Subject: Re: CCL:Koopmans' theorem, heat, and light

From: "art'" <[email-masked]>
Date: Thu, 22 Feb 2001 01:20:16 +0100

Hi,

I am not so strong on theorethical level of quantumchemistry, but I have some,
maybe, stupid questons. Please - be patient :) :

What you mean about that the remaining DOUBLY occupied orbitals are not stable
with respect to variation? Does it mean that MO structure and energy is sensible
to basis set or DFT functional? What about hybrid DFT from that point of view ?
May be I missundertood, if I think that KS orbitals from pure DFT describes ONLY
frontier MO sufficiently well - that thought came from the rest discussion
before.

> Koopmans' "theorem" states that, if you take a closed-shell wave function
> expressed as a single Slater determinant, and either remove an electron
> > from the highest occupied orbital or add an electron to the lowest virtual
> orbital, then the new singly occupied orbital is stable with respect to any
> subsequent variation involving the unoccupied orbitals. This is a rigorous
> mathematical proof, and as such qualifies as a theorem.
>
> Note that, the theorem does NOT say that the remaining DOUBLY occupied
> orbitals are stable with respect to variation.

> As for DFT, it has been shown, again with complete rigor, that the energy
> of the highest Kohn-Sham orbital for a closed-shell system is PRECISELY
> the negative of the ionization potential WHEN THE EXACT FUNCTIONAL IS USED.
> As everyone knows, that exact functional remains somewhat elusive, so the
> actual quality of KS eigenvalues for estimating IPs is variable, depending
> on choice of approximate functional.

Arturas Z.