Eigenfunctions ofS2by a Spin Operator Method

Abstract

An operator is derived which is a function of step-up and step-down operators pertaining to spin angular momentum, and which creates a state of definite multiplicity when operating on a single determinant of spatial and spin orbitals. This paper is concerned with the problem of finding all of the orthogonal singlets for a $2N$-electron system in terms of the spin operator. The five orthogonal singlets corresponding to the six-electron spin degeneracy problem are studied in detail by means of the branching diagram. The fourteen orthogonal singlets corresponding to the eight-electron problem and the forty-two orthogonal singlets corresponding to the ten-electron problem are written down. Some remarks are made concerning the application of this method to a configuration interaction investigation.