FUNCTIONAL-ANALYSIS CONCEPTS AND HARTREE-FOCK INSTABILITY CONDITIONS

Concepts of functional analysis, namely, regular points, tangent subsp aces, constraint surfaces, Lagrangian matrix restricted to the tangent subspace of a constraint surface, are presented in connection with th e Hartree-Fock (HF) problem. The energy functional in LCAO approximati on is considered to be a polynomial function of several variables subj ect to subsidiary conditions. General HF equations and instability con ditions for the unrestricted Hartree-Fock (UHF) solutions are derived from this standpoint.