Optimization of orbitals for multiconfigurational reference states

The problem of finding orbitals, which make the total energy stationary, when the ground state or reference state is of the multiconfigurational form, is analyzed in this paper. Particular attention is given to the quadratically convergent methods. Orbital variations are generated by unitary transformations and an expansion of the total energy through second order in the parameters used to define these transformations provides a characterization of the stationary point, which is reached at convergence, as well as estimates of second order properties. Effective one-particle potentials are analyzed and it is emphasized that only certain blocks of the Fock matrix are determined by the generalized Brillouin theorem. In an analysis of the convergence properties of the various methods it is shown that the Hartree–Fock procedure can be brought to converge for stable states of a given symmetry if the blocks of the Fock matrix, which are not determined by the Brillouin theorem, are chosen in an appropriate fashion. The procedures, which we discuss, are finally compared to currently employed techniques including direct energy optimization procedures, energy weighted steepest descent methods and generalizations of Roothaans equations.