Bandstructure and CRPA of SrVO3: Difference between revisions

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{{Template:gw}}
{{Template:gw}}
 
== Task ==  
== Task ==


Calculation of the GW bandstructure of SrVO<sub>3</sub> using VASP and [http://www.wannier.org WANNIER90].
Calculation of the GW bandstructure of SrVO<sub>3</sub> using VASP and [http://www.wannier.org WANNIER90].
----
----


Line 19: Line 17:
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.


== The DFT groundstate calculation and bandstructure with <tt>wannier90</tt>==
== DFT groundstate calculation ==
 
The first step is a conventional DFT (in this case PBE) groundstate calculation.
Everthing starts with a conventional DFT (in this case LDA) groundstate calculation:


*{{TAG|INCAR}} (see INCAR.DFT)
*{{TAG|INCAR}} (see INCAR.DFT)
   
   
  {{TAGBL|System}}  = SrVO3                                                                                                                                              
  {{TAGBL|SYSTEM}}  = SrVO3                       # system name
                                                                                                                                                                 
  {{TAGBL|NBANDS}} = 36                           # small number  of bands
  {{TAGBL|NBANDS}} = 36                                                                                                                                                  
  {{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
                                                                                                                                                               
  {{TAGBL|EDIFF}} = 1E-8                          # high precision for groundstate calculation
  {{TAGBL|ISMEAR}} = -5                                                                                                                                                   
  {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states                                                                           
                                                                                                                                                             
  {{TAGBL|EDIFF}} = 1E-8                          # high precision for groundstate calculation                                                                          
                                                                                                                                                             
  {{TAGBL|KPAR}} = 2                                                                                                                                                      
                                                                                                                                                             
{{TAGBL|LORBIT}} = 11   
{{TAGBL|LWANNIER90_RUN}} = .TRUE.                #execute wannier90 in library mode                                                                                                                                                                                                                                                                                       


Copy the aforementioned file to {{TAG|INCAR}}:
Copy the aforementioned file to {{TAG|INCAR}}:
Line 44: Line 32:
  cp INCAR.DFT INCAR
  cp INCAR.DFT INCAR


*{{TAG|KPOINTS}}
The {{TAG|POSCAR}} file describes the structure of the system:
<pre>
Automatically generated mesh
      0
Gamma
4 4 4
0 0 0
</pre>
 
'''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.
 
*{{TAG|POSCAR}}
*{{TAG|POSCAR}}
<pre>
<pre>
Line 71: Line 49:
  +0.0000000000  +0.5000000000  +0.5000000000
  +0.0000000000  +0.5000000000  +0.5000000000
</pre>
</pre>
This file remains unchanged in the following.


*wannier90.win (see wannier90.win.dft)
The {{TAG|KPOINTS}} file describes how the first Brillouin zone is sampled.
 
In the first step we use a uniform k-point sampling:
[http://www.wannier.org WANNIER90] takes its input from the file {{FILE|wannier90.win}}.
*{{TAG|KPOINTS}} (see KPOINTS.BULK)
To construct Wannier functions for the Vanadium ''t<sub>2g</sub>'' manifold in SrVO<sub>3</sub>, and plot the dispersion of the associated bands along R-G-X-M, one may use the following settings:
 
<pre>
<pre>
bands_plot = true
Automatically generated mesh
 
      0
begin kpoint_path
Gamma
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000
  4 4 4
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000
  0 0 0
X 0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000
M 0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000
end kpoint_path
 
num_wann =    3
 
num_bands=    3
 
 
# DFT energy window
dis_win_min = 6.4
dis_win_max = 9.0
 
begin projections
V:dxy;dxz;dyz
end projections
</pre>
</pre>


Copy the above to {{FILE|wannier90.win}}:
'''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 wannier90.win.dft wannier90.win
 
and run vasp.
 
If all went well, the Vanadium ''t<sub>2g</sub>'' band dispersion thus obtained, may conveniently be visualized with ''gnuplot'':
 
gnuplot -persist ./wannier90_band.gnu
 
:'''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).
 
