The theory of symmetry-preserving Kramers pair creation operators is
reviewed and formulas for applying these operators to configuration
interaction calculations are derived. A new and more general type
of symmetry-preserving pair creation operator is proposed and shown
to commute with the total spin operator and with all of the
symmetry operations which leave the core Hamiltonian of a many-electron
system invariant. The theory is extended to cases where orthonormality
of orbitals of different configurations cannot be assumed.