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,HSE 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 see for example ref.

In this tutorial we will show how to perform self-consistent GW on the eigenvalues only with the Yambo code.

• Generate an input file for a G₀W₀ calculation as explained in the GW basics tutorial doing:
  yambo -X p -g n -p p -V qp -F yambo_g0w0_input.in
  

• run your first GW calculation doing:
  yambo –F yambo_g0w0_input.in -J G0W0
  

• at the end of the run you will get a quasi-particle file o-G0W0.qp.
  Now you can read this new quasi-particle band structure and perform another GW.
  

• copy your gw input in a new file:
  cp yambo_g0w0_input.in yambo_g1w1_input.in
  

• modify the yambo_g1w1_input.in to force Yambo to read the previous quasi-particle corrections
  

GfnQPdb= "E < ./G0W0/ndb.QP" and XfnQPdb= "E < ./G0W0/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:

1. XfnQPdb= "E < ./GW0/ndb.QP"

As example you can consider the results on hexgonal-Boron Nitride in ref.