Local Orbital Equations for Excited States

Previously, we have developed computationally tractable, local orbitals techniques for computing the charge density of the ground state of a crystal in the Hartree‐Fock limit. In the present paper, we extend our previous concepts to the question of the virtual orbitals of a Hartree‐Fock system. Such orbitals may become useful in constructing the states of excitons, excited states of impurity centers or for LCAO calculations of energy bands. These orbitals also provide a convenient basis for performing configuration interaction calculations. This is demonstrated in a simple case, that of the helium atom. Finally we develop equations for the virtual orbitals which are correct to first order in interatomic overlap.