THE FORM OF SPIN ORBITALS FOR OPEN-SHELL RESTRICTED HARTREE-FOCK REFERENCE FUNCTIONS

A new set of spin orbitals is proposed for single-reference correlation procedures based on an open-shell restricted Hartree-Fock (RHF) reference function. The spatial parts of the new spin orbitals are from an open-shell RHF calculation. The spin part of the doubly occupied (or unoccupied) orbitals is the usual alpha or beta spin function, but the spin part of the singly occupied and singly virtual orbitals takes the form sigma+ = (1/square-root 2) (alpha + beta) and sigma- = (1/square-root 2) (alpha - beta), respectively. These spin orbitals form a complete, orthonormal set. The RHF single determinant based on these spin orbitals is an S2 eigenfunction, but a linear combination of S(z) eigenfunctions. The advantage of these spin orbitals is that equations for perturbation theory or coupled-cluster theory are symmetric in the spin indices and hence the number of independent parameters to be determined is dramatically reduced.