Delta-Potential Function Model. II. Aromatic Hydrocarbons

Abstract

The pi electrons are considered as following a one‐dimensional network through the molecule as in the free electron model. The potential energy is taken as zero everywhere except at each pi‐carbon nucleus where it goes to minus infinity as a negative delta function. By a procedure of linear combination of atomic orbitals, suitably defined, exact solutions of the Schrödinger equation are easily obtained. Negative one‐electron energy levels, of which there may be as many as there are pi‐carbon nuclei, are interpreted as bound states, with energy zero or positive as ionized states. This model stands between the free electron model on the one hand and the LCAO molecular orbital model on the other. It goes beyond the former in that it can predict not only excitation energies and resonance energies, but also ionization potentials. It surpasses the latter in that exact solutions are obtainable. Numerical results are qualitatively of the right order of magnitude after adjustment of the strength of the delta function which is the one and only variable parameter.