Group Theoretical Classification of Instabilities and Interconnection Relation of the Unrestricted Hartree-Fock Solutions in a Molecular System with a Spatial Point Symmetry. I: General Theory

Abstract

This paper describes a general theory on classification of instabilities and interconnection relation between UHF solutions in a molecular systems with a spatial point symmetry. It is shown that an instability of a UHF solution is characterized by an irreducible single valued representation over the real number field (R-rep) of the invariance group of the UHF solution. The general expression of the instability matrix characterized by an R-rep is given. It is shown that the possible symmetry of a UHF solution bifurcating from an instability is determined by the R·rep which characterizes the instability. Some criterions are given to determine what subgroup of the original invariance group can be the invariance group of the solution produced by an instability belonging to an R-rep. A general procedure is given to obtain all R-reps of the invariance group of a UHF solution.