Use of the Hartree-Fock approximation in computing electron affinities

The implications are explored of a recently demonstrated theorem deriving upper bounds on the Hartree-Fock ground-state energy of a system consisting of N+1 electrons in the potentials of a finite number of nuclei fixed in a bounded region of space, in terms of energies of single-determinantal wave functions for the system of N electrons in the identical nuclear framework. A conjectured generalization of the theorem is shown to be true. The application of the theorem to a criticism of computations on first-row atoms and ions is discussed, and it is concluded that the use of wave functions which do not satisfy the theorem may be appropriate in the application of the Hartree-Fock approximation to the calculation of electron affinities of certain systems.