关注：

1）  GW计算结果的处理：能带费米能级位置的确定，DOS的获得等

2）  计算输入文件中NBANDS的选取原则

3） 理解每一步的含义，编写一个脚本一步完成下述过程

参考网址：

http://cms.mpi.univie.ac.at/wiki/index.php/Bandstructure_of_SrVO3_in_GW

 Bandstructure of SrVO3 in GW

  Performing a GW calculation with VASP is a 3-step procedure:

 a DFT groundstate calculation,

 a calculation to obtain a number of virtual orbitals,【能带数量的确定，与计算量的大小】

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.

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

System  = SrVO3

NBANDS = 36

ISMEAR = -5

EMIN = -20 ; EMAX = 20 ; NEDOS = 1000  # usefull energy range for density of states

EDIFF = 1E-8                           # high precision for groundstate calculation

KPAR = 3

#KPAR is the number of -points that are to be treated in parallel (available as of VASP.5.3.2). The set of -points is distributed over KPAR groups of compute cores, in a round-robin fashion.

#We recommend to set NPAR on these machines to

Copy the aforementioned file to INCAR:

cp INCAR.DFT INCAR

• KPOINTS

Automatically generated mesh      

0

Gamma

4 4 4

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.

• POSCAR

   

  SrVO3
  3.77706  #taken from 9x9x9 with sigma=0.2 ismear=2
  +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
  

1.1  Analysis of the DOS

Add the following line to your INCAR file:

LORBIT = 11

and rerun VASP.

In addition to the total density-of-states (DOS), the DOSCAR file now contains blocks of information with the site-projected lm-decomposed DOS as well. The site-projected lm-decomposed band character is written to the PROCAR file. 

To plot the total DOS and the Vanadium t_2g and e_g partial-DOS using gnuplot, execute the following command:

./plotdos

Mind: Check the OUTCAR file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.

1.2. Bandstructure using WANNIER90

Add the following line to your INCAR to have VASP call WANNIER90:

LWANNIER90_RUN = .TRUE.

WANNIER90 takes its input from the file wannier90.win. To construct Wannier functions for the Vanadium t_2g manifold in SrVO₃, and plot the dispersion of the associated bands along R-G-X-M, one may use the following settings:

• wannier90.win.dft

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, 24-36  #为什么不画出这些能带？，如何确定该参数

begin projections
V:dxy;dxz;dyz
end projections

Copy the above to wannier90.win:

cp wannier90.win.dft wannier90.win

and restart VASP.

The Vanadium t_2g band dispersion thus obtained, may conveniently be visualized with gnuplot:

gnuplot -persist plotme.dft

Mind: Here the eigenvalues have been shifted such that the Fermi level is a 0 eV. 【为什么这个时候费米能级又设为零点了呢】

 2. Obtain DFT virtual orbitals 

• INCAR.DFT.all

   

System  = SrVO3

ISMEAR = -5
EMIN = -20 ; EMAX = 20 ; NEDOS = 1000  # usefull energy range for density of states

ALGO = Exact  ; NELM = 1               # exact diagonalization one step suffices
EDIFF = 1E-8                           # high precision for groundstate calculation
NBANDS = 96                           # need for a lot of bands in GW【NBANDS数量如何确定？】
LOPTICS = .TRUE.                       # we need d phi/ d k  for GW calculations

KPAR = 3

Copy the aforementioned file to INCAR:

cp INCAR.DFT.all INCAR

and 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.DFT.96bands

cp WAVEDER WAVEDER.DFT.96bands 

2.1The dielectric function 

The frequency dependent dielectric function in the independent-particle (IP) picture is written 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

【介电函数，真空的介电函数是？】

3.The GW calculation

• INCAR.GW0

System  = SrVO3

ISMEAR = -5
EMIN = -20 ; EMAX = 20 ; NEDOS = 1000 # usefull energy range for density of states

NBANDS = 96                           # need for a lot of bands in GW

ALGO = GW0                             #
NELM = 1                               # one step so this is really G0W0
PRECFOCK = Fast                        # select fast mode for FFT's
ENCUTGW = 100                         # energy cutoff for response function
NOMEGA = 200                           # metal, we need a lot of frequency points
MAXMEM = 2500                         # memory per core
NKRED = 2                              # sample down the GW to a coarse 2x2x2 grid

KPAR = 3

Copy the aforementioned file to INCAR:

cp INCAR.GW0 INCAR

and restart VASP.

