Stability Conditions for the Solutions of the Hartree—Fock Equations for Atomic and Molecular Systems. Application to the Pi-Electron Model of Cyclic Polyenes

Abstract

The stability conditions which ensure that the Hartree—Fock determinant minimizes the energy expectation value are rederived using the language familiar in quantum chemistry. These stability conditions are then specified for the case of closed‐shell electronic systems which allow additional simplification of the conditions as well as a certain classification of the instabilities. Examples of the instabilities of different types are presented and the case of the so‐called singlet instabilities—most interesting from the physical point of view—is studied in detail for the pi‐electron model of cyclic polyenes.