THE HARTREE-FOCK POTENTIAL AND ITS USE IN PERTURBATION-THEORY

Analytical expressions are given for the matrix elements of the U(N-1) and U(N-2) Hartree-Fock potentials used in perturbation theory to gen erate singly and doubly excited states. Formulae are derived for all o ff-diagonal Lagrange multipliers encountered. When correctly defined, U(N-1) and U(N-2) turn out to be so-called Silverstone-Huzinaga potent ials, and therefore simultaneous orthogonality and a physically correc t asymptotic behaviour of the virtual orbitals are ensured. The equati ons for the diagonal and off-diagonal matrix elements of the potential that underlie the theorems of Koopmans and Brillouin respectively, ca n directly be generalized from the U(N-1) to the U(N-2) Case, although the modification of Koopmans' theorem is not trivial.