The ground-state energy, as predicted by the CQED-RHF method, departs from the RHF energy in all three cases, with the largest deviation coming from λ z case (see Table ), which would be expected given the permanent dipole moment is oriented along the z-axis. However, the deviations seen by the λ y and λ yz cases point to subtle effects arising from the quadrupolar terms in the quadratic self energy and the 2-electron contribution to the quadratic self energy. To quantify these various contributions, we look at the changes in the various contribu-tions to the CQED-RHF energy with and without coupling to the photon field. For example, we define the change in the canonical RHF 1-electron energy resulting from the photon field in the λ yz case as