Shared-mode assisted resonant energy transfer in the weak coupling regime

Recent work has suggested that correlations in the environments of chromophores can lead to a change in the dynamics of excitation transfer in both the coherent and incoherent limits. An example of this effect that is relevant to many single molecule experiments occurs in the standard Förster model for resonant energy transfer (RET). The standard formula for the FRET rate breaks down when the electronic excitations on weakly interacting donor and acceptor couple to the same vibrational modes. The transfer rate can then no longer be factored into donor emission and acceptor absorption lineshapes, but must be recast in terms of a renormalized phonon reorganization energy accounting for the magnitude and sign of the excitation-vibration couplings. In this paper, we derive theoretically how the FRET rate depends on the shared mode structure and coupling, examine the simplified case of Gaussian lineshapes and then provide a quantitative calculation for a system of current interest.