Spin-dependent unitary group approach. II. Derivation of matrix elements for spin-dependent operators

Abstract

This paper is concerned with matrix elements of spin-dependent operators. We present a detailed derivation of the matrix elements of the operators Δ(n)ij and Δ(n+1)ij shown in the article by Gould and Paldus [J. Chem. Phys. 92, 7394 (1990]) to lead to the matrix elements of all spin-dependent operators within the Gel’fand spin-adapted basis; as required for spin-dependent CI and the calculation of relativistic energy level shifts. Besides being useful for spin-dependent CI calculations, involving the incorporation of spin–orbit and spin–spin type electronic interactions, our results can be used for the calculation of spin-dependent properties coming from a wave function with well defined spin. Such wave functions can now be routinely computed using any one of numerous unitary group based program systems, hence the usefulness of our formalism for chemical properties. In particular we give an application of this formalism to the calculation of the spin density of a molecule using a spin-adapted wave function. In a future publication we will show how our formalism involving the Δ(n) operator leads to compact formulas for the shifts in the electronic energy spectrum of a molecule due to relativistic effects. We briefly describe our numerical implementation of these new matrix elements as used for the calculation of the spin density of a molecule.