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[matthieu verstraete <matthieu.jean.verstraete@gmail.com>]

You are (1) using a plasmon pole model, and (2) doing perturbative GW,
so there is formally no guarantee for corrections far from the Fermi
level.

Nevertheless, you are right, this is wierd, and looks like it is all
coming from the renormalization Z which is huge for just that state.
It is also possible that you need many more bands or a different
frequency treatment (eg contour deformation) to get higher energies
right, as the screening has to be correct out to higher energies for
sigma to be ok. Have you checked how high in band index and energy the
corrections in Hybertsen+Louie go?

Matthieu

On Tue, Oct 6, 2009 at 8:49 AM, Alexey Kosobutsky <kosobutsky@list.ru> wrote:
> Dear Abinit users,
>
> I am interested in the calculation of the correct position of Si conduction
> band levels.
> For lower conduction bands the results of GW calculation (obtained with
> using of Abinit 5.8.4) seem to be reasonable, but qusiparticle corrections
> for levels starting from 11-12 are rather strange: many of them are negative
> with large absolute values.
> For example, for k-point (-0.125, -0.250, 0.000) from a 4x4x4 mesh I have
> obtained the following result:
>
> k =   -0.125  -0.250   0.000
> Band     E0 <VxcLDA>   SigX SigC(E0)      Z dSigC/dE  Sig(E)    E-E0       E
>    1  -5.418 -10.505 -17.059   6.668   0.597  -0.676 -10.437   0.068  -5.350
>    2   2.652 -10.845 -13.432   2.000   0.744  -0.344 -11.281  -0.437   2.215
>    3   4.563 -10.815 -12.460   1.081   0.762  -0.312 -11.246  -0.431   4.132
>    4   4.641 -10.851 -12.328   0.940   0.763  -0.310 -11.261  -0.410   4.231
>    5   7.998  -9.855  -5.904  -3.727   0.775  -0.290  -9.681   0.174   8.172
>    6   9.579 -10.423  -5.761  -4.418   0.762  -0.312 -10.238   0.185   9.764
>    7  10.380 -10.413  -5.576  -4.581   0.758  -0.320 -10.220   0.194  10.574
>    8  10.627  -9.563  -4.653  -4.594   0.767  -0.303  -9.320   0.242  10.869
>    9  13.367 -10.468  -4.758  -5.488   0.737  -0.358 -10.304   0.164  13.531
>   10  14.235  -9.918  -4.040  -5.494   0.741  -0.350  -9.634   0.284  14.520
>   11  15.745  -8.530  -2.655  -5.884   0.722  -0.385  -8.536  -0.007  15.739
>   12  17.387  -8.595  -2.469  -6.227   0.695  -0.438  -8.666  -0.070  17.317
>   13  19.090  -9.078  -2.448  -6.954   0.654  -0.528  -9.290  -0.212  18.878
>   14  20.359  -9.098  -2.371  -7.261   0.623  -0.605  -9.431  -0.332  20.027
>   15  23.609  -9.946  -2.666  -9.303   0.432  -1.316 -10.820  -0.874  22.735
>   16  23.992  -9.955  -2.619  -9.848   0.464  -1.157 -11.120  -1.165  22.827
>   17  25.101  -8.495  -1.678  -9.661   0.720  -0.389 -10.543  -2.048  23.053
>   18  27.486 -10.036  -2.321  -8.687   2.669   0.625 -12.629  -2.592  24.894
>   19  27.716 -10.426  -2.445  -9.965   8.090   0.876 -26.477 -16.051  11.665
>   20  29.017 -10.024  -2.232  -8.679   1.023   0.023 -10.932  -0.908  28.109
>   21  32.152 -10.437  -2.111  -8.320   1.730   0.422 -10.426   0.011  32.163
>   22  33.120 -10.525  -2.214  -8.377   0.810  -0.234 -10.578  -0.053  33.067
>   23  34.348 -10.485  -2.040  -7.689   1.144   0.126  -9.619   0.866  35.214
>   24  35.686  -9.563  -1.642  -7.270   1.029   0.029  -8.892   0.671  36.357
>   25  37.497  -9.407  -1.464  -6.995   1.005   0.005  -8.454   0.953  38.450
>   26  38.027 -10.288  -1.976  -6.171   1.425   0.298  -7.238   3.050  41.077
>   27  38.070  -9.253  -1.467  -6.888   1.528   0.345  -7.881   1.372  39.442
>   28  39.153  -9.729  -1.659  -5.469   0.687  -0.455  -7.941   1.788  40.941
>   29  39.671  -9.579  -1.471  -6.684   0.580  -0.725  -8.753   0.826  40.497
>   30  40.535  -9.818  -1.569  -6.329   0.846  -0.182  -8.194   1.624  42.159
>