3.1 Analysis of the DOS

Again, add the following line to your INCAR file:

LORBIT = 11

set

ALGO = None

and rerun VASP.

To plot the total DOS and the Vanadium t_2g and e_g partial-DOS using gnuplot, execute the following command:

./plotdos

Mind: Check the OUTCAR file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.

3.2 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 

3.3 Bandstructure using WANNIER90

Again, add the following line to your INCAR to have VASP call WANNIER90:

LWANNIER90_RUN = .TRUE.

and use the following WANNIER90 input:

• wannier90.win.gw

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

Copy the above to wannier90.win:

cp wannier90.win.gw wannier90.win

and run VASP.

To compare the Vanadium t_2g band dispersion in the GW approximation with the LDA bandstructure, run the following command:

gnuplot -persist plotme.gw

Mind: Here the eigenvalues have been shifted such that the Fermi level is a 0 eV.【能带结构时，费米能级已调整至0点处，这与态密度图绘制不一样】

 ploteme.gw内容：

set nokey
set xrange [0: 4.28044]
set yrange [-10.00000 : 10.00000]
set xtics (" R "  0.00000," G "  1.44064," X "  2.27240," M "  3.10416," G "  4.28044)  【高对称性点的坐标如何确定的】
set grid
plot "wannier90_band.dat" using ($1):($2-9.19221526) with lines,\
    "bndstr.dat" using ($1/0.681253*4.28044):($2+6.90184028-8.01486705) with lines【为什么bndstr.dat绘图时数据如此设置？】

grep  E-fermi  OUTCAR*
OUTCAR: E-fermi :   9.1892     XC(G=0): -12.3536     alpha+bet :-17.7849
OUTCAR-01: E-fermi :   9.1892     XC(G=0): -12.3536     alpha+bet :-17.7849
OUTCAR-02: E-fermi :   8.0149    XC(G=0): -12.3538     alpha+bet :-17.7849
OUTCAR-03: E-fermi :   9.1892     XC(G=0): -12.3497     alpha+bet :-17.7849

3.4 A more accurate GW calculation

As you might have noticed in the previous example the Vanadium t_2g bands look a bit wobbly along G-X and X-M. In the present example, this turns out to be an artifact of the downsampling of the GW. Try removing (or comment out) the line

NKRED = 2

from the INCAR file, set

ALGO = GW0

restore the DFT solution,

cp WAVECAR.DFT.96bands WAVECAR

cp WAVEDER.DFT.96bands WAVEDER

and redo the GW step.

4.  A comparison to the 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 selfconsistent calculation, we will recalculate the one-electron energies and DOS (ALGO=Eigenval) using the HSE functional with DFT orbitals as input:

• INCAR.HSE

System  = SrVO3

ISMEAR = -5
EMIN = -20 ; EMAX = 20 ; NEDOS = 1000  # usefull energy range for density of states

EDIFF = 1E-8                          # high precision for groundstate calculation

KPAR = 3
LHFCALC = .TRUE.  ; HFSCREEN = 0.2  ; NBANDS = 48
PRECFOCK = Fast   ; NELM = 1
ALGO = Eigenval

LWAVE = .FALSE.                        # do not write the wave functions

Copy the aforementioned file to INCAR:

cp INCAR.HSE INCAR

and restart VASP.

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

4.1  Analysis of the DOS

Again, add the following line to your INCAR file:

LORBIT = 11

and rerun VASP.

To plot the total DOS and the Vanadium t_2g and e_g partial-DOS using gnuplot, execute the following command:

./plotdos

Mind: Check the OUTCAR file for the position of the Fermi level. These DOSs have not been shifted such that the Fermi level is at 0 eV.

4.2 Bandstructure using WANNIER90

As before, add the following line to your INCAR to have VASP call WANNIER90:

LWANNIER90_RUN = .TRUE.

and use the following WANNIER90 input:

• wannier90.win.hse

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

Copy the above to wannier90.win:

cp wannier90.win.hse wannier90.win

and redo the HSE calculation.

To compare the HSE Vanadium t_2g band dispersion with the LDA bandstructure, run the following command:

gnuplot -persist plotme.hse

Mind: Here the eigenvalues have been shifted such that the Fermi level is a 0 eV.