[Pw_forum] Problem with nbnd in clusters

[Cyrille Barreteau]

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
>_______________________________________________
>Pw_forum mailing list
>Pw_forum at pwscf.org
>http://www.democritos.it/mailman/listinfo/pw_forum
>  
>


-- 
==================================================================
Cyrille Barreteau  | phone : +33 (0)1 69 08 29 51
CEA Saclay         | fax   : +33 (0)1 69 08 84 46
DSM/DRECAM/SPCSI   | email cyrille.barreteau at cea.fr
Batiment 462       |
91191 Gif sur Yvette Cedex  FRANCE
          ~~~~~~~~~~~~~~~~~~~~~~~~
http://www-drecam.cea.fr/spcsi/index.php
http://www-drecam.cea.fr/Images/Pisp/cbarreteau/cbarreteau_fr.html
http://www-drecam.cea.fr/Phocea/Membres/Cours/index.php
==================================================================