'''Mind''': Here the eigenvalues have been shifted such that the Fermi level is a 0 eV.
 
=== Analysis of the DOS ===
 
In the above we have set:
 
{{TAGBL|LORBIT}} = 11
 
Therefore, in addition to the total density-of-states (DOS), the {{FILE|DOSCAR}} file contains blocks of information with the site-projected ''lm''-decomposed DOS as well. The site-projected ''lm''-decomposed band character is written to the {{FILE|PROCAR}} file.
 
To plot the total DOS and the Vanadium ''t<sub>2g</sub>'' and ''e<sub>g</sub>'' partial-DOS using ''gnuplot'', execute the following command:


  ./plotdos
  cp KPOINTS.BULK KPOINTS


'''Mind''': Check the {{FILE|OUTCAR}} file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.
and run VASP. If all went well, one should obtain a {{TAG|WAVECAR}} file containing the PBE wavefunction.


== Obtain DFT virtual orbitals ==
== 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}}):


*{{TAG|INCAR}} (see INCAR.DIAG)
*{{TAG|INCAR}} (see INCAR.DIAG)
 
  {{TAGBL|System}} = SrVO3
  {{TAGBL|SYSTEM}} = SrVO3                         # system name
   
  {{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
  #{{TAGBL|ISMEAR}} = -5                          # does not work for LOPTICS=.TRUE.
  {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
  {{TAGBL|ISMEAR}} = 1 ; {{TAGBL|SIGMA}} = 0.2
  {{TAGBL|ALGO}} = Exact                           # exact diagonalization
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
  {{TAGBL|NELM}} = 1                               # one electronic step suffices, since WAVECAR from previous step is present
   
  {{TAGBL|ALGO}} = Exact  ; {{TAGBL|NELM}} = 1               # exact diagonalization one step suffices
{{TAGBL|EDIFF}} = 1E-8                          # high precision for groundstate calculation
  {{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
  {{TAGBL|LOPTICS}} = .TRUE.                      # we need d phi/ d k  for GW calculations for long-wave limit
     
{{TAGBL|KPAR}} = 2


Copy the aforementioned file to {{TAG|INCAR}}:
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:
cp {{TAGBL|WAVECAR}} WAVECAR.DIAG
cp {{TAGBL|WAVEDER}} WAVEDER.DIAG
Also make a backup of the charge density for later:
cp {{TAGBL|CHGCAR}} CHGCAR.DIAG


cp INCAR.DIAG INCAR
=== The dielectric function ===


and restart VASP.
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.
 
At this stage it is a good idea to make a safety copy of the {{FILE|WAVECAR}} and {{FILE|WAVEDER}} files since we will repeatedly need them in the calculations that follow:
 
cp WAVECAR WAVECAR.DFT.96bands
cp WAVEDER WAVEDER.DFT.96bands
 
=== The dielectric function ===
 
The frequency dependent dielectric function in the independent-particle (IP) picture is written to the {{FILE|OUTCAR}} and {{FILE|vasprun.xml}} files.
In the {{FILE|OUTCAR}} you should search for
In the {{FILE|OUTCAR}} you should search for


Line 168: Line 100:
   frequency dependent      REAL DIELECTRIC FUNCTION (independent particle, no local field effects)
   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
To visualize the real and imaginary parts of the frequency dependent dielectric function (from the {{FILE|vasprun.xml}}) you may execute


  ./plotoptics2
  ./plotoptics2


== The GW calculation ==
== 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)
*{{TAG|INCAR}} (see INCAR.GW0)
 
  {{TAGBL|System}} = SrVO3
  {{TAGBL|SYSTEM}} = SrVO3                         # system name
     
  {{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
  {{TAGBL|ISMEAR}} = -5
  {{TAGBL|KPAR}} = 2                              # parallelization of k-points in two groups
  {{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
{{TAGBL|ALGO}} = GW0                            # GW with iteration in G, W kept on DFT level
   
