On the Pi-Electron Approximation and Its Possible Refinement

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Abstract
The pi‐electron approximation is defined to be the approximation in which the following two restrictions are imposed upon the total approximate electronic wave functions for some group of molecular states: (I) The wave function for each state satisfies the sigma‐pi separability conditions: (A) the wave function has the form Ψ = [(Σ) (II)], where (Σ) and (II) are antisymmetrized functions describing the so‐called sigma and pi electrons, respectively, and the outer brackets connote antisymmetrization with respect to sigma‐pi exchange; (B) each of (Σ), (II), and Ψ is normalized to unity; (C) each of (Σ), (II), and Ψ is well‐behaved. (II) The sigma description is the same for all states. Imposition of these restrictions is shown to be sufficient to validate the customary procedure in which the pi electrons in a molecule are treated apart from the rest. A formula is given for the pi‐electron Hamiltonian to be used when the pi‐electron approximation is invoked. Present day pi‐electron theories are examined, and lines for carrying out improved calculations are suggested. An iterative procedure is proposed for treating both sigma and pi electrons wherein first a sigma function is assumed (which defines a ``core'' in the field of which the pi electrons move), then a pi function is computed (which defines a ``peel'' in the field of which the sigma electrons move), then a new sigma function is computed, and so on. Certain generalizations of the quantum‐mechanical argument are made which give it wider applicability, and several illustrations are drawn from pi‐electron theory and elsewhere.

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