Equations-of-motion method including renormalization and double-excitation mixing

The equations-of-motion method is discussed as an approach to calculating excitation energies and transition moments directly. The proposed solution [T. Shibuya and V. McKoy, Phys. Rev. A 2, 2208 (1970)] of these equations is extended in two ways. First we include the proper renormalization of the equations with respect to the ground state particle-hole densities. We then show how to include the effects of two-particle-hole components in excited states which are primarily single-particle-hole states. This is seen to be equivalent to a single-particle-hole theory with a normalized interaction. Applications to various diatomic and polyatomic molecules indicate that the theory can predict excitation energies and transition moments accurately and economically.