A general formula obtained from induced moments for the retarded van der Waals dispersion energy shift between two molecules with arbitrary electric multipole polarizabilities: I. Ground state interactions

An expression for the dispersion energy shift arising from the interaction of two ground state polarizable molecules of arbitrary electric multipole moment order is obtained. The physical viewpoint adopted is one in which an electric polarizable body subject to vacuum fluctuations associated with an electric displacement field gives rise to an induced multipole moment. The moments induced at each centre couple to the retarded electric multipole-multipole resonant interaction tensor, resulting in a direct evaluation of the generalized formula for the dispersion potential between the pair. The present approach is compared and contrasted to a previous derivation of the interaction energy which required the Casimir-Polder potential as its starting point and employed fourth-order time-dependent perturbation theory. Although the functional forms obtained for the generalized energy shift differ in the two methods, identical expressions result for specific contributions to the dispersion potential. This is shown explicitly for the first few lowest order cases, comprising molecules possessing electric dipole, quadrupole and octupole polarizability characteristics. In this paper, the present approach is used to calculate energy shifts between an excited and an unexcited molecule.