Subject: CCL:HOMO/LUMO energy gap

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Tue, 4 Mar 2003 13:03:43 +0100

Eike Huebner:

> can anyone point me to a paper where the reasons for the too large
> energy gap between calculated (Hartree-Fock) HOMO-LUMO orbitals in
> comparison to the longest wavelenght absorbtion is discussed? In
> fact I am looking not for a lot of examples or calculations but for
> a more general paper (which can be cited aswell) discussing why HF
> calculations give much too short longest wavelength absorbtions
> compared to the experiment.

Dear Eike!

The volume by Klessinger and Michl has a Section 1.2 where the use of 
molecular orbital (MO) models in the description of electronic 
transitions is explained: 

Martin Klessinger, Josef Michl: "Lichtabsorption und Photochemie 
organischer Molekuele", VCH 1989, ISBN 3-527-26085-4

Later editions and in English are available. - Basically, equating a 
molecular orbital energy difference to an electronic excitation 
energy is wrong, primarily for two reasons:

1)
The energy required to promote an electron from MO i to MO j is not 
equal to the energy difference e(j) - e(i).  The promotion energy 
E(i-->j) can be expressed as   

  E(i-->j) = e(j) - e(i) - v(i,j)

where the term -v(i,j) represents the interaction between a hole in
orbital i and an electron in orbital j.  This term may be relatively
small if the two molecular orbitals are spatially separated, but in
general, v(i,j) amounts to several electron volts and is by no means
negligible.

2)
The wavefunction |i-->j> of an excited electronic configuration is not
in general a good approximation to an eigenfunction of the
many-electronic Hamilton operator H.  Generally, matrix elements
corresponding to <i-->j|H|k-->l> are not close to zero.  Hence,
excited configurations tend to interact, and a proper description must
include Configuration Interaction, (CI).  Of particular importance is
the first order CI between near-degenerate configurations of the same
symmetry, f.inst. for alternant hydrocarbons where it gives rise to
"plus" and "minus" states. - Inclusion of multiply excited
configurations (like i,k-->j,l etc.) in the CI formally accounts for
electronic correlation effects, thus leading to a description going
beyond the orbital picture.  However, semiempirical CI-procedures
(PPP, CNDO/S, INDO/S, ZINDO, etc.) usually limit the CI expansion to
singly excited configurations, and account for correlation effects by
empirical adjustment of parameters in the models. 

Yours, Jens >--<

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JENS SPANGET-LARSEN         Office:         +45 4674 2710
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