关注：

1） GW计算的VASP实现过程及物理含义

2） 数据处理

Recipe for GW calculations

GW calculations always require the  calculation of a standard DFT WAVECAR file in  an initial step, using for instance the following INCAR file:  System  = Si NBANDS = 96 ISMEAR = 0 ; SIGMA = 0.05  ! small sigma is required to avoid partial occupancies LOPTICS = .TRUE.

Note, that the a significant number of empty bands is required for GW calculations, so that it might be better to perform the calculations in two steps:

first a standard grounstate calculation with few unoccupied orbitals only,

System  = Si groundstate occupied orbitals ISMEAR = 0 ; SIGMA = 0.05  ! small sigma is required to avoid partial occupancies EDIFF = 1E-8               ! required tight tolerance for groundstate orbitals

and second a calculation of a large number of unoccupied orbitals

System  = Si unoccupied orbitals ALGO = Exact               ! use exact diagonalization of the Hamiltonian NELM = 1                   ! since we are already converged stop after one step NBANDS = 96                ISMEAR = 0 ; SIGMA = 0.05  ! small sigma is required to avoid partial occupancies LOPTICS = .TRUE.Furthermore note that the flag LOPTICS=.TRUE. is required in order to write the file WAVEDER, which contains the derivative【导数】 of the orbitals with respect to the k-points ; more precisely the matrix [compare (6.80)]

Calculation of this matrix requires the knowledge of the Hamiltonian, and therefore needs to be done in the preparatory DFT or hybrid functional run.

The actual GW calculations are performed in a second step using an INCAR file such as (it is convenient to add  a single line):

System  = Si NBANDS = 96 ISMEAR = 0 ; SIGMA = 0.05 LOPTICS = .TRUE. ALGO = GW0 ; NOMEGA = 50

The head and wings of the dielectric matrix are constructed using k.p perturbation theory (this requires the file WAVEDER). In the present release the interaction between the core and the valence electrons is always treated on the Hartree Fock level [111].

For hybrid functionals, the three step procedure will accordingly involve the following INCAR files.

In the first two steps, converged HSE03 orbitals are determined (usually HSE03 calculations should be preceeded by standard DFT calculations, we have not documented this step here, see Sec. 6.71.11):  System  = Si groundstate occupied orbitals ISMEAR = 0 ; SIGMA = 0.05 ALGO = Damped ; TIME = 0.5  ! or ALGO = Conjugate LHFCALC = .TRUE. ; AEXX = 0.25 ; HFSCREEN = 0.3  EDIFF = 1E-6      ! required tight tolerance for groundstate orbitalsSecond determine the HSE03 orbitals for unoccupied states:  System  = Si unoccupied orbitals NBANDS = 96 ALGO   = Exact    ! perform exact diagonalization NELM = 1          ! since we are already converged stop after one step ISMEAR = 0 ; SIGMA = 0.05 LHFCALC = .TRUE. ; AEXX = 0.25 ; HFSCREEN = 0.3  LOPTICS = .TRUE.As before, in the GW step, the head and the wings of the response matrix are  determined by reading the required data from the WAVEDER file.  System  = Si NBANDS = 96 ISMEAR = 0 ; SIGMA = 0.05 ALGO = GW0 ; NOMEGA = 50  

Convergence with respect to the number of empty bands NBANDS and with respect to the number of frequencies NOMEGA must be checked carfully

参数介绍：

Default:    
NOMEGA =50 for $ GW$ calculations
NOMEGA specifies the number of frequency grid points.

example03: Silicon, 4 valence bands + 4 conduction bands;
         interpolated bandstructure

 cat silicon.win 

num_bands         =   12      
num_wann          =   8

dis_win_max       = 17.0d0
dis_froz_max      =  6.4d0
dis_num_iter      =  120

dis_mix_ratio     = 1.d0

num_iter          = 50
num_print_cycles  = 10

Begin Atoms_Frac
Si  -0.25   0.75  -0.25
Si   0.00   0.00   0.00
End Atoms_Frac
   
Begin Projections    
Si : sp3
End Projections  

# Bandstructure plot
restart         =  plot
bands_plot      =  true
   
begin kpoint_path
L 0.50000  0.50000 0.5000 G 0.00000  0.00000 0.0000
G 0.00000  0.00000 0.0000 X 0.50000  0.00000 0.5000
X 0.50000 -0.50000 0.0000 K 0.37500 -0.37500 0.0000
K 0.37500 -0.37500 0.0000 G 0.00000  0.00000 0.0000
end kpoint_path

bands_num_points 40
bands_plot_format gnuplot xmgrace

vi silicon.amn

reated on 25Feb2006 at 11:03:51
  12   64    8
   1    1    1    -315.325490567895 -503.972348172530
   2    1    1     892.950763763228   76.260721634836
   3    1    1      -1.817901199005  199.674481480512
   4    1    1     -26.791281928432  275.688279394745
   5    1    1     405.082554987119  159.308451527596
   6    1    1     378.240989138255 -149.462940708796
   7    1    1    -147.098869412458 -474.609025004632
   8    1    1    -313.063657380152 -383.229242644965
   9    1    1      -0.374156033144    0.673230254664
  10    1    1       0.263162087870    0.169987246996
  11    1    1      83.370978059515  214.147777069540
  12    1    1       0.000000000000    0.000000000000
   1    2    1    -311.253759961033 -497.464663439936
   2    2    1    -450.381729557685  -87.756716189127
   3    2    1     464.441049721847 -175.196618159547
   ...

   12   8    64........

vi  silicon.mmn

Created on 25Feb2006 at 11:03:51
   12    64     8
   1    2      0   0   0
  -0.992978083715    0.061238823496
   0.017221339195   -0.026154529082
   0.006141013971    0.003272263313
   0.008078452768    0.005612329171
   0.030583546868    0.036842196859
   0.044719384551    0.004857238077
   0.010885800242   -0.053352814347
   0.001723615409    0.009086690442
  -0.000000440624   -0.000000251824
  -0.000000030799    0.000000761034

vi silicon.eig
          1           1  -5.82184795595698
          2           1   6.22851352806726
          3           1   6.22851352806730
          4           1   6.22851352806730
          5           1   8.79933035559658
          6           1   8.79933054461364
          7           1   8.79933072556404
          8           1   9.70555033956545
          9           1   13.9976360773248
         10           1   13.9976368312392
         11           1   14.0125669847628
         12           1   17.4551158815455
          1           2  -5.00835175674957
          2           2   2.27542882218500

......

          12         64