On the convergence of the hartree-fock selfconsistency procedure

Abstract

A dynamical viewpoint on the electronic system of a molecule is systematically introduced. It is shown that the conventional quantum-chemical consideration can be treated as a particular case of a more general approach connected with taking into account the time-dependence of molecular-orbital coefficients. Possible physical reasons for such a time-dependence are analysed. The Poincaré mapping for the collective electron dynamics in a molecule has been derived as a mapping of the idempotent matrix set into itself. Convergence conditions for this mapping as well as for the conventional Hartree-Fock selfconsistency procedure have been studied using the well-known fixed-point theorems. A possible physical significance of the divergence of Hartree-Fock selfconsistency procedure is discussed and some ways of extending the scope of the conventional quantum-chemical approaches are proposed.