From: MALLON@rzmain.rz.uni-ulm.de (Rainer "RaMa" Mallon)
Subject: Dispersion Interaction in Benzene.
Organization: University of Ulm, Germany
Date: Thu, 10 Sep 1992 11:57:34 GMT
X-News-Reader: VMS NEWS 1.24

I am posting this article to sci.chem and to sci.phys .


Hello !

In my diploma work I am dealing with methods of Molecular Modeling. The
method I use is a semi - empirical quantummechanical one named PCILO
(Perturbative Configuration Interaction Using Localized Orbitals). To
make it easy to understand how this method works let me first explain
it going through the initials of the abbrevetion.

LO : means we are dealing with localized orbitals. How do we get them ?
     we know the s and p orbitals we obtain from analysing the harmonic
     oscillator. Lets call the s and p orbitals atomic orbitals (AO). To
     get a description of the bond between two atoms we assume there are
     only two hybrid-orbitals (HO) making up the bond, one belonging to each
     atom involved. These HOs are made up of AOs. (sp, sp2, sp3).
     At this point we are able to give a description of our a molecule in
     a non excited state, just by buiding a Hartree-Product with all our
     obtained descriptions of the bonds (we will call a bonding orbital a
     molecular oribtal furtheron). First we assume that no bond is in an
     excited state, so we got something like a ground state of the molecule.
     Then we allow simply and doubly excited configurations, meaning that
     one or two electrons switch to an excited state. (This swichting does
     not necesserily mean that the electron stays with the bond it
     originated from. It may leave and *travel* into another orbital where
     it will have to occupy an exicted level due to the fact that the non-
     excited levels are and stay occupied). So this gives us some more
     "allowed" configurations for example there are now n single excited
     configurations, n being the number of the bonds in our molecule.
     And there are n(n-1)/2 doubly excited configurations.

CI : We will now proceed and do a description of our molecule using the
     configurations produced above. This we do by using a configuration
     interaction (CI) method. We add those configurations and
     weigh them with a factor. Our next problem is how to get the weighing
     coefficients.

P  : Assuming that the nonexcited configuration is real close to the
     result, we are doing a non-time-dependent perturbation expansion
     (Raleigh-Schroedinger-perturbation-expansion). Due to some trick
     (which I am not going to explain in detail, Keywords are Moller-Plesset,
     Epstein-Nesbet) the results of the perturbation expanison may be
     interpreted physically. We obtain a resulting term for our systems
     wavefunction and energy each. Special about these terms are the
     following facts :


     - the term of first order Psi(1) and E(1) did vanish due to the
       above mentioned trick, a special decomposition of our Hamiltonian.

     - The terms of second order Psi(2) and E(2) now reflect an interaction
       of those excited configurations with the groundstate configuration.
       This allows to say which interaction of which bonds gives what
       addition to the systems total energy.


Let us now take a look at those excited configurations again.

1. simply excited configurations

   There are two ways of getting a simply excited configuration :

   a. the electron gets excited, but stays with the bond it originated from.
      This leads to a polarisation of the bond.

   b. The electron gets excited and *decides* :-) to go and travel around.
      This is a charge delocation effect. If the electron stays in the
      molecule it originated from we call this charge shift, if it heads
      forward to another molecule this will be called charge transfer.


2. doubly excited configurations

   Like in 1. there are several cases to discuss. But I am only intersted in
   the following :

   Two bonds are losing electrons to the excited state, but both electrons
   stay with their originating bonds. Now those excited orbitals are doing
   an interaction which we call dispersion-interaction.


Now I am getting close to the problem I am dealing with.

Benzene (c6h6) is a molecule with a mesomeric structure. The HOs used for
describing the bonds are of type sp2. The pi - eletrons do form a delocalized
electronic system.

A part of my work is to do a visualization of the effects mentioned above.
When I do the display of the strongest dispersion interactions in benzene I
get some amazing results.

My expectation (please note : classically thoughts now) would be that bonds
being next neighbours (I am talking of the ring-system here) would interact
the most. Next would then be the interactions between overnext partners.

The results i get to see are exactly the opposite. Strongest are overnext
bonds interactions, then we find the next neighbours interactions. My first
thought was that the treatment of the mesomeric structure containes still
some errors, but this was proved as wrong. Each c-c bond is treated as
1.5 times single bond and so are the interactions.

Now I am thinking of some quantummechanical effect that could explain this.


Perhaps somebody has an idea or a clue ? I would be glad to get some opinions
from you. I am right now thinking about an effect caused by the spin of the
electrons involved (-> Paulis principle etc.) But I havent reached a state
of clear thought yet.

Thanks for reading,
	        RaMa.
                   


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| Rainer "RaMa" Mallon           |       I am an instant swimmer ...  |
| University of Ulm, Germany     |       ... just add water !         |
| Department of Applied Physics  |                                    |
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