Knowledge Bank

A simplified complete LCAO molecular orbital theory'' is outlined which is designed for correlation and prediction of electronic spectra and other properties of unsaturated organic molecules, Primitive applications of the theory are described. Simplified complete LCAO MO theory starts from the so-called $\pi$-electron approximation, in which the unsaturation, or $\pi$-electrons of a molecule, are treated apart from the rest, the latter being manifest only in the effective core'' in the field of which the former move. Wave functions for various states of the $\pi$-electrons are built up from 2p atomic orbitals on the individual atoms, and energies of the various states are computed in a prescribed manner which includes in a natural way a correction for the inadequacy of the $\pi$-electron approximation. The theory combines the advantages of the conventional semiempirical LCAO MO method with the advantages of the conventional purely theoretical method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction. The degree to which the semiempirical LCAO method can successfully correlate organic spectra has been examined in detail by $Platt.1$ He finds the method good, but stresses that consideration of configuration interaction is essential for ultimate understanding of band positions and intensities. Configuration interaction is not quantitatively provided for in this method, however, and furthermore it does not take proper cognizance of electronic interaction---it makes no distinction between singlet and triplet states, for example. Simplified complete LCAO MO theory may be regarded as a quantitative prescription for inclusion of configuration interaction effects in a semiempirical LCAO MO theory from which internal inconsistencies have been removed. The method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction, as developed by Goeppert-Mayer and $Sklar,2$ $Craig,3$ and $Roothaan,4$ provides a proper theoretical framework for a consistent theory. In its purely theoretical form this method is impractical, however; it lacks the empirical element which one must expect in a genuinely useful theory, and its mathematics is unwieldy---benzene is the most complex molecule on which the method has been fully $tested,5$ and the organic chemist may reasonably expect more! Simplified complete LCAO MO theory incorporates an empirical element into the antisymmetrized product method. This by itself would not yield a wieldy method, but through the introduction of a certain approximate representation for atomic 2p orbitals a sweeping simplification of the mathematics is achieved which makes applications to complex molecules feasible.