View source for Bandstructure of SrVO3 in GW

{{Template:gw}}

== Task ==

Calculation of the GW bandstructure of SrVO<sub>3</sub> using VASP and [http://www.wannier.org 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 [http://www.wannier.org 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 <tt>doall.sh</tt> script to be an overview of the steps described below.

== The DFT groundstate calculation and bandstructure with <tt>wannier90</tt>==

Everthing starts with a conventional DFT (in this case LDA) groundstate calculation:

*{{TAG|INCAR}} (see INCAR.DFT)
 {{TAGBL|System}}  = SrVO3
 {{TAGBL|NBANDS}} = 36
 {{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|LORBIT}} = 11
 {{TAGBL|LWANNIER90_RUN}} = .TRUE.                #execute wannier90 in library mode

Copy the aforementioned file to {{TAG|INCAR}}:

 cp INCAR.DFT INCAR

*{{TAG|KPOINTS}}
<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}}
<pre>
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
</pre>

*wannier90.win (see wannier90.win.dft)

[http://www.wannier.org WANNIER90] takes its input from the file {{FILE|wannier90.win}}.
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>
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


# DFT energy window
dis_win_min = 6.4
dis_win_max = 9.0

begin projections
V:dxy;dxz;dyz
end projections
</pre>

Copy the above to {{FILE|wannier90.win}}:

 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

'''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.

== Obtain DFT virtual orbitals ==

*{{TAG|INCAR}} (see INCAR.DIAG)

 {{TAGBL|System}}  = SrVO3
 #{{TAGBL|ISMEAR}} = -5                           # does not work for LOPTICS=.TRUE.
 {{TAGBL|ISMEAR}} = 1 ; {{TAGBL|SIGMA}} = 0.2
 {{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
 {{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|LOPTICS}} = .TRUE.                       # we need d phi/ d k  for GW calculations
 {{TAGBL|KPAR}} = 2

Copy the aforementioned file to {{TAG|INCAR}}:

 cp INCAR.DIAG INCAR

and restart VASP.

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

  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

== The GW calculation ==

*{{TAG|INCAR}} (see INCAR.GW0)

 {{TAGBL|System}}  = SrVO3
 {{TAGBL|ISMEAR}} = -5
 {{TAGBL|EMIN}} = -20 ; {{TAGBL|EMAX}} = 20 ; {{TAGBL|NEDOS}} = 1000  # usefull energy range for density of states
 {{TAGBL|NBANDS}} = 96                            # need for a lot of bands in GW
 {{TAGBL|ALGO}} = GW0                             #
 {{TAGBL|NELM}} = 1                               # one step so this is really G0W0
 {{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

:'''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).

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 ===

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

== A comparison to the 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:

*{{TAG|INCAR}} (see INCAR.HSE)

 {{TAGBL|System}}  = SrVO3
 {{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.

Copy the aforementioned file to {{TAG|INCAR}}:

 cp INCAR.HSE INCAR

Use the following [http://www.wannier.org WANNIER90] input:
*wannier90.win (see wannier90.win.hse)
<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, 24-48

begin projections
V:dxy;dxz;dyz
end projections
</pre>

Copy the above to {{FILE|wannier90.win}}:

 cp wannier90.win.hse wannier90.win

*{{TAG|WAVECAR}}
'''Mind''': This calculation (and the ones following below) needs to restart from a set of converged DFT wave functions, therefore:

 cp WAVECAR.DFT.96bands WAVECAR

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.

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.

== Download ==
[http://www.vasp.at/vasp-workshop/examples/SrVO3_GW_band.tgz SrVO3_GW_band.tgz]
 
{{Template:gw}}

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