Abstract
The expression for the total energy, as given in Slater's hyper-Hartree-Fock procedure is analyzed, and the most obvious choice of a 2-particle density matrix consistent with this energy expression is presented. This choice is the only possible one, if there are no numerical relations among the two-electron integrals. It is shown that this 2-matrix is, in general, neither non-negative nor antisymmetric, and therefore cannot be derived from any antisymmetric full density matrix. This potential lack of representability is indeed realized, for the spin-polarized HHF calculations reported by Slater, Mann, Wilson, and Wood on the atoms Co, Ni, and Cu, where it is found that the 2-matrix has a negative occupation number for a permutationally symmetric natural geminal. A viewpoint is presented whereby the HHF method may still be justified, in spite of these deficiencies. Alternatives to the HHF method are presented which do not have these deficiences. These methods are valid for some, but not all, of the purposes for which the HHF method was developed.
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