Matrix Elements of Spin-Interaction Operators

Methods are given for calculating matrix elements of an arbitrary two-electron spin-dependent operator, using wavefunctions based on open-shell spin-projected spin—orbital products. The formalism is developed both in terms of the entire spin space of the desired multiplicity and in terms of the projection operators discussed by Löwdin. The results are also specialized to the important case of orthogonal spatial orbitals. The methods are illustrated by application to the Fermi-contact interaction.