{{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|PRECFOCK}} = Fast                        # fast mode for FFTs
{{TAGBL|ALGO}} = GW0                            #
  {{TAGBL|ENCUTGW}} = 100                          # small energy cutoff for response function suffices for this tutorial
{{TAGBL|NELM}} = 1                              # one step so this is really G0W0
  {{TAGBL|NOMEGA}} = 200                          # large number of real frequency points for Hilbert transforms of W and self-energy
  {{TAGBL|PRECFOCK}} = Fast                        # select fast mode for FFT's
  {{TAGBL|ENCUTGW}} = 100                          # energy cutoff for response function
  {{TAGBL|NOMEGA}} = 200                          # metal, we need a lot of frequency points
   
{{TAGBL|KPAR}} = 2
 
Copy the aforementioned file to {{TAG|INCAR}}:
 
cp INCAR.GW0 INCAR
 
and restart VASP.
 
=== Analysis of the DOS and bandstructure with <tt>wannier90</tt> ===
 
*{{TAG|INCAR}} (see INCAR.NONE)
 
{{TAGBL|System}}  = SrVO3
   
{{TAGBL|ISMEAR}} = -5
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
   
{{TAGBL|ALGO}} = None ; {{TAGBL|NELM}} = 1                # exact diagonalization one step suffices
{{TAGBL|NBANDS}} = 96                            # need for a lot of bands in GW
   
{{TAGBL|LORBIT}} = 11
   
{{TAGBL|LWANNIER90_RUN}} = .TRUE.
 
Again, copy the aforementioned file to {{TAG|INCAR}}:
 
cp INCAR.GW0 INCAR
 
And use the following input for <tt>wannier90</tt>:
*wannier90.win (see wannier90.win.gw)
<pre>
bands_plot = true                                                                                                                                             
                                                                                                                                                             
begin kpoint_path                                                                                                                                             
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000                                                                                 
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000                                                                                 
X  0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000                                                                                 
M  0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000                                                                                 
end kpoint_path                                                                                                                                               
                                                                                                                                                             
num_wann =    3                                                                                                                                               
                                                                                                                                                             
num_bands=    3                                                                                                                                               
                                                                                                                                                             
exclude_bands : 1-20, 24-96                                                                                                                                   
                                                                                                                                                             
begin projections                                                                                                                                             
V:dxy;dxz;dyz                                                                                                                                                 
end projections
</pre>
 
and restart VASP.
 
If all went well, the Vanadium ''t<sub>2g</sub>'' band dispersion thus obtained, may conveniently be visualized with ''gnuplot'':


gnuplot -persist ./wannier90_band.gnu
Restarting VASP will overwrite the present {{TAGBL|WAVECAR}} and {{TAGBL|vasprun.xml}} file. Make a copy them for later.  
 
  cp {{TAGBL|WAVECAR}} WAVECAR.GW0
:'''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).
cp {{TAGBL|vasprun.xml}} vasprun.GW0.xml
 
To plot the total DOS and the Vanadium ''t<sub>2g</sub>'' and ''e<sub>g</sub>'' partial-DOS using ''gnuplot'', execute the following command:
 
  ./plotdos
 
'''Mind''': Check the {{FILE|OUTCAR}} file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.


=== The dielectric function ===
=== The dielectric function ===
Line 260: Line 132:
  ./plotchi
  ./plotchi


== A comparison to the HSE hybrid functional ==
== 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:
To illustrate the kind of results one would obtain for SrVO<sub>3</sub> using the [[:Category:Hybrid_functionals|DFT/Hartree-Fock hybrid functional HSE]], without actually doing a full self-consistent 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)
*{{TAG|INCAR}} (see INCAR.HSE)
{{TAGBL|SYSTEM}} = SrVO3                        # system name
{{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
{{TAGBL|KPAR}} = 2                              # parallelization of k-points in two groups
{{TAGBL|ALGO}} = Eigenval                        # calulate eigenvalues
{{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


