Subject: Orbitals

From: Rene Fournier - 1999-07-07 <renef)at(yorku.ca>
Date: Fri, 30 May 2003 11:27:21 -0400 (EDT)

I agree with Lou Noodleman's point that we have many mathematical
models with different degrees of rigor to approach reality
without ever quite reaching it (sounds like calculus...).
And I do like orbitals, especially Kohn-Sham orbitals, a lot.
But I think there's a difference between, say, an approximate 
electron density -- far from reality because it is inaccurate --
and a set of orbitals -- far from reality because we're not sure
exactly what kind of measurements they should be compared to.

That being said, theoretical arguments and comparisons to
experiments support the view that KS orbital energies are good
approximations to relaxed vertical ionization potentials
(Chong, Gritsenko, Baerends, J Chem Phys 116 (2002) 1760),
that differences of virtual and occupied KS orbital energies
are good approximations to excitation energies (A Savin,
CJ Umrigar, X Gonze, Chem Phys Lett 288 (1998) 391), that
KS orbitals give good approximations to spherically averaged
momentum distributions obtained by electron momentum spectroscopy
(P Duffy, DP Chong, ME Casida, DR Salahub, Phys Rev A 50 (1994)
4707;  S Hamel, P Duffy, ME Casida, DR Salahub Journal of Electron
Spectroscopy and Related Phenomena (2002?)).  To me, KS orbitals
are meaningful, and are useful for quantitative comparisons even
though it's not 100% clear what they should be compared with.
Whether they are "real" in some particular philosophical system
is not as important for me...  but it's still interesting!  :)

-- Rene Fournier.
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