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[deyulu@yahoo.com]

Fabien:
      Thank you for your explanation, but I don't agree with your argument. 
In doing scissor+G0W0, self-consistent GW on the energies-only, one should 
use 
H', i.e., H_{KS}+scissor or H_{KS}+Delta sigma, to evaluate quasi-particle 
energies.
      It applies also to the commutator trick. If we takes the 1st order app.
on H' to assume it is diagonal, one has:
< v | r | c > = < v | [ H' , r ] | c > / (E'_v - E'_c),
where E'_v and E'_c are quasi-particle energies instead of KS energies.
      For a wide range of materials, it has been shown in Fiorentitni and 
Balderesch's paper (PRB, 51:17916, 1995) that the effect of Delta sigma can
be largely attributed to a static screened exchange term, which commutes with 
r. Then it leads to < v | r | c > = < v | [ H_{KS} , r ] | c > / (E'_v - 
E'_c).
      In my opinion, this expression is consistent with the formula for G!=0
terms.

     Best
     
Deyu***************************************************************************
Deyu Lu (Ph.D)

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