Scaling relations and optimization of excitonic energy transfer rates between one-dimensional molecular aggregates

We theoretically study the distance, chain length, and temperature dependence of the electronic couplings as well as the excitonic energy transfer rates between one-dimensional (1D) chromophore aggregates. In addition to the well-known geometry dependent factor that leads to the deviation from Förster’s classic R(DA)(–6) scaling on the donor–acceptor separation, nonmonotonic dependence on aggregate size and the breakdown of far-field dipole selection rules are also investigated in detail and compared to prior calculations. Our analysis provides a simple, unifying framework to bridge the results of the ground state electronic couplings at low temperatures and those from the classical rate-summation at high temperatures. At low temperatures and in the near-field limit, the exciton transfer integral scales as R(DA)(–1), in analogy to that of electric monopoles. For the case of aligned 1D J-aggregates, we predict a maximal excitonic energy transfer rate at temperatures on the order of the intra-aggregate coupling strength.