Subject: Re: CCL:How to define HOMO-LUMO gap in open shell system ?

From: Ulrike Salzner <salzner = fen.bilkent.edu.tr>
Date: Tue, 05 Jul 2005 10:11:55 +0300

Dear Ricardo,
I have a partial answer to your question. I have done calculations on
polyenes in the neutral ground states and on cations, which are open-
shell systems. I give you the results for C12H14 and C12H14+ as
examples. The experimental excitation energy of the neutral in the gas
phase is 3.65 eV (d'Amico, JACS, 1980, 102, 1777).I do not know of
experimental values for the cation. The only information I have is that
doped conducting polymers have "midgap gap states" with about half the
excitation energies of the neutral forms. But this involves counter
ions.

The HOMO-LUMO gap of neutral C12H14 with the B3P86 functional with 30%
HF exchange and a polarized split valence basis set is 3.49 eV. TDDFT
(same functional) gives 3.26 eV and TDHF 3.78 eV. The HOMO-LUMO
transition is the dominant transition in the excited state wavefunction.
With a CASSCF calculation including 12 electrons and all 12 pi-orbitals
the first excited states lies at 3.89 eV.

The cation has the following orbital energies (DFT same functional as
above). alpha: HOMO 10.06 eV, LUMO 6.94 eV, beta: HOMO 10.83 eV, LUMO
7.80 eV. Thus there are three possible gaps: alpha HOMO-LUMO: 3.12 eV,
beta HOMO-LUMO 3.30 eV, alpha-beta HOMO-LUMO 2.27 eV. The lowest TDDFT
excitation energy with large oscillator strength is 2.42 eV. This is
close to the alpha HOMO beta LUMO gap but in the TDDFT wave function
there is no such transition. The excited state arises from several
excitations with HOMO-LUMO transistions within alpha and beta space
being dominant. I am working on CASSCF calculations but these are not
finished.

My conclusion at the moment: be careful, it seems to work for the wrong
reason.

Regards,
Ulrike

On Mon, 2005-07-04 at 05:45 -0700, Ricardo Oliveira wrote:
>  Dear all,
> 
>  I have noticed that some excitation energies , in
> closed shell systems, have energies similar to the
> HOMO-LUMO gap.
> 
>  Considering that the term 'HOMO-LUMO gap' is not very
> appropriate for open shell systems, how can we do a
> rough estimate of the excitation energies in this
> case?
> Shall they be somewhat similar to the homo-somo(singly
> occupied orbital) gap?
> Can the gaps mentioned by Ding Xunlei,on his CCL
> communication, have any meaning at all?
> 
> Thanks
> 
> Ricardo O Esplugas
> Dept of Chemistry
> Sussex University
> UK
> 
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-- 
Ulrike Salzner
Associate Professor
Department of Chemistry
Bilkent University
06800 Bilkent, Ankara
Turkey