A derivation of general open-shell SCF equations for atoms and molecules with a Green function method

A new general method is described for obtaining SCF orbitals for electronic systems without restrictions of the symmetry of the open shells. With a Green's function method an optimal SCF operator is constructed for each state of a given configuration. The unperturbed one-particle Green's function is optimal with this operator and permits a quasiparticle interpretation. The SCF equations are derived in matrix formulation convenient for numerical applications within a limited basis set. It is shown that the SCF orbitals thus obtained satisfy the necessary conditions for the energy to be stationary. An application of the SCF method is given for the three lowest S states of the helium atom.