Evaluation of Matrix Elements of Spin-Dependent Operators for N-Electron Systems. I One-Body Operators
Ian L. Cooper, Jeremy I. Musher · The Journal of Chemical Physics · 1972
The properties of the symmetric group are utilized to obtain a decomposition of matrix elements of spin-dependent operators into sums of products of space- and spin-dependent matrix elements. The Wigner-Eckart theorem is then applied, and results in an expression for the matrix elements in terms of reduced matrix elements in both space and spin and a set of coupling coefficients. The coupling coefficients and the reduced spin-matrix elements are evaluated for N=2, 3, 4, and the corresponding reduced spatial matrix elements are evaluated in the simplest case of an orbital approximation.