For molecules and also for molecular solids, the G_{0}W_{0} 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 G_{0}W_{0} 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= "none"`

and

`XfnQPdb= "none"`

in

`GfnQPdb= "E < ./ndb.QP"`

and

`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. [3] for a discussion. Moreover evGW removes almost all dependency from the initial functional see figure 2 of Ref. [2].

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"`

References:

[1] Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach

, Appl. Phys. Lett. **99**, 171909 (2011)

[2] 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)

[3] 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)