Intermolecular interactions in a radiation field via the method of induced moments

Abstract

Molecular quantum electrodynamics is employed to calculate a generalized formula for the energy shift between a pair of molecules that have electric polarizability of arbitrary multipole order and are in the presence of an intense electromagnetic field. In contrast to a previous calculation of the dipole-dipole contribution, which required fourth-order time-dependent perturbation theory for its evaluation, the present approach involves calculating the interaction between the multipole moments induced at each center by the incident beam and the resonant multipole-multipole coupling tensor together with the average value of the spatial correlation function of the displacement field for an $N$-photon state. The theory developed applies to the situation where the molecular pair is held fixed relative to the direction of propagation of the radiation field or is allowed to be completely randomly oriented. Explicit results are obtained for dipole-quadrupole and quadrupole-quadrupole polarizable molecules. For oriented systems the energy shift for linear and circular polarizations is examined for incident radiation propagating in directions parallel and perpendicular to the intermolecular join, and the asymptotic behavior is obtained at the limits of short and large separation distance. After performing a pair orientation average, the energy shift in the near zone is found to exhibit an ${R}^{\ensuremath{-}1}$ power-law behavior with separation distance, while the far zone has a modulated ${R}^{\ensuremath{-}2}$ dependence in all of the cases considered. None of the energy shifts obtained display discriminatory characteristics, with respect to either the handedness of the incident beam or the individual species.