Subject: CCL: RE: Orbitals

From: "Shobe, Dave" <dshobe.-at-.sud-chemieinc.com>
Date: Wed, 28 May 2003 16:09:12 -0400

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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