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[thanusit@kku.ac.th]

Dear Abinit forum members,

In an attemp to calculate the GW corrected band structure of the crystalline 
silicon,I have gone through the abinit tutorials "tgw_x" and 
"../paral/tM.in", and built an input file as listed below. The idea is to get 
the GW corrections for several k-points and bands using the KSS and SCR files 
which are previously determined from the SCF ground state charge density. 
Then, the GW full band structure will be calculated by the interpolating 
approach suggested in the abinit tutorial tgw_9.  

Firstly, the  ground state KSS and SCR files were obtained by the runnig the 
commented "#Disabled Section" in the input file given below, with only one GW 
calculation at Gamma. This is simmilar to what is done in the tutorial tM.in 
excepting that few parameters were changed to those obtained from the 
convergence studies in the tgw_x tutorials. The k-points appeared in the list 
to generate the KSS files from the ground state charge density were then 
selected for GW calculations. Only 9 k-points can be assigned for a double 
loop (maximum number allowed by abinip). The Gamma, L, and X-equivalent (0.5 
0.5 0.0) points were also in the list and seleced. The GW corrections were 
then calculated at each k-points for the band pairs 1&2, 3&4, 5&6, 7&8, and 
9&10, via a double loop and multiple data set entry. The calculation was 
successfully completed by using the parallellized version of abinit 5.4.3 
(abinip), opereated on Scientific Linux 5.0(32 bits) with the Intel core 2 
duo Q6600, 2.4GHz. 

However,as an inexperienced Abinit user and a non-developer,  I have some 
curious questions. 

1. Is the mentioned procedure of GW correction the the ground state bands, 
e.g. using fixed KSS and SCR input files for determining the GW corrections 
to all k points and bands, theoretically and technically sensible?
2. Is this what have been technically decribed as a cumbersome calculation? 

From the output file, I managed to manually extract the GW results from the 
end of each data set. An example is given below for the gammar and the 
X-equivalent points.

------------------------------------------------------------------------------
 k =    0.000   0.000   0.000
 Band     E0 <VxcLDA>   SigX SigC(E0)      Z dSigC/dE  Sig(E)    E-E0       E
    1  -6.191 -10.391 -17.212   7.267   0.555  -0.802 -10.143   0.247  -5.944
    2   5.812 -11.198 -12.373   0.843   0.774  -0.293 -11.455  -0.257   5.555
    3   5.812 -11.198 -12.373   0.843   0.774  -0.293 -11.455  -0.256   5.556
    4   5.812 -11.198 -12.373   0.843   0.774  -0.293 -11.455  -0.257   5.555
    5   8.354 -10.021  -5.843  -3.686   0.774  -0.292  -9.641   0.380   8.734
    6   8.354 -10.021  -5.843  -3.686   0.774  -0.292  -9.640   0.380   8.734
    7   8.354 -10.021  -5.843  -3.686   0.774  -0.292  -9.641   0.380   8.734
    8   8.936 -10.747  -6.107  -4.171   0.768  -0.302 -10.387   0.361   9.297
    9  13.416  -8.050  -2.714  -5.047   0.752  -0.329  -7.832   0.217  13.634
   10  13.839  -9.996  -4.304  -5.005   0.752  -0.330  -9.480   0.516  14.355

k =    0.500   0.500   0.000
 Band     E0 <VxcLDA>   SigX SigC(E0)      Z dSigC/dE  Sig(E)    E-E0       E
    1  -2.029 -10.722 -15.701   4.793   0.670  -0.493 -10.846  -0.125  -2.154
    2  -2.029 -10.722 -15.701   4.793   0.670  -0.493 -10.846  -0.125  -2.154
    3   2.911 -10.531 -12.961   2.030   0.755  -0.325 -10.833  -0.302   2.609
    4   2.911 -10.531 -12.961   2.030   0.755  -0.325 -10.833  -0.302   2.609
    5   6.449  -9.056  -5.304  -3.291   0.790  -0.265  -8.691   0.365   6.813
    6   6.449  -9.056  -5.304  -3.291   0.790  -0.265  -8.691   0.365   6.813
    7  15.756 -10.527  -3.801  -6.522   0.680  -0.470 -10.388   0.138  15.894
    8  15.756 -10.527  -3.801  -6.521   0.681  -0.469 -10.387   0.139  15.896
    9  17.048 -10.430  -4.023  -5.989   0.709  -0.411 -10.134   0.296  17.343
   10  17.048 -10.430  -4.023  -5.989   0.709  -0.411 -10.133   0.297  17.344

--------------------------------------------------------------------------------

As a quick check, the difference between the energy at the top of the valence 
band (band 4) at gamma point and that at the X point (band 5) was found to be 
1.258 eV. With the fact that the conduction band minimum of Si is slightly 
shifted to the left of X point, the calculated energy gap should be slightly 
smaller than 1.258eV. So, this looks good to me when compared to the 
experimental value of 1.17eV.


Suppose the obtained data are reliable, 

3. how to perform the interpolating approach to get a GW corrected full band 
structure?
4. Regarded to the data given above, does "the plot of the GW correction with 
respect to the 0-order LDA energy for each state" (suggested at the end of 
the abinit tutorial tgw_9) refer to "the plot of E0 as a function of E-E0 at 
all calculated k-points within the same band",  
5. If (4) is the case, will plots are entirely difference from each others, 
e.g their slopes? 


