Cluster expansion of the wavefunction. The open-shell orbital theory including electron correlation

Abstract

A previously developed new approach to the orbital theory with the formalism of the cluster expansion of a wavefunction is applied to open-shell electronic systems in order to include the electron correlation effect within the conventional formalism of the orbital theory. The open-shell orbital theory involving the electron correlation is defined as ‖Φ〉=𝒫 exp[iFK+iFM]‖0〉. The 𝒫 is the projection operator to resolve the stability dilemma and the FK and FM are the excitation operators for closed-shell and open-shell orbitals, respectively. The new orbital theories, which are called Modified SEHF (MSEHF) theory and complex GSO theory, have been proposed with special choices of F and 𝒫. They are analyzed in contrast to the conventional orbital theories such as UHF, SEHF, CMO, and GVB theories in the form of the limited CI based on their own natural orbitals. The MSEHF theory includes the correlation effect effectively in open-shell systems and constitutes a natural extension of the closed-shell SEHF theory (the conventional SEHF theory fails in open-shell systems). The complex GSO theory is the most suitable orbital theory to include the electron correlation effect within the orbital theory (to include spin correlation we have to adopt the symmetry-adapted-cluster (SAC) expansion formalism as shown previously).