Dispersion energies between molecules involving one in an electronically excited state are calculated using fourth-order perturbation theory within the framework of the multipolar form of quantum electrodynamics. There are significant differences between the energies for these cases and those where both molecules are in their ground states. The calculations are performed within the electric-dipole approximation for the interaction of the molecules with the electromagnetic field. The energies found are valid for all separations beyond the electronic overlap region. The results of previous investigations are shown to be incomplete and the origin of the incompleteness is traced to the neglect of certain real-photon contributions. The energies obtained in this paper are in agreement with our earlier calculations based on a form of response theory. They are made up of two types: one resulting from virtual-photon exchange and the other from real photons. The virtual-photon term has the same structure as the Casimir-Polder potential for ground-state molecules. The real-photon term is a polynomial in the inverse intermolecular separation ${\mathit{R}}^{\mathrm{-}1}$, in contrast to the modulated contributions in the previous incomplete investigations. The asymptotic forms for the total energy are discussed. The far-zone behavior is dominated by the real-photon term and shows an ${\mathit{R}}^{\mathrm{-}2}$ dependence. The near-zone behavior shows an ${\mathit{R}}^{\mathrm{-}6}$ dependence, arising in the multipolar formalism from both virtual- and real-photon exchange.

• Received 14 October 1994

DOI:https://doi.org/10.1103/PhysRevA.51.3660