Unitary group approach to the many‐electron problem. I. Matrix element evaluation and shift operators

Abstract

Abstract This is the first paper in a series of three directed toward the evaluation of spin‐dependent Hamiltonians directly in the spin‐orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U ( n ) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.