Localized and delocalized π-electron energies in MO and VB theory

Looyenga has recently pointed out at an apparent anomaly between the valence-bond and molecular-orbital descriptions of a single Kekulé structure, whereby in the VB model there are repulsions between non-bonded electrons in adjacent double bonds, which do not appear in the MO model. It is shown that if proper account is taken of atomic overlap integrals, and if the wave function is put into determinantal form, this difference disappears. Thus the difference between localized and delocalized π-electron energies in the two models is closely similar. In the MO description of a Kekulé structure, negative π-bond orders appear across the formally ‘single’ bonds. On delocalization these may or may not be converted to postive bond orders. Two different ways are described for easy calculation of these negative bond orders and numerical examples are provided. These negative bond orders are important for any proper study of hyperconjugation, as is shown by consideration of ethane and methylacetylene.