Subject: CCL:G:GAUSSIAN-localization

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Wed, 7 May 1997 11:58:13 +0100

Turski Przemyslaw:

> I have a small request for people who use Gaussian 94.
> I have problems with localization.
> For example in methane CH4 I expected to got 4 equivalent orbitals
> (hibridization sp3) localized on each bond C-H, but it just didn't work.

The molecular orbitals obtained from a Hartree-Fock calculation are 
the so-called canonical orbitals that diagonalize the Fock operator.  
These molecular orbitals are typically "delocalized" over the whole 
of the molecule, they are orthogonal and transform according to the 
irreducible representations of the molecular symmetry point group.  
The canonical orbitals are sometimes characterized as "spectroscopic" 
orbitals; e.g., they have a unique physical significance within the 
context of Koopmans' theorem.  

But molecular orbitals are one-electron wavefunctions and are not 
observables.  In principle, they only serve as convenient building 
blocks in the construction of many-electron wavefunctions.  In fact, 
the determinantal many-electron wavefunction resulting from a 
Hartree-Fock calculation is invariant towards a unitary 
transformation of the occupied orbitals.  It is thus possible to 
transform the canonical set of orbitals into a set of "localized" 
orbitals (a number of localization criteria have been suggested).  
The localized orbitals generally correspond to bond orbitals and 
lone-pairs, and thus preserve the conventional picture dating from 
G.N. Lewis' famous 1916 paper on electron-pair bonds.  However, in 
some cases orbital localization breaks down, f.ex. for aromatic 
pi-systems. 

Localized orbitals can be produced with G94 by using the AIM keyword 
with the BO option, see "Gaussian 94. User's Reference", p 30.  

Jens >--<

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JENS SPANGET-LARSEN  
Department of Chemistry      Phone:  +45 46757781 + 2710
Roskilde University (RUC)    Fax:    +45 46757721 
P.O.Box 260                  E-Mail: [email-masked]
DK-4000 Roskilde, Denmark    http://frederik.ruc.dk/dis/chem/psos
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