> As one can see, the QP correction E-E0 can be as large as -16 eV (for 19th
> band) that looks quite unphysically. The content of input file used for
> calculation is shown below, it is modified tgw1_1.in file with sufficiently
> high (as I think) values of convergence controlling parameters. The
> corresponding log file is attached, the majority of warnings notify about
> "Values of Re Sig_c are not linear". The question is: how to calculate high
> levels of conduction band with sufficient accuracy?
>
> Best wishes,
> Alexey
>
>
> Input file:
> # Crystalline silicon
> # Calculation of the GW corrections
> # Dataset 1: ground state calculation and of the kss file for 10 k-points in
> IBZ
> # Dataset 2: calculation of the screening (epsilon-1 matrix for W)
> # Dataset 3: calculation of the Self-Energy matrix elements (GW corrections)
>
> ndtset      3
>
> # Definition of parameters for the calculation of the KSS file
> nbandkss1   -1         # Number of bands in KSS file (-1 means the maximum
> possible)
> nband1       9         # Number of (occ and empty) bands to be computed
> #istwfk1     10*1
>
> # Calculation of the screening (epsilon-1 matrix)
> optdriver2  3        # Screening calculation
> gwpara2     2
> getkss2     -1       # Obtain KSS file from previous dataset
> nband2      54       # Bands to be used in the screening calculation
> ecutwfn2    4.0      # Cut-off energy of the planewave set to represent the
> wavefunctions
> ecuteps2    8.0      # Cut-off energy of the planewave set to represent the
> dielectric matrix
> ppmfrq2    16.7 eV  # Imaginary frequency where to calculate the screening
>
> # Calculation of the Self-Energy matrix elements (GW corrections)
> optdriver3  4        # Self-Energy calculation
> gwpara3     1
> getkss3     -2       # Obtain KSS file from dataset 1
> getscr3     -1       # Obtain SCR file from previous dataset
> nband3       150       # Bands to be used in the Self-Energy calculation
> ecutwfn3     8.0     # Planewaves to be used to represent the wavefunctions
> ecutsigx3    8.0     # Dimension of the G sum in Sigma_x
>                     # (the dimension in Sigma_c is controlled by npweps)
> nkptgw3      2               # number of k-point where to calculate the GW
> correction
> kptgw3                       # k-points
>   -0.125  -0.250   0.000
>   -0.125   0.250   0.000
> bdgw3    1 30  1 30           # calculate GW corrections for 2 k-points for
> bands from 1 to 30
>
> # Data common to the three different datasets
>
> # Definition of the unit cell: fcc
> acell  3*10.217        # 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 k-point grid
> kptopt  1            # Option for the automatic generation of k points,
> nkpt    10
> ngkpt   4 4 4
> nshiftk 4
> shiftk  0.5 0.5 0.5  # These shifts will be the same for all grids
>        0.5 0.0 0.0
>        0.0 0.5 0.0
>        0.0 0.0 0.5
> istwfk  10*1         # This is mandatory in all the GW steps.
>
> # Use only symmorphic operations
> symmorphi 0
>
> # Definition of the planewave basis set (at convergence 16 Rydberg 8
> Hartree)
> ecut 8.0          # Maximal kinetic energy cut-off, in Hartree
>
> # Definition of the SCF procedure
> nstep   10        # Maximal number of SCF cycles
> toldfe  1.0d-6    # Will stop when this tolerance is achieved on total
> energy
> 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.
>
>
> # This line added when defaults were changed (v5.3) to keep the previous,
> old behaviour
>  iscf 5
>
>
>



-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Prof. Matthieu Verstraete

Universite de Liège
Institut de Physique, Bat. B5, 3/7
Allée du 6 aout, 17
B- 4000 Sart Tilman, Liège
Belgium

Phone : +32 4 366 90 17
Fax   : +32 4 366 36 29

Mail : matthieu.jean.verstraete@gmail.com