SCF theory for excited states

Equations of Hartree-Fock type are formulated for a many-electron system described by a wave function containing any number of open and closed shells. The solutions define ‘optimal orbitals’ which minimize the average energy of the states of a configuration in which each shell contains a specified number of electrons. Analogues of the Koopmans theorem are constructed. The results obtained are of special interest in discussing highly excited states (e.g. in ESCA and Auger spectroscopy) where ‘holes’ may be present in both inner and outer shells.