{{TAGBL|System}}  = SrVO3
Restart VASP and make a copy of the wavefunction for post-processing
   
  cp {{TAGBL|WAVECAR}} WAVECAR.HSE
{{TAGBL|ISMEAR}} = -5
{{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
   
{{TAGBL|EDIFF}} = 1E-8                          # high precision for groundstate calculation
   
{{TAGBL|KPAR}} = 2
  {{TAGBL|LHFCALC}} = .TRUE.  ; {{TAGBL|HFSCREEN}} = 0.2  ; {{TAGBL|NBANDS}} = 48
{{TAGBL|PRECFOCK}} = Fast  ; {{TAGBL|NELM}} = 1
{{TAGBL|ALGO}} = Eigenval
   
{{TAGBL|LWAVE}} = .FALSE.                        # do not write the wave functions
   
{{TAGBL|LORBIT}} = 11 
   
{{TAGBL|LWANNIER90_RUN}} = .TRUE.


== Post-processing: Density of states and Bandstructure for PBE, GW and HSE ==


Copy the aforementioned file to {{TAG|INCAR}}:
===  Density of States ===
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
{{TAGBL|ISMEAR}} = -5                            # Bloechl's tetrahedron method (requires at least 3x3x3 k-points)
{{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|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


  cp INCAR.HSE INCAR
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.


Use the following [http://www.wannier.org WANNIER90] input:
===  Bandstructure with <tt>wannier90</tt>===
*wannier90.win (see wannier90.win.hse)
The bandstructure can be calculated via Wannier interpolation using <tt>wannier90</tt> in the library mode
<pre>
*{{TAG|INCAR}} (see INCAR.WAN)
bands_plot = true
{{TAGBL|SYSTEM}} = SrVO3                        # system name
 
{{TAGBL|ISMEAR}} = 0                            # Gaussian smearing
begin kpoint_path
{{TAGBL|ALGO}} = NONE                            # no electronic changes required
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000
{{TAGBL|NELM}} = 1                              # one electronic step suffices, since WAVECAR from previous step is present
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000
{{TAGBL|NBANDS}} = 48                            # number of bands used
X  0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000
{{TAGBL|LWAVE}} = .FALSE.                        # do not overwrite WAVECAR
M  0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000
{{TAGBL|LCHARG}} = .FALSE.                      # do not overwrite CHGCAR
end kpoint_path
{{TAGBL|LWANNIER90_RUN}} = .TRUE.                # run wannier90 in library mode
 
Use the corresponding wannier90.win.XXX file as input for <tt>wannier90</tt>
num_wann =    3
cp wannier90.win.XXX wannier90.win
 
where XXX=PBE, GW0 or HSE and looks similar to
num_bands=   3
bands_plot = true
 
exclude_bands : 1-20, 24-48
begin kpoint_path
 
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000
begin projections
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000
V:dxy;dxz;dyz
X  0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000
end projections
M  0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000
</pre>
end kpoint_path
 
Copy the above to {{FILE|wannier90.win}}:
# number of wannier states
 
num_wann =    3
cp wannier90.win.hse wannier90.win
 
# number of bloch bands
*{{TAG|WAVECAR}}
num_bands=   96
'''Mind''': This calculation (and the ones following below) needs to restart from a set of converged DFT wave functions, therefore:
 
# GW energy window for t2g states
cp WAVECAR.DFT.96bands WAVECAR
dis_win_min = 7.4
 
dis_win_max = 9.95
and run vasp.
 
begin projections
If all went well, the Vanadium ''t<sub>2g</sub>'' band dispersion thus obtained, may conveniently be visualized with ''gnuplot'':
V:dxy;dxz;dyz
end projections


Use the corresponding WAVECAR.XXX file as input
cp WAVECAR.XXX {{TAGBL|WAVECAR}}
and restart VASP. If all went well, the Vanadium t2g band dispersion thus obtained, may conveniently be visualized with gnuplot:
  gnuplot -persist ./wannier90_band.gnu
  gnuplot -persist ./wannier90_band.gnu


:'''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).
:'''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).


