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A theory of electron correlation in nonclosed-shell states, such as excited states of atoms and molecules, triplet states, free radicals, and transient species, is developed. A general (multiconfiguration) restricted Hartree—Fock (GRHF) wavefunction is taken as the starting point. When near degeneracies are not strong enough to cause large orbital and charge deformations, Roothaan-type restricted Hartree—Fock (RHF) open-shell orbital theories are used. The first-order Schrödinger equation with RHF as the zeroth-order wavefunction is solved. Various correlation processes (near-degeneracy-type internal correlations, semi-internal pair correlations in which only one electron is ejected out of the Hartree—Fock sea, external pair correlations as in closed shells, and spin and symmetry orbital average polarization effects) are obtained in a form separated from one another. The second-order energy also includes ``cross-pair correlation effects,'' an open-shell phenomenon that need be taken into account in the evaluation of electronic spectral levels and stability of open-shell systems. The first-order solution yields the main open-shell correlation processes, which are generalized to the variational theory in II with means for evaluation of the separate effects.
Silverstone et al. (Tue,) studied this question.