Inter-relations between VB & MO theories for organic II-networks

Abstract

This chapter discusses the Valence-Bond (VB) and Molecular-Orbital (MO) theories—there are review and comparison of the two. A natural question concerns the possibility of mathematical inter-relations between these VB and MO theories, especially because each of them may be viewed to be based on rather disparate pictures: the VB picture being built from localized orbitals arranged into (one or more) correlated many-electron structures, whereas the MO picture is built from delocalized orbitals in a single uncorrelated (determinantal) structure. Each picture can be viewed as complementary. That is, each theoretical picture is viewed as naught but a different representation of the same underlying quantum reality. Attention is focused on the rather well studied such models for π-electron networks in neutral (that is; non-ionic) organic molecules. Some aspects of the questions about mathematical inter-relations concern the presentation in terms of molecular graphs, these being natural mathematical representations of the classic valence structures of molecules. Such a graph G consists firstly of sites corresponding to atomic π-centers and secondly of edges corresponding to bonds between pairs of atoms. The mathematical field of graph theory provides a natural framework for classic chemical bonding ideas of modern quantum chemistry, the simple VB and MO models for a particular molecule being entirely determined by their graphs. The general inter-relations considered between VB and MO models then can be expected to be expressed in terms of graph-theoretic language, for general classes of molecules. Both the simple VB and MO models for organic π-networks are quantum–mechanical models explicitly expressible in terms of their molecular graphs. The chapter discusses the Pauling–Wheland VB model, Heisenberg model, and Hückel MO model. There is discussion on MO-based elaborations and cross-derivations, Hückel rule, polymers and excitations, and the prospects of VB and MO theories.