Mediation of resonance energy transfer by a third molecule

The influence of a third molecule on the rate of resonance energy transfer is studied using diagrammatic perturbation theory within the framework of molecular quantum electrodynamics. Two distinct mechanisms are identified. One corresponds to direct transfer between donor and acceptor while the other involves relay of energy by the third species. Fermi Golden rule transition rates valid for all separation distances beyond wave function overlap are evaluated for these two processes as well as for the interference term between direct and indirect exchange, thereby extending previous work which was limited to the near-zone only. Short- and long-range limits are also obtained in each case. It is found that in the near-zone the indirect rate contribution exhibits inverse sixth power dependence on relative distances of emitter and absorber relative to the third body, in contrast to its far-zone counterpart, which exhibits inverse square behavior. The interference term, however, displays inverse cubic dependence on all three distance vectors at short-range and inverse behavior in the far-zone. Interestingly, for a collinear arrangement of the three molecules in the near-zone, the interference term is negative, reducing the overall rate of energy transfer. The results obtained are interpreted in terms of microscopic and macroscopic pictures of transfer occurring within a surrounding medium.