Ordinary field‐theoretic methods for self‐consistent wave functions which describe bond formation and dissociation. II. Commutative coupling case

Abstract

AbstractHartree–Bogoliubov–Valatin (HBV) theory may be implemented with Lipkin Hamiltonians to obtain self‐consistent BCS wave functions which describe bond formation and dissociation. These wave functions are in turn vacuua for Nambu's representation of Feynman–Dyson–Goldstone diagrammatic perturbation theory, and hence provide suitable references for the many‐body treatment of correlation. Exact SCF solutions of the HBV equations are equivalent to special even‐replacement MC–SCF solutions. The latter are similar to generalized valence bond theory, and require one Fock operator for each one‐particle shell. The commutative coupling case of HBV theory is realized when the number‐conserving renormalized one‐body and number‐nonconserving pairing operators commute. In this case, a set of orbital equations which involves a single Fock operator may be solved. Since this could prove to be a significant simplification for large systems, the commutative coupling and exact solutions are compared here for the fragmentation of H2 and F2. Results suggest that commutative coupling orbitals will be useful for the aforementioned many‐body theory.