View source for Bandstructure and CRPA of SrVO3

{{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.

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

*{{TAG|INCAR}} (see INCAR.DFT)
 
 {{TAGBL|SYSTEM}}  = SrVO3                        # system name
 {{TAGBL|NBANDS}} = 36                            # small number  of bands
 {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
 {{TAGBL|EDIFF}} = 1E-8                           # high precision for groundstate calculation
 {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups

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

 cp INCAR.DFT INCAR

The {{TAG|POSCAR}} file describes the structure of the system:
*{{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>
This file remains unchanged in the following.

The {{TAG|KPOINTS}} file describes how the first Brillouin zone is sampled.
In the first step we use a uniform k-point sampling:
*{{TAG|KPOINTS}} (see KPOINTS.BULK)
<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.
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.

== 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)
 
 {{TAGBL|SYSTEM}} = SrVO3                         # system name
 {{TAGBL|ISMEAR}} = 0                             # Gaussian smearing
 {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
 {{TAGBL|ALGO}} = Exact                           # exact diagonalization
 {{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|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 {{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

=== 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 {{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

== 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|ISMEAR}} = 0                             # Gaussian smearing
 {{TAGBL|KPAR}} = 2                               # parallelization of k-points in two groups
 {{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|PRECFOCK}} = Fast                        # fast mode for FFTs
 {{TAGBL|ENCUTGW}} = 100                          # small energy cutoff for response function suffices for this tutorial
 {{TAGBL|NOMEGA}} = 200                           # large number of real frequency points for Hilbert transforms of W and self-energy

Restarting VASP will overwrite the present {{TAGBL|WAVECAR}} and {{TAGBL|vasprun.xml}} file. Make a copy them for later. 
 cp {{TAGBL|WAVECAR}} WAVECAR.GW0
 cp {{TAGBL|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 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 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)
 
 {{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

Restart VASP and make a copy of the wavefunction for post-processing
 cp {{TAGBL|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 
*{{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

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.

===  Bandstructure with <tt>wannier90</tt>=== 
The bandstructure 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
 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 {{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

:'''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).

=== 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 {{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.

{{Template:gw}}

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