Self-consistent GW on eigenvalues only
In this tutorial you will learn how to perform self-consistent GW on eigenvalues only for G or both G and W. For molecules systems and also for many solids, the G0W0 approach often gives poor results. The main reason of this failure is that the DFT starting point with 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 a hybrid functional like PBE0, B3LYP, M062X etc.. or to perform a self-consistent GW. In general in self-consistent GW also the wave-function should be updated, but for many systems DFT wave-functions are already quite good and a self-consistency on eigenvalues only can be sufficient, for a discussion in
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
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: 1) copy your gw input in a new file: cp yambo_gw_input.in yambo_gw1_input.in
2) modifty the fileyambo_gw1_input.in to force Yambo to read the previous quasi-particle corrections
GfnQPdb= "E < ./GW0/ndb.QP" and XfnQPdb= "E < ./GW0/ndb.QP"
repeat point 1) and 2) for the GW1, GW2, etc… 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 < ./GW0/ndb.QP"