaussian smearing
EDIFF = 1E-8       # high precision for groundstate calculation
KPAR = 2           # parallelization of k-points in two groups

Copy the aforementioned file to INCAR: 

cp INCAR.DFT INCAR

The POSCAR file describes the structure of the system: 

SrVO3
3.84652  #cubic fit for 6x6x6 k-points
 +1.0000000000  +0.0000000000  +0.0000000000 
 +0.0000000000  +1.0000000000  +0.0000000000 
 +0.0000000000  +0.0000000000  +1.0000000000 
Sr V O
 1 1 3
Direct
 +0.0000000000  +0.0000000000  +0.0000000000 
 +0.5000000000  +0.5000000000  +0.5000000000 
 +0.5000000000  +0.5000000000  +0.0000000000 
 +0.5000000000  +0.0000000000  +0.5000000000 
 +0.0000000000  +0.5000000000  +0.5000000000

This file remains unchanged in the following.

The KPOINTS file describes how the first Brillouin zone is sampled. In the first step we use a uniform k-point sampling: 

Automatically generated mesh
 0
Gamma
 4 4 4
 0 0 0

Mind: this is definitely not dense enough for a high-quality description of SrVO3, but in the interest of speed we will live with it.

Run VASP. If all went well, one should obtain a WAVECAR file containing the PBE wavefunction.

Obtain DFT virtual orbitals and long-wave limit

Use following INCAR file to increase the number of virtual states and to determine the long-wave limit of the polarizability (stored in WAVEDER): 

SYSTEM = SrVO3     # system name
ISMEAR = 0         # Gaussian smearing
KPAR = 2           # parallelization of k-points in two groups
ALGO = Exact       # exact diagonalization
NELM = 1           # one electronic step suffices, since WAVECAR from previous step is present
NBANDS = 96        # need for a lot of bands in GW
LOPTICS = .TRUE.   # we need d phi/ d k  for GW calculations for long-wave limit

Restart VASP. At this stage it is a good idea to make a safety copy of the WAVECAR and WAVEDER files since we will repeatedly need them in the calculations that follow: 

cp WAVECAR WAVECAR.PBE
cp WAVEDER WAVEDER.PBE

CRPA Calculation

Calculate the CRPA interaction parameters for the t2g states by using the PBE wavefunction as input 

cp WAVECAR.PBE WAVECAR
cp WAVEDER.PBE WAVEDER

And use following input file as

  • INCAR (see INCAR.CRPA) and run vasp
SYSTEM = SrVO3            # system name
ISMEAR = 0                # Gaussian smearing
NCSHMEM = 1               # switch off shared memory for chi
ALGO = CRPA               # Switch on CRPA
NBANDS = 96               # CRPA needs many empty states
PRECFOCK = Fast           # fast mode for FFTs
NTARGET_STATES = 1 2 3    # exclude wannier states 1 - 3 in screening
LWRITE_WANPROJ = .TRUE.   # write wannier projection file
Warning: As of version 6.2.0 run this tutorial successfully by adding following lines to INCAR. For older version copy wannier90.win.CRPA to wannier90.win and omit following lines in INCAR. 
NUM_WANN = 3 
WANNIER90_WIN = "
num_bands=   96

# because bands 21, 22, 23 do not cross with other bands
# one can exclude all other bands in wannierization
# and omit the definition of an energy window like so
exclude_bands = 1-20, 24-96

begin projections
 V:dxy;dxz;dyz
end projections
"

The CRPA interaction values for can be found in the OUTCAR: 

spin components:  1  1, frequency:    0.0000    0.0000

screened Coulomb repulsion U_iijj between MLWFs:
        1         2         3
   1    3.3746    2.3385    2.3385
   2    2.3385    3.3746    2.3385
   3    2.3385    2.3385    3.3746

screened Coulomb repulsion U_ijji between MLWFs:
        1         2         3
   1    3.3746    0.4429    0.4429
   2    0.4429    3.3746    0.4429
   3    0.4429    0.4429    3.3746

screened Coulomb repulsion U_ijij between MLWFs:
        1         2         3
   1    3.3746    0.4429    0.4429
   2    0.4429    3.3746    0.4429
   3    0.4429    0.4429    3.3746 

averaged interaction parameter
screened Hubbard U =    3.3746   -0.0000
screened Hubbard u =    2.3385    0.0000
screened Hubbard J =    0.4429   -0.0000
N.B.: The frequency point can be set by OMEGAMAX in the INCAR. For instance to evaluate the CRPA interaction matrix at eV, add
 OMEGAMAX = 10

to the INCAR and restart VASP. In contrast, adding following two lines to the INCAR 

 OMEGAMAX = 10 
 NOMEGAR = 0

tells VASP to calculate the interaction on the imaginary frequency axis at . This can be used to evaluate at a specific Matsubara frequency point.

