How to understand the hybrid functional calculation in GW?

Zhang Xiaole · Post by **Zhang Xiaole** » Mon Apr 01, 2013 10:47 am

Dear users,
Recently, i used the hybrid functional as implemented in the latest version of abinit. In this post, i want to list some questions really confused me.
1) in my understanding, the standar GW calculation can be intepreted as E^{QP}=E^{KS}+Z*<i|{Sigma_x+Sigma_c}|i>-V_{xc},
For Sigma_x is the Fock exchange self-energy which can be obtained just do a HF calculation, For Sigma_x is the screen correlation self-energy which can be obtained just do a screen calculation.
if i used the hybrid functional, however, only HF calculation is available, and in the ouput, the final QP energy is equal to <hHartree>+<Sigma_x>. Why? what dos the term <hHartree> mean? is there any link between the hybrid funcional+HF and GW calculation?
Besides, i know in the hybrid functional, some LDA or GGA exchange-correlation is replaced by Fock exchange. However, it is still very hard for me to find out the link between hybrid function in HF calculation and GW calculaion.
Any replies would be appreciated.

Sheleon