The ABINIT Users Mailing List ( CLOSED )

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

Dear Audrius,

If you are really interested in getting reliable HOMO and LUMO energies
for solids, the GW part of abinit is perfectly suited to that issue.
You'll need no supercell, no charged systems...
This is not exactly the answer to your question, but this is just a work 
around.

Fabien



Audrius Alkauskas wrote:
> Dear ABINITioners
>
> The question I have might seem the one you met already in the forum but 
> it is more subtle. This is more a periodic-DFT than ABINIT question, but 
> I still want to ask it.
>
> Let us assume I have a large periodic cell (ultimatel very large) of 
> some bulk material. I calculate the eigen-spectrum of a neutral solid. 
> Say, I get e_{HOMO} and e_{LUMO} energies of the highest-occupied and 
> lowest-unoccupied states (top of valence and bottom of conduction band). 
> I know that these energies are defined only up to an arbitrary constant 
> C. If I would shift my local potential by C, my eigenvalues would shift 
> by the same magnitute even though total energy would remain the same.
> I can do this, for example, by letting G=0 term of the Hartree potential 
> to be C isntead of zero.
>
> Now, say, I charge the system by one electron. Let us assume that the 
> cell is so large that LDA XC potential changes very little, as well as 
> all other potentials. Also, compensating background produces just a 
> negligibly small potential change. In this case, would the local 
> potential in periodic DFT codes remain (or be chosen to be) the same as 
> in the case of the neutral cell? If so, then the total energy 
> differences that I should get should more or less correspond to 
> eigenvalues of the neutral system, i.e., the total energy of the 
> negatively charged solid is arbitrary, but also only up to a constant C.
> That is, if I would calculate an energy needed  to add electron I would 
> get exactly energy of the LUMO (which depends on C, but as soon as C is 
> fixed, the total energy differences (for example 
> E_{total}^{-}-E_{total}^{0}) should correspond to Kohn-Sham eigenvalues 
> of the large neutral solid). Is that right? I don't know whether I was 
> able to formulate my question properly.
>
> I know all the problems related to XC discontinuity, Kohn-Sham gap etc.
> Also, my question relates only to solids, but not to molecules, for 
> which total energy differences can give a better estimation of the true 
> gap than the Kohn-Sham gap.
> My worry is somewhat different. I just wonder why total energy 
> differences of solids reproduce Kohn-Sham spectrum in some DFT codes and 
> with certain pseudopotentials, but not in the others. In principle they 
> should, if I keep cell geometry, pseudopotentials, etc, the same, and 
> just change the charge state.
>
> Regards
>
> Audrius