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Recipe for selfconsistent GW calculations

Selfconsistent GW calculations are only supported in a QP picture.
As for GW0, it is possible to update the eigenvalues only (`ALGO`=GW),
or the eigenvalues and one-electron orbitals (`ALGO`=scGW).
In all cases, a quasiparticle picture is maintained, i.e. satellite peaks (shake ups and shake downs)
can not be accounted for in the selfconsistency cycle.
Selfconsistent GW calculations can be performed by simply repeatedly calling VASP using:

System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
ALGO = GW # eigenvalues only or alternatively
ALGO = scGW # eigenvalues and one electron orbitals

For `scGW0` or `scGW` non diagonal terms in the Hamiltonian are
accounted for, e.g. the linearized QP equation is diagonalized, and
the one electron orbitals are updated.[114]
Alternatively (and preferably),
the user can specify an electronic iteration counter using `NELM`:

System = Si
NBANDS = 96
ISMEAR = 0 ; SIGMA = 0.05
ALGO = GW # or ALGO = scGW
NELM = 3

In this case, the one electron energies (=QP energies) are updated 3 times
(starting from the DFT eigenvalues) in both G and W.
For `ALGO = scGW` (or `ALGO = QPGW` in VASP.5.2.13),
the one electron energies and *one electron orbitals* are updated
3 times.[114]
As for `ALGO = scGW0`, the ``static'' COHSEX approximation can be selected by setting
`NOMEGA = 1` [115].
To improve convergence to the groundstate, the charge density
is mixed using a Kerker type mixing starting with VASP.5.2.13 (see Sec. 6.49).
The mixing parameters
`AMIX`, `BMIX`, `AMIX_MAG`, `BMIX_MAG`, `AMIN`
can be adjusted, if convergence problems are encountered.
Alternatively the mixing may be switched off by setting
`IMIX=0` and controlling the step width for the orbitals
using the parameter `TIME` (which defaults to 0.4).
This selects a fairly sophisticated damped MD algorithm,
that is also used for DFT methods when ALGO is set the ``Damped''.
In general, this method is more reliable for metals and materials with
strong charge sloshing.

N.B. Requests for support are to be addressed to: vasp.materialphysik@univie.ac.at