Theory of the Unrestricted Hartree-Fock Equation and Its Solutions. IV: Behavior of UHF Solutions in the Vicinity of Interconnecting Instability Threshold

Abstract

A perturbational and local (in the adiabatic parameter space) UHF equation in the vicinity of an instability threshold is derived. It becomes an algebraic equation and the group theoretical symmetries of the initial UHF solution and the instability impose constraints on the parameters in it. All possible local behavior of UHF solutions and the local structures of their existence domains are determined in the vicinity of non-degenerate and doubly degenerate instability thresholds.