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Recipe for G$ _0$W$ _0$ 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 of the orbitals with respect to the k-points $ k$; more precisely the matrix [compare (6.78)]

$\displaystyle \langle \phi_{n'k} \vert \frac{\partial \phi_{nk}}{\partial k_i} ...
...tial ({\bf H} - \epsilon_{nk} {\bf S})}{\partial k_i} \vert \phi_{nk} \rangle.
$

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 orbitals
Second 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.


next up previous contents index
Next: Recipe for partially selfconsistent Up: Frequency dependent GW calculations Previous: LWAVE: selfconsistent GW   Contents   Index
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