A quantum dynamical comparison of the electronic couplings derived from quantum electrodynamics and Forster theory: application to 2D molecular aggregates

The objective of this study is to investigate under what circumstances Forster theory of electronic (resonance) energy transfer breaks down in molecular aggregates. This is achieved by simulating the dynamics of exciton diffusion, on the femtosecond timescale, in molecular aggregates using the Liouville-von Neumann equation of motion. Specifically the focus of this work is the investigation of both spatial and temporal deviations between exciton dynamics driven by electronic couplings calculated from Forster theory and those calculated from quantum electrodynamics. The quantum electrodynamics (QED) derived couplings contain medium- and far-zone terms that do not exist in Forster theory. The results of the simulations indicate that Forster coupling is valid when the dipole centres are within a few nanometres of one another. However, as the distance between the dipole centres increases from 2 nm to 10 nm, the intermediate- and far-zone coupling terms play non-negligible roles and Forster theory begins to break down. Interestingly, the simulations illustrate how contributions to the exciton dynamics from the intermediate- and far-zone coupling terms of QED are quickly washed-out by the near-zone mechanism of Forster theory for lattices comprising closely packed molecules. On the other hand, in the case of sparsely packed arrays, the exciton dynamics resulting from the different theories diverge within the 100 fs lifetime of the trajectories. These results could have implications for the application of spectroscopic ruler techniques as well as design principles relating to energy harvesting materials.