A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.

A semi-empirical theory is outlined which is designed for the correlation and prediction of the wavelengths and intensities of the first main visible or ultraviolet absorption bands and other properties of complex unsaturated molecules, and preliminary application of the theory is made to ethylene and benzene. The theory is formulated in the language of the purely theoretical method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction, but departs from this theory in several essential respects. First, atomic orbital integrals involving the core Hamiltonian are expressed in terms of quantities which may be regarded as semi-empirical. Second, an approximation of zero differential overlap is employed, and an optional uniformly charged sphere representation of atomic π-orbitals is introduced, which greatly simplify the evaluation of electronic repulsion integrals and make applications to complex molecules containing heteroatoms relatively simple. Finally, although the theory starts from the π-electron approximation, in which the unsaturation electrons are treated apart from the rest, provision is included for the adjustment of the σ-electrons to the π-electron distribution in a way which does not complicate the mathematics. Electronic energy levels in the theory are expressed in terms of ionization potentials of atoms, resonance integrals of bonds, Coulomb repulsion integrals between two π-electrons on the same atom and between two π-electrons on different atoms, and penetration integrals between π-electrons and neutral atoms. Preliminary applications to ethylene and benzene in which only the carbon-carbon resonance integral is treated as an empirical quantity show that the theory can reproduce the results of the purely theoretical method with very little labor. The reasonableness of considering all of the above quantities as semi-empirical is pointed out, however, and it is through a detailed examination and exploitation of this in the second paper of this series that correction for the inadequacies of the π-electron approximation is made and improved agreement with experiment is attained.