Subject: CCL:HOMO-LUMO vs. lambda max

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Thu, 27 Apr 2000 14:13:17 +0100

Yeoh Hak Koon:

> What are the reservations or objections of equating the HOMO-LUMO energy gap 
> to the maximum wavelength peak (lambda max) in a UV-Vis spectra? 

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 orbital i to orbital j is not 
at all 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         Phone:  +45 4674 2000  (RUC)
Department of Chemistry             +45 4674 2710  (direct)
Roskilde University (RUC)   Fax:    +45 4674 3011 
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