Subject: CCL:Summary: DFT and Koopmans' theorem

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Mon, 19 Feb 2001 16:06:54 +0100

Christoph van Wuellen:

> >  > To summarize most of the responses, Koopmans' theorem does not hold for
> >>  DFT.  Of course, DFT is not an MO method, so it doesn't make sense to even
> >>  talk about HOMOs or LUMOs
> >  >...
> 
> so what? Koopman's theorem is no theorem and does not hold for anything, at
> least not in a mathematical sense. For Hartree-Fock, it is sometimes a good
> approximation because of error compensation. it is no "theorem".

"Does not hold for anything, at least in the mathematical sense"? 

For closed-shell species, "Koopmans' Theorem" holds excactly, in the 
mathematical sense, provided the assumption of "Koopmans' Approximation" is 
made (essentially: the frozen Hartree-Fock-orbital assumption and neglect of 
configuration interaction). Obviously, Koopmans' approximation frequently 
breaks down, but this does not affect the validity of Koopmans' theorem.

Yours, Jens >--<

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From: [email-masked] (Alan Shusterman)
Date: 19 Feb 2001 09:14:53 PST

--- You wrote:

--- end of quote ---

This attitude is reasonable if one is wondering how best to calculate IP and
EA. Koopmans does not give accurate IP and EA, a flaw that is built in to the
"theorem".

Complete dismissal of Koopmans' theorem does not make sense to me, however,
given the large number of chemists who rely on it as a guide to chemical
reactivity. Chemists who think about chemical reactivity in terms of MO
energies (and Frontier MO properties) are relying on the notion that these
energies indicate how easily a molecule can gain/lose an electron. If you like,
you can tell them these energies indicate no such thing (an exaggeration,
yes?), but what tools would you give them to use instead? Should the way they
think about reactivity be limited to methods that give state-of-the-art
numerical accuracy?

-Alan

====

Alan Shusterman

Department of Chemistry

3203 SE Woodstock Blvd

Reed College

Portland, OR 97202

503-771-1112, ext. 7699