Sorry for posting this lengthy messege. Hope to hear some advices.


Best regards,
Thanusit Burinprakhon
Physics Department, Khon Kaen University,
Thailand.

Input File (based on ../paral/tM.in)
----------------------------------------------------------------------------
# Crystalline silicon
# Calculation of the GW correction to Kohn Sham band 
# Use pre-deterimined KSS and SCR data

mkmem     0            # Without this line "abinip" keeps crashing. 
ndtset    45           # To cover 9 k-points with 5 pairs of adjacent bands 
at   
                       # each k
udtset    9  5          

kptopt   1             # Option for the automatic generation of k points
ngkpt    4 4 4         # Density of k points

#Disabled Section
# Dataset1: usual self-consistent ground-state calculation
# Definition of the k-point grid
# nkpt1    10
# nshiftk1  4
# shiftk1  0.5 0.5 0.5  # This grid is the most economical
#         0.5 0.0 0.0
#         0.0 0.5 0.0
#         0.0 0.0 0.5
# prtden1  1         # Print out density

# Dataset2: calculation of kss file
# Definition of k-points
# nkpt2    19             # A set of 19 k-points containing Gamma
# nshiftk2  4
# shiftk2  0.0 0.0 0.0    # This grid contains the Gamma point
#          0.0 0.5 0.5
#          0.5 0.0 0.5
#          0.5 0.5 0.0
# istwfk2  19*1           # Option needed for Gamma
# iscf2    -2             # Non self-consistent calculation
# getden2  -1             # Read previous density file
# nband2   9
# nbandkss2 100        # Number of bands to store in KSS file

# Dataset3: Calculation of the screening (epsilon^-1 matrix)
# optdriver3   3       # Screening calculation
# getkss3     -1       # Obtain KSS file from previous dataset
# nband3      25       # Bands to be used in the screening calculation
# ecutwfn3    4.0      # Planewaves to be used to represent the wavefunctions
# ecuteps3    6.0      # Dimension of the screening matrix
# ppmfrq3    16.7 eV   # Imaginary frequency where to calculate the screening
# End of the disabled part

# Calculation of the Self-Energy matrix elements (GW corrections)
inclvkb 0             # No idea what is this for
# General parameter
optdriver    4        # Self-Energy calculation
getkss       1        # Obtain KSS from the pre-dertermined KSS file
getscr       1        # Obtain SCR file from the pre-dertermined SCR file
nband        100      # Bands to be used in the Self-Energy calculation
ecutwfn      5.0      # Planewaves to be used to represent the wavefunctions
ecutsigx     6.0      # Dimension of the G sum in Sigma_x
                      # (the dimension in Sigma_c is controlled by npweps)
nkptgw       1        # number of k-point where to calculate the GW correction

# k-points where to calculate GW correction
# kptgw 1? to 9? coressponds to kpt:1,3,5,7,9,11,14,18 and 19 that
# appeared in the k-point grid used for the KSS and SCR calculation

kptgw1?   -0.12500 -0.12500  0.00000
kptgw2?   -0.25000 -0.25000  0.00000
kptgw3?   -0.12500  0.37500  0.00000
kptgw4?   -0.12500  0.50000  0.12500
kptgw5?   -0.25000 -0.37500  0.12500
kptgw6?   -0.12500  0.12500  0.00000
kptgw7?    0.50000  0.50000  0.00000  # X-equivalent?
kptgw8?    0.50000  0.00000  0.00000  # L
kptgw9?    0.00000  0.00000  0.00000  # (Gamma)

# Bands to calculate GW correction
bdgw?1      1  2               
bdgw?2      3  4 
bdgw?3      5  6 
bdgw?4      7  8 
bdgw?5      9  10 

# Definition of the unit cell: fcc
acell  3*5.43 angstrom       # This is equivalent to   10.217 10.217 10.217
rprim  0.0  0.5  0.5         # FCC primitive vectors (to be scaled by acell)
       0.5  0.0  0.5
       0.5  0.5  0.0

# Definition of the atom types
ntypat  1         # There is only one type of atom
znucl 14          # The keyword "znucl" refers to the atomic number of the 
                  # possible type(s) of atom. The pseudopotential(s) 
                  # mentioned in the "files" file must correspond
                  # to the type(s) of atom. Here, the only type is Silicon.
                         
# Definition of the atoms
natom 2           # There are two atoms
typat  1 1        # They both are of type 1, that is, Silicon.
xred              # Reduced coordinate of atoms
      0.0  0.0  0.0
      0.25 0.25 0.25

# Definition of the planewave basis set (at convergence 16 Rydberg 8 Hartree)
ecut 6.0          # Maximal kinetic energy cut-off, in Hartree

# Definition of the SCF procedure
nstep   100       # Maximal number of SCF cycles
diemac  12.0      # Although this is not mandatory, it is worth to
                  # precondition the SCF cycle. The model dielectric
                  # function used as the standard preconditioner
                  # is described in the "dielng" input variable section.
                  # Here, we follow the prescription for bulk silicon.
tolwfr  1.0d-10   
nsym 0
symmorphi 0
# This line added when defaults were changed (v5.3) to keep the previous, old 
behaviour
  iscf 5