The ABINIT Users Mailing List ( CLOSED )

[Fabien Bruneval <fabien.bruneval@polytechnique.fr>]

Hi Deyu!

This is subtle a point, but abinit code is right (as always?!).
Let me explain what the code does:

You want to calculate terms such as < v | r | c >, where v stands for 
valence wavefunctions, c for conduction wfs and where r is the position 
operator.
The r operator is not periodic, but the bra and ket are. So the easiest 
way out is to use the trick:

< v | r | c > = < v | [ H , r ] | c > / (E_v - E_c).

Therefore, the energies in the denominator are the one corresponding to 
the Hamiltonian that you have introduced. So far, this Hamiltonian can 
be anything, it just needs to have the periodicity of the crystal.

In practice, we have chosen the Hamiltonian that corresponds to the 
wavefunctions in the bra and the ket and, as a consequence, the energies 
should be consistent with this choice.

To summarize, when you use KS wavefunctions, like in G0W0, scissor+G0W0, 
self-consistent GW on the energies-only, the code is perfectly 
consistent and you should not change the energies in the denominator!

I have to confess that there is a small inconsistency, when one performs 
self-consistent GW calculation on the wavefunctions, because we still 
use the commutator of the KS Hamiltonian and not the one of the GW 
Hamiltonian. This "approximation" is pretty harmless, since the effect 
of the commutator is really small in bulk systems. For nanostructures, 
this may require some fix...

If you want a reference on the commutator trick, you can find it in 
Baroni and Resta, Phys. Rev. B 33, 7017-7021 (1986).

Bye.

Fabien





deyulu@yahoo.com wrote:
> Hello, abinit users:
>        I think there is a bug in the source code cchi0q0.F90.
> When computing polarizability chi0 at long wave length limit (q->0), the 
> code uses the quasi-particle energies instead of KS orbital energies.
> The quasi-particle energies could be simply KS orbital energies plus a scissor 
> operator or the output from a previous GW calculation.
> In the calculation of the G=0 component using perturbation theory, however, 
> KS orbital energies are used. In order to fix this bug, one should change:
>
>  rhotwx(:)=-rhotwx(:)/ediff
>
> to
>
>  rhotwx(:)=-rhotwx(:)/egwdiff
>
>
>        Best
>        Deyu
>
> ***************************************************************************
> Deyu Lu (Ph.D)
>
> 190 Chemistry Building
> University of California, Davis 
> One Shields Avenue
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