Mapping Molecular Orbital–Configuration Interaction to Valence Bond Wave Functions

Chapter 4 reports a simple algebraic method for transforming any molecular orbital (MO) wave function into a valence bond (VB) wave function of classical type, dealing with purely localized atomic orbitals (AOs) or hybridized AOs. The MO wave function may be of a single-determinant type or involve many MO determinants (following extensive configuration interaction). The first step is to generate a complete and nonredundant set of VB structures for the electronic system at hand, by means of a graphical method due to Rumer. Then expand each MO determinant into its constituents, AO determinants, using the concept of half-determinants which considerably reduces the computational effort. Finally, the so-transformed MO wave function is projected over the Rumer set of VB structures to obtain their coefficients. The weight of each VB structure can be calculated by means of the Chirgwin–Coulson formula. The method is applied to butadiene and ozone.