[Pw_forum] Problem with nbnd in clusters

[Stefano de Gironcoli]

I think that given a DFT functional form the GS is, by definition, the 
solution that gives the lowest energy and that in those cases where the 
"true" functional would lead to degeneracy (open shell atoms to name a 
typical system) the approximate DFT's we all use will break the symmetry 
and produce a cylindrical (or even lower) symmetrical solution (for 
Jahn-Teller related reasons). This is the case for C and O atoms for sure.
stefano

Cyrille Barreteau wrote:
> Well this is an interesting discussion which deviates from the original
> "technical" problem.
>
> If you want to obtain the "right" configuration of an atom standard
> LSDA is surely not the appropriate method and the strong degeneracy
> that wou will obtain will lead to "existential" questions such as
> "how to fill degenerate states".
>
> First you must include spin-orbit coupling which will induce a
> some splitting (and give you second Hund's rule).
> But if you want to get the third Hund's rule you also have
> to include the so-called orbital polarization (with B Racah
> parameter), that you can obtain in a full LSDA+U method
> including all the matrix elements of the Coulomb interaction
>
> At the very end I think you never have any degeneracy (ouf):-)
>
> Let us also not that this degeneracy problem is of course very
> relevant for cluster physics and often linked to Jahn-Teller
> distorsion (but maybe atoms would also like to distort and
> become elliptic:-)
>
>    cyrille
>
>
>
>
> Nicola Marzari wrote:
>
>   
>>> I agree that symmetrization (due to the periodization) induces a 
>>> degeneracy but the
>>> "real" system that I want to simulate (a dimer alone in space) has even more
>>> symmetries. In particular it has a rotational symmetry that will never 
>>> be there
>>>    
>>>
>>>       
>> Well, this is the part I've never understood - that's why I was 
>> mentioning the boron atom. I wouldn't necessarily agree that your
>> dimer charge density should have the same symmetry of the ionic
>> potential - as much as a dissociated H2+ molecular ion doesn't have
>> mirror symmetry on the plan bisecting the bond, as you dissociate the
>> molecule, or antiferromagnetic MnO has a lower electronic-structure
>> symmetry, since the Mn are inequivalent from the point of view of spin
>> density.
>>
>> Also, the potential in atoms is spherical, but I'm sure there are
>> solutions lower in energy that are cylindrical. Think at a transition
>> metal with only one d electron: do you fill up 1 orbital 1.0, 2 orbitals
>> 0.5, 3 orbitals 0.33333, 5 orbitals 0.2 ? Only the last is spherical,
>> all others are cylindrical, although of course an ensemble of
>> measurements on atoms will always converge on the spherical limit.
>>
>> Am I the only one worrying about this ? It seems a key problem
>> that I've never seen addressed - Englisch and Englisch in 1983
>> had a paper on the fact that fractional occupations are somewhat
>> not compatible with v-representability, but I don't recall it very well.
>>
>>
>> 			nicola
>>
>>
>> ---------------------------------------------------------------------
>> Prof Nicola Marzari   Department of Materials Science and Engineering
>> 13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
>> tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu
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