Self-consistent GW on eigenvalues only: Difference between revisions

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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 G<sub>0</sub>W<sub>0</sub> approach often gives poor results.   
In this tutorial you will learn how to perform '''self-consistent GW on eigenvalues only''' for G or both G and W ('''evGW'''). For molecules systems and also for many solids, the G<sub>0</sub>W<sub>0</sub> 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.  
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 [https://en.wikipedia.org/wiki/Hybrid_functional#PBE0 PBE0], [https://en.wikipedia.org/wiki/Hybrid_functional#B3LYP B3LYP],[https://en.wikipedia.org/wiki/Hybrid_functional#HSE HSE] etc..  or to perform a self-consistent GW.
In order to overcome this problem a possible solution is to use as starting point a hybrid  functional like [https://en.wikipedia.org/wiki/Hybrid_functional#PBE0 PBE0], [https://en.wikipedia.org/wiki/Hybrid_functional#B3LYP B3LYP],[https://en.wikipedia.org/wiki/Hybrid_functional#HSE HSE] etc..  or to perform a self-consistent GW.
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# repeat point 1) and 2) for the G1W1, G2W2, etc… until the differences between <span style="color:green">o-GnWn.qp</span> and <span style="color:green">o-Gn+1Wn+1.qp</span> are small enough.
# repeat point 1) and 2) for the G1W1, G2W2, etc… until the differences between <span style="color:green">o-GnWn.qp</span> and <span style="color:green">o-Gn+1Wn+1.qp</span> are small enough.


Usually self-consistent GW converges in about 3/4 iterations. Notice that in many molecular systems the self-consistency on the eigenvalues only (evGW) can modify the level orders.
Usually self-consistent GW converges in about 3/4 iterations. Notice that self-consistency on the eigenvalues can modify the energy level orders.
Moreover evGW removes large part of initial dependency of the GW from the DFT functional.
Moreover '''evGW''' removes large part of dependency of the GW results from the DFT functional.


<span style="color:#FF0000"> Convergence issues</span>:
<span style="color:#FF0000"> Convergence issues</span>:

Revision as of 21:21, 19 February 2021

In this tutorial you will learn how to perform self-consistent GW on eigenvalues only for G or both G and W (evGW). 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.[1]

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

  1. 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
  2. run your first GW calculation doing:
    yambo –F yambo_g0w0_input.in -J G0W0
  3. 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.
  4. copy your gw input in a new file: cp yambo_g0w0_input.in yambo_g1w1_input.in
  5. 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"
  6. repeat point 1) and 2) for the G1W1, G2W2, etc… until the differences between o-GnWn.qp and o-Gn+1Wn+1.qp are small enough.

Usually self-consistent GW converges in about 3/4 iterations. Notice that self-consistency on the eigenvalues can modify the energy level orders. Moreover evGW removes large part of dependency of the GW results from the DFT functional.

Convergence issues:

Internal and external self-consistency in Yambo:

Ff you want to perform self-consistency only on G and not on W you can comment the line:

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


As example you can consider the results on hexgonal-Boron Nitride in ref.[2]

Self-consistent GW on eigenvalues
  1. ↑ C. Faber et al. J. Chem. Phys. 139, 194308 (2013)
  2. ↑ Artus L. et al. Ellipsometry Study of Hexagonal Boron Nitride using Synchrotron Radiation: Transparency Window in the Far‐UVC
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