This may only show that my mind is *Really* contaminated by the calculational methods, but I tend to think of the orbitals as the mathematical building blocks out of which the wave function is constructed, as a linear combination of the determinants thereof. A multi-electron wave function is just too complicated to comprehend in its entirety.
But (I think this is true) if you include the contributions of all determinants made from the entire set of orbitals--i.e. full CI with no approximations--the orbitals are not unique and any set of orbitals that "spans the vector space," as a mathematician would put it, can be used.
--David Shobe
Süd-Chemie Inc.
phone (502) 634-7409
fax (502) 634-7724
email dshobe.-at-.sud-chemieinc.com
Don't bother flaming me: I'm behind a firewall.
P.S. I wonder if one could define the HOMO at least by reversing Koopman's theorem and calculating the HOMO from the electron density difference between the molecule and its "vertical" radical cation. And similarly with the LUMO using the vertical radical anion, if it exists. Or does one necessarily run into Guosheng Wu's paradox of knowing X^2 but not knowing X?
-----Original Message-----
From: Alan.Shusterman.-at-.directory.Reed.EDU
[mailto:Alan.Shusterman.-at-.directory.Reed.EDU]
Sent: Wednesday, May 28, 2003 1:50 PM
To: chemistry.-at-.ccl.net
Subject: CCL:Orbitals
Some of the postings on this subject have cited *correlations* between orbital properties and physical observables as evidence that orbitals "in some sense" exist.
example: If MOs have no physical reality for multielectron
species, why (a) is Koopmans'
theorem useful, why (b) do photoelectron spectra match
the predictions of MO
energy-level diagrams, and why (c) does the Hueckel 4n+2 rule,
which is based on
MO diagrams, work? (E. Lewars)
example: Orbitals can also, in a sense, be observed experimentally. (M. Johansson)
I'm sympathetic to these statements, but I prefer Jens' point of view.
I am writing not to cast my vote, but to point out an interesting (to me, anyway) parallel. I teach organic chemistry every fall semester, and every year I must convince my students that *resonance contributors* do not exist even though one can correlate physical observables with the properties of these contributors.
Some may still insist that, "if we routinely think of object X to make a prediction, then object X exists, at least in our minds". This is an interesting idea, but I don't think that it relates well to "existence" in the way chemists use this word.
I'd like to thank everyone who has contributed to this discussion so far. It has been interesting.
-Alan
====
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
academic.reed.edu/chemistry/alan/
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