Studies in Configuration Interaction. I. Matrix Elements between Spin-Coupled Functions

Rules are presented for the derivation of matrix elements of all one- and two-body operators between arbitrary spin-coupled functions arising from arbitrary orbital configurations. The coupling scheme used is essentially that employed in valence bond theory, but the results are completely general, including, for example, the matrix elements of spin-dependent operators which couple functions with different spin eigenvalues. In later papers these rules will be applied to various spin-coupling problems.