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[Michel Côté <michel.cote@umontreal.ca>]

Dear all,

Le 14/04/06 04:40, « Nicola Marzari » <marzari@MIT.EDU> a écrit :

> 
> 
> Dear Andrew,
> 
> what baffles me is finding an answer to this question:
> "What is the correct set of occupation numbers to use in the
> calculation of the energy of an atom or an ion, when using LDA/GGA".
> 
> One answer is, as you mention, to let the electrons spread equally in
> the partially-filled subshell.
> 
> Another is to take the occupations that minimize the total energy (I
> believe that often these two choices are equivalent, but I do not know
> if they are always equivalent. E.g. in a d shell with 1 minority
> electron, you could have e.g. 5*0.2, 2*0.5, and 3*0.33333, all making
> "chemical sense").
> 
> A third choice is to use integer occupations, always (e.g. since
> fractional occupations ae not v-representable (if I recall correctly
> Englisch and Englisch 1984), or simply because a fractional
> occupation makes no sense, in an atom, unless if you have the exact
> grand-canonical exchange-correlation potential.
> 
> A fourth choice is to take ensemble averages of integer occupations results.
> 
> I haven't found, in my cursory explorations, a satisfactory answer -
> this seems particularly relevant for cases when systematic tests
> are done on atomization energies (e.g. by the chemistry community),
> where the difference in atomic energies by strategies above are much
> larger than the average error in atomization energies.
> 

Is there a chemist in the room?

Actually, I called a colleague here, Matthias Ernzerhof (the E of the PBE
functional) who is a chemist to ask him that question. For the tests, the
chemists use real wave functions (px, py, pz) and they all have the same
energy. One of the problem that Becke answered was if spherical harmonic are
used instead (Y11, Y10, Y1-1), in principle the energy should be the same
but wave functions that have a current (complex, Y11 et Y1-1) will result in
a different answer if the functional does not have a current part.

About the symmetry of the charge, Matthias said that they do it on purpose
to break the symmetry so that they have the lowest energy. So for Boron for
example, one p orbital is occupied instead of 1/3 in each. However, he
mentioned that this is still an issue.

Michel