For molecules and also for molecular solids, the G0W0 approach often gives poor results. The main reason of this failure is the DFT starting point. In fact local or semi-local exchange correlation functionals give a too small gap compared with the experimental one, and a single shot GW is not able to correct this error. In order to overcome this problem a possible solution is to use as starting point an exchange correlation functional that contains the exchange as the PBE0, B3LYP, M062X etc.. or to perform a self-consistent GW.
Today I will show how to perform self-consistent GW on the eigenvalues only with the Yambo code. This approximation works very well for molecular systems[1,2,3].
Generate an input file for a G0W0 calculation as explained in the tutorial “Basic concepts of the GW approximation” doing:
yambo -d -k hartree -g n -p p -V qp -F yambo_gw_input.in
Then change the follwing lines in the
yambo_gw_input.in file :
GfnQPdb= "E < ./ndb.QP"
XfnQPdb= "E < ./ndb.QP"
Run your first GW calculation doing: yambo –
F yambo_gw_input.in -J GW0
When the run ends you will get a quasi-particle file o-GW0.qp. Now you can read this new quasi-particle band structure and perform another GW step doing:
2) run yambo -F yambo_gw_input.in -J GW1
repeat point 1) and 2) until the differences between o-GWn.qp and o-GWn+1.qp are small enough.
Usually self-consistent GW converges in about 4/5 iterations. Notice that in many molecular systems the self-consistency on the eigenvalues only (evGW) is a very good approximation because the error coming from the non-self consistent wave-functions is very small, see Ref.  for a discussion. Moreover evGW removes almost all dependency from the initial functional see figure 2 of Ref. .
Notice that if you want to perform self-consistency only on G and not on W you can comment the line:
XfnQPdb= "E < ./ndb.QP"
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 Correlation effects in the optical spectra of porphyrin oligomer chains: Exciton confinement and length dependence
C. Hogan, M. Palummo, J. Gierschner and A. Rubio, J. Chem. Phys. 138, 024312 (2013)
 Many-body Green’s function GW and Bethe-Salpeter study of the optical excitations in a paradigmatic model dipeptide J. Chem. Phys. 139, 194308 (2013)