Here, Êp q and êpr qs are the 1-and the 2-electron excitation operators respectively, J q p is the Coulomb interaction with the zero-order electron density, V q p and v qs pr are the one-and twoelectron on-top potentials evaluated at the zero-order densities, and h const is a constant which only depends on the zero-order densities. The zero-order densities are taken to be the weighted average of densities within the state-average manifold.