Self-consistent GW on eigenvalues only with the Yambo code

yambo codeFor 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
Then change the follwing lines in the file :
GfnQPdb= "none"
XfnQPdb= "none"
GfnQPdb= "E < ./ndb.QP"
XfnQPdb= "E < ./ndb.QP"
Run your first GW calculation doing: yambo –F -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:

1) copy ndb.QP from the GW0 folder to the main folder

2) run yambo -F -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"

[1] Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach
X. Blase and C. Attaccalite, 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
C. Faber, P. Boulanger, I. Duchemin, C. Attaccalite and X. Blase
J. Chem. Phys. 139, 194308 (2013)

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