On the nature of long range electronic coupling in a medium: Distance and orientational dependence for chromophores in molecular aggregates

The electronic coupling that mediates energy transfer in molecular aggregates is theoretically investigated using the principles of quantum electrodynamics (QED). In this context, both the electromagnetic tensor and rate equation relating to these couplings are re-examined with a focus on the role of the relative distance and orientation of transition dipole moment pairs, considering near-, intermediate-, and far-zone contributions to the coupling. The QED based coupling terms are investigated both analytically and numerically, and they are physically interpreted in terms of the character of the mediating (virtual) photons. The spatial dependence of the couplings for a two-dimensional molecular aggregate of ordered and isotropic transition dipole moments is numerically calculated. Further, Pauli Master Equations are employed for a one-dimensional chain of molecules and donor-acceptor pairs, to investigate the importance of intermediate- and far-zone contributions to the electronic coupling on electronic energy transfer dynamics. The results indicate that although Förster theory is often qualitatively and quantitatively correct for describing electronic energy transfer (EET) processes, intermediate- and far-zone coupling terms could sometimes be non-negligible for correctly describing EET in natural and artificial, mesoscopic, solar energy harvesting systems. In particular, the results indicate that these terms are non-negligible when using Förster resonance energy transfer spectroscopic ruler techniques for distances >10 nm.