The spin-optimized SCF general spin orbitals. Theoretical formulation

Abstract

A new orbital theory is proposed, in which general spin orbitals (GSO) are introduced in the spin-optimized (SO) SCF scheme. In this SO–SCF–GSO theory, the effective Hamiltonian for each orbital takes the form of a 2×2 matrix composed of the eigenfunctions for two-component spinors. It is found that the GSO’s thus defined should still satisfy a general form of Koopmans’ theorem. The SO–SCF GSO’s are to be obtained by solving two sets of coupled SCF equations for the spin coupling coefficients and the linear combination coefficients for basis functions. Using an STO-6G basis set of the double ζ quality, sample calculations have been carried out for the doublet state of the linear H3 system for which the bond lengths are fixed at 1.470 and 2.984 bohr. The total energy obtained is ∼3 kcal/mole lower than the values which have resulted from the SO–SCF–DODS and the spin-extended Hartree–Fock (SEHF) GSO calculations with the same basis set. The resulting orbitals are found to be more delocalized over the entire system than those obtained by the SO–SCF–DODS theory.