Damping and higher multipole effects in the quantum electrodynamical model for electronic energy transfer in the condensed phase

The interplay between electronic coupling, spectral linewidth, and rate of electronic energy transfer between chromophores is examined in the context of a quantum electrodynamical (QED) model. The QED framework properly allows us to identify the partitioning between the near and far zone mechanisms for transfer of energy between chromophores dispersed in condensed phase (liquid or solid) host media. The extent to which coupling is modified by the medium is investigated. A general QED treatment of higher multipole contributions to the coupling between transition moments is also derived, whence interactions involving electric dipole, quadrupole and octopole as well as magnetic dipole and quadrupole interactions are examined explicitly. A new formulation is presented wherein expressions for the multipolar coupling tensors are obtained in terms of spherical Bessel functions, providing a clear, compact representation of the retarded coupling interaction and its distance-dependence. The irreducible tensor formulation of the coupling is discussed, highlighting features concerning the exact form of the orientation factors that have often in the past escaped notice. The detailed method of implementing a rotational averaging of the resultant interaction tensors is demonstrated, finally leading to a novel and concise representation for multipolar couplings of arbitrary order. The coupling between bacteriochlorophyll 𝑎 chromophores is discussed as an example.