Subject: Re: CCL:Orbitals and reality

From: Lou Noodleman <lou:at:scripps.edu>
Date: Fri, 21 Jan 2005 15:11:20 -0800 (PST)

Dear Phil Hultin, Alan Shusterman and CCL group,
About May of last year, I sent a post to CCL on this topic.
My view then and now (a little more philosophically then)
is that "orbitals" are not reality itself, but rather an extremely
valuable concept useful for describing reality. 
That is, the orbital concept
is "a map, but not the territory". At that time, I mentioned e-2e inelastic
scattering experiments, which report the electron momentum distribution
function (orbital densities in momentum space) for individual molecular
orbitals and at the same time the experiment reports the ionization potentials
IP(n) of the various ion states from the neutral ground state.
Roughly speaking, these experiments report the shapes of the molecular orbitals.
The cation states can correspond to the main one-hole ionization lines and also
to their shakeup satellites.  Specifically, these orbitals are well defined
and are called Dyson orbitals. For example, see Pang et al., J. Chem. Phys.112,
8043 (2000) for a combined experimental-theoretical/computational study.
Typically, the high-lying molecular orbitals are well-defined experimentally
(those that lie at less than about 14 eV (IP) for saturated hydrocarbons),
while deeper lying orbitals show more mixing and eventually "a breakdown of the
orbital picture of ionization" for the inner valence shell C(2s), at about 23 eV
and deeper. Also, in work in my own research group, we showed that the
delocalized molecular orbital picture of ionization breaks down for inner
 electron shells and for lone pairs in dimers and for symmetry equivalent groups
(examples: N2, O3, Cr(CO)6, Se(CN)2) when electron relaxation from the "passive
electrons (and their orbitals)" is stronger than the bonding or antibonding
interactions between the symmetry equivalent lone pairs or inner shell electrons. Then a localized excitation dominates, with a much smaller splitting
bonding/antibonding for the relaxed hole state.
(Noodleman et al., Chem. Phys. 64, 159-166, 1982, and Jonkers et al., Mol. Phys.
46, 609-620, 1982)
 As in the examples above, these are questions of physics and chemistry,
comparing calculations and experiment, and not (mainly) of philosophy.
It is true that sets of occupied orbitals can be transformed to other
sets (equally valid) under a unitary transformation, for example, 
delocalized MO's to localized MO's, but this is not true
 for ionization states or optical excitations. Further, not only electron 
density, but also kinetic energy matters, and for excited states,
transition moments determine intensities. While in principle, electron orbitals
can be circumvented in the analysis with reduced density matrices and transition
density matrices, but how do you compute, use, and understand these without
simpler tools.
In practice, orbitals are the simplest way to incorporate
both electron kinetic energy and electron density (also spin density) in
descriptions of atoms, molecules, and solids. Here I understand that I differ
> from Bader's ideas, although I like forces and the virial theorem as much
as the next fellow.
 Also, a "mean field" (orbital) description is
always valuable. Niels Bohr has emphasized a number of complementarity relations
(as in the Heisenberg Uncertainty Principle). In addition to "position-momentum", "Energy-time", and "particle-wave", the complementary variable to "accuracy"
is "clarity". Einstein has recommended that a good theory be "as simple as
possible, but no simpler". In my mind, this strongly supports the use of the
orbital concept.
Louis Noodleman
Dept. of Molecular Biology, TPC15
The Scripps Research Institute
La Jolla, CA 92037
.