In addition, the bare Coulomb interaction matrix is calculated for a high VCUTOFF and low energy cutoff ENCUTGW and written in that order to the OUTCAR file. Look for the lines similar to: 

spin components:  1  1

bare Coulomb repulsion V_iijj between MLWFs:
        1         2         3
   1   16.3485   15.0984   15.0984
   2   15.0984   16.3485   15.0984
   3   15.0984   15.0984   16.3485

bare Coulomb repulsion V_ijji between MLWFs:
        1         2         3
   1   16.3485    0.5351    0.5351
   2    0.5351   16.3485    0.5351
   3    0.5351    0.5351   16.3485

bare Coulomb repulsion V_ijij between MLWFs:
        1         2         3
   1   16.3485    0.5351    0.5351
   2    0.5351   16.3485    0.5351
   3    0.5351    0.5351   16.3485

averaged bare interaction
bare Hubbard U =   16.3485   -0.0000
bare Hubbard u =   15.0984   -0.0000
bare Hubbard J =    0.5351    0.0000

CRPA calculation with spacetime Algorithm

Note that the same frequency grid is used as for ALGO=RPA (RPA correlation energy calculation) and can not be changed directly. To calculate the CRPA interaction for a set of automatically chosen imaginary frequency points use once again the PBE wavefunction as input 

cp WAVECAR.PBE WAVECAR
cp WAVEDER.PBE WAVEDER

Currently, this step requires the WANPROJ file from previous step, no wannier90.win file is necessary. You can also, delete WANPROJ and define a wannier projection as in the previous step in the INCAR.

Select the space-time CRPA algorithm with following file: 

SYSTEM = SrVO3             # system name
ISMEAR = 0                 # Gaussian smearing
NCSHMEM = 1                # switch off shared memory for chi
ALGO = CRPAR               # Switch on CRPA on imaginary axis
NBANDS = 96                # CRPA needs many empty states
PRECFOCK = Fast            # fast mode for FFTs
NTARGET_STATES = 1 2 3     # exclude wannier states 1 - 3 in screening
NCRPA_BANDS = 21 22 23     # remove bands 21-23 in screening, currently required for space-time algo
NOMEGA = 12                # use 12 imaginary frequency points
NTAUPAR = 4                # distribute 12 time points into 4 groups

Run VASP and make a copy of the output file 

cp OUTCAR OUTCAR.CRPAR

After a successful run, the interaction values are written to the OUTCAR file. Here is the result for the first frequency point: 

spin components:  1  1, frequency:    0.0000    0.2248

screened Coulomb repulsion U_iijj between MLWFs:
        1         2         3
   1    3.3798    2.3436    2.3436
   2    2.3436    3.3798    2.3436
   3    2.3436    2.3436    3.3798

screened Coulomb repulsion U_ijji between MLWFs:
        1         2         3
   1    3.3798    0.4433    0.4433
   2    0.4433    3.3798    0.4433
   3    0.4433    0.4433    3.3798

screened Coulomb repulsion U_ijij between MLWFs:
        1         2         3
   1    3.3798    0.4433    0.4433
   2    0.4433    3.3798    0.4433
   3    0.4433    0.4433    3.3798

averaged interaction parameter
screened Hubbard U =    3.3798   -0.0000
screened Hubbard u =    2.3436    0.0000
screened Hubbard J =    0.4433   -0.0000
N.B.: The number of frequency points should be large enough to guarantee for an accurate Fourier transformation of the CRPA polarizability matrix from the imaginary time to imaginary frequency domain. See ACFDT/RPA calculations for more information.

Downloads

CRPA_of_SrVO3.zip

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