'''Mind''': Here the eigenvalues have been shifted such that the Fermi level is a 0 eV.
=== Alternative way to calculate the PBE bandstructure ===
 
VASP allows to interpolate the PBE bandstructure from the PBE charge density
To plot the total DOS and the Vanadium ''t<sub>2g</sub>'' and ''e<sub>g</sub>'' partial-DOS using ''gnuplot'', execute the following command:
  cp CHGCAR.DIAG CHGCAR
 
  cp WAVECAR.DIAG WAVECAR
./plotdos
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
0.00000000  0.00000000  0.00000000  !G
The following {{TAGBL|INCAR}} file tells VASP to interpolate the bandstructure:
*{{TAG|INCAR}} (see INCAR.BSTR)
{{TAGBL|SYSTEM}} = SrVO3                        # system name
{{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 bandstructure 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.


'''Mind''': Check the {{FILE|OUTCAR}} file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.
== Download ==
[http://www.vasp.at/vasp-workshop/examples/SrVO3_GW_band.tgz SrVO3_GW_band.tgz]
{{Template:gw}}
{{Template:gw}}


Latest revision as of 15:08, 8 April 2022

Task

Calculation of the GW bandstructure of SrVO3 using VASP and WANNIER90.

Performing a GW calculation with VASP is a 3-step procedure: a DFT groundstate calculation, a calculation to obtain a number of virtual orbitals, and the actual GW calculation itself. In this example we will also see how the results of the GW calculation may be postprocessed with WANNIER90 to obtain the dispersion of the bands along the usual high symmetry directions in reciprocal space.

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

./doall.sh

And compare the output of the different steps (DFT, GW, HSE) by: 

./plotall.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. Copy the aforementioned file to KPOINTS: 

cp KPOINTS.BULK KPOINTS

and 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.DIAG
cp WAVEDER WAVEDER.DIAG

Also make a backup of the charge density for later: 

cp CHGCAR CHGCAR.DIAG

The dielectric function

As a bonus, VASP determines the frequency dependent dielectric function in the independent-particle (IP) picture and writes the result to the OUTCAR and vasprun.xml files. In the OUTCAR you should search for 

 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 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 WAVECAR
cp WAVEDER.DIAG WAVEDER

The following INCAR file selects the 'single shot' GW calculation also known as G0W0: 

SYSTEM = SrVO3                         # system name
ISMEAR = 0                             # Gaussian smearing
KPAR = 2                               # parallelization of k-points in two groups
ALGO = GW0                             # GW with iteration in G, W kept on DFT level
NELM = 1                               # one electronic step suffices, since WAVECAR from previous step is present
NBANDS = 96                            # need for a lot of bands in GW
PRECFOCK = Fast                        # fast mode for FFTs
ENCUTGW = 100                          # small energy cutoff for response function suffices for this tutorial
NOMEGA = 200                           # large number of real frequency points for Hilbert transforms of W and self-energy

Restarting VASP will overwrite the present WAVECAR and vasprun.xml file. Make a copy them for later. 

cp WAVECAR WAVECAR.GW0
cp vasprun.xml vasprun.GW0.xml

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 SrVO3 using the DFT/Hartree-Fock hybrid functional HSE, without actually doing a full self-consistent calculation, we will recalculate the one-electron energies and DOS (ALGO=Eigenval) using the HSE functional with DFT orbitals as input 

cp WAVECAR.DIAG WAVECAR

Use the following INCAR file: 

SYSTEM = SrVO3                         # system name
ISMEAR = 0                             # Gaussian smearing
KPAR = 2                               # parallelization of k-points in two groups
ALGO = Eigenval                        # calulate eigenvalues
NELM = 1                               # one electronic step suffices, since WAVECAR from previous step is present
NBANDS = 48                            # small number of bands suffice
PRECFOCK = Fast                        # fast mode for FFTs
LHFCALC = .TRUE.                       # switch on Hartree-Fock routines to calculate exact exchange
HFSCREEN = 0.2                         # HSE06 screening parameter

