THERE ARE NO UNFILLED SHELLS IN UNRESTRICTED HARTREE-FOCK THEORY

We prove that in an exact, unrestricted Hartree-Fock calculation each energy level of the Hartree-Fock equation is either completely filled or completely empty. The only assumption needed is that the two-body i nteraction is-like the Coulomb interaction- repulsive; it could, howev er, be more complicated than a simple potential; e.g., it could have t ensor forces and velocity dependence. In particular, the Hartree-Fock energy levels of atoms and molecules, often called shells, are never p artially filled.