Problem with bond-interactions in PCILO

From: mallon-: at :-rzmain.rz.uni-ulm.de
Subject: Problem with bond-interactions in PCILO
Date: Wed, 23 Sep 92 11:38:02 +0200
 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 abbreveation.
 LO : means we are dealing with localized orbitals. How do we get them ?
      We know the s and p orbitals we obtain from analysing H - problem.
      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 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 switching 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 excicted 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 loosing 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 the problem I am dealing with :
 Benzene (c6h6) is a molecule with a mesomeric structure. The HOs uses 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 I 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           |
 |
 | University of Ulm, Germany     |       I am an instant swimmer ...  |
 | Department of Applied Physics  |       ... just add water !         |
 | mallon-: at :-main01.rz.uni-ulm.de    |                                    |
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