Functional analysis concepts and Hartree-Fock instability conditions

Abstract

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