Restart VASP and make a copy of the wavefunction for post-processing 

cp WAVECAR WAVECAR.HSE

Post-processing: Density of states and Bandstructure for PBE, GW and HSE

Density of States

The DOS of the PBE, GW and HSE solution can be calculated in a post-processing step with 

SYSTEM = SrVO3                         # system name
ISMEAR = -5                            # Bloechl's tetrahedron method (requires at least 3x3x3 k-points)
ALGO = NONE                            # no electronic changes required
NELM = 1                               # one electronic step suffices, since WAVECAR from previous step is present
NBANDS = 48                            # number of bands used
EMIN = -20 ; EMAX = 20                 # smallest/largest energy included in calculation
NEDOS = 1000                           # sampling points for DOS
LORBIT = 11                            # calculate l-m decomposed DOS
LWAVE = .FALSE.                        # do not overwrite WAVECAR
LCHARG = .FALSE.                       # do not overwrite CHGCAR

and requires the apropriate 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 DOSCAR, make a copy of this file 

cp 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.

Bandstructure with wannier90

The bandstructure can be calculated via Wannier interpolation using wannier90 in the library mode 

SYSTEM = SrVO3                         # system name
ISMEAR = 0                             # Gaussian smearing
ALGO = NONE                            # no electronic changes required
NELM = 1                               # one electronic step suffices, since WAVECAR from previous step is present
NBANDS = 48                            # number of bands used
LWAVE = .FALSE.                        # do not overwrite WAVECAR
LCHARG = .FALSE.                       # do not overwrite CHGCAR
LWANNIER90_RUN = .TRUE.                # run wannier90 in library mode

Use the corresponding wannier90.win.XXX file as input for wannier90 

cp wannier90.win.XXX wannier90.win

where XXX=PBE, GW0 or HSE and looks similar to 

bands_plot = true

begin kpoint_path
R  0.50000000  0.50000000  0.50000000  G  0.00000000  0.00000000  0.00000000
G  0.00000000  0.00000000  0.00000000  X  0.50000000  0.00000000  0.00000000
X  0.50000000  0.00000000  0.00000000  M  0.50000000  0.50000000  0.00000000
M  0.50000000  0.50000000  0.00000000  G  0.00000000  0.00000000  0.00000000
end kpoint_path

# number of wannier states
num_wann =    3

# number of bloch bands
num_bands=   96

# GW energy window for t2g states
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 

cp WAVECAR.XXX WAVECAR

and restart VASP. If all went well, the Vanadium t2g band dispersion thus obtained, may conveniently be visualized with gnuplot: 

gnuplot -persist ./wannier90_band.gnu
N.B.: Most modern versions of gnuplot will respond with an error message unless you remove the first line of wannier90_band.gnu (some deprecated syntax issue).

Alternative way to calculate the PBE bandstructure

VASP allows to interpolate the PBE bandstructure from the PBE charge density 

 cp CHGCAR.DIAG CHGCAR
 cp WAVECAR.DIAG WAVECAR

by adapting the KPOINTS file as follows: 

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
0.00000000  0.00000000  0.00000000   !G

The following INCAR file tells VASP to interpolate the bandstructure: 

SYSTEM = SrVO3                         # system name
ISMEAR = 0                             # Gaussian smearing
EDIFF = 1E-7                           # tight convergence criterion
NBANDS = 36                            # 36 bands are sufficient
LWAVE = .FALSE.                        # do not overwrite WAVECAR
LCHARG = .FALSE.                       # do not overwrite CHGCAR
ICHARG = 11                            # use CHGCAR file for interpolation
LORBIT = 11                            # compute lm-decomposed states
EMIN = -20 ; EMAX = 20                 # smallest/largest energy included in calculation
NEDOS = 1000                           # sampling points for DOS

This PBE bandstructure 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.

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