[Pw_forum] Problem with nbnd in clusters

[Nicola Marzari]

> 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


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Prof Nicola Marzari   Department of Materials Science and Engineering
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