Spin Degeneracy and the Stability of Hartree–Fock States

Abstract

The stability of a Hartree–Fock determinant under a splitting of the doubly occupied orbitals with simultaneous symmetry projection is studied. As a consequence of the spin degeneracy, the energy is given by the lowest root to a secular equation. It is found that even for an infinitesimal splitting of the orbitals there will be a discontinuous, finite lowering of the energy for both closed‐shell and open‐shell states. Numerical illustrations are given by the Li and Be atoms, the H₄ molecule, and the benzene molecule.