Open shell self-consistent-field theory

A prescription is given for constructing a single Fock operator for an open shell system when the one-electron, spinless density matrix is diagonal in the occupied orbitals. This Fock operator may be used when there are two or more open shells of the same symmetry, but an upper bound to the total energy is obtained only for the lowest energy state of any symmetry. We apply the prescription to the class of systems considered by Roothaan and Bagus, and show that it is an extension of Roothaan’s coupling operator theory. In calculations on 14 open shell atomic states the Roothaan–Bagus equations required more CPU time to converge than ours in every case, and more iterations in six cases. Level shifting of the proposed Fock operator did not consistently improve the convergence rate.