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

Abstract

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 nonnegligible when using Förster resonance energy transfer spectroscopic ruler techniques for distances >10 nm.

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

“…For example in the case of EET in mesoscopic energy harvesting devices such as thin film molecular aggregates and quantum dot arrays, or biological photosynthetic units where excitation may be transferred between antenna complexes, where EET can potentially occur over long distances [31][32][33][34][35][36][37][38][39]. It has already been suggested [40], that contributions from intermediate-zone interactions may explain deviations from the R −6 distance dependence on the rate of EET, seen in some FRET studies [41][42][43].…”

A spectroscopic ruler for intermediate-zone FRET measurements

“…The parameter ( ) , g ω R is analogous to the electronic coupling. The three different regimes of EET can be clearly seen in equation (5), namely the near-zone, 6 1 R term, the intermediate-zone, 4 1 R term and the farzone, 2 1 R term. Note that only in the case of EET occurring in highly absorbing media do 3 1 R and 5 1 R terms appear.…”

“…These two processes were once thought to be independent mechanisms, however it is now known that they represent two limits of a unified theory of EET. 2,3 The Unified Theory of EET was derived from quantum electrodynamics (QED), and very interestingly also predicted that when the reduced wavelength is of the order of the distance between the donor and the acceptor an intermediatezone of energy transfer exists that has a 4 1 R dependence on the rate of EET. We have recently published two papers, one investigating electronic coupling and rate constants, 4 and the other quantum dynamics, 5 indicating that the 4 1 R term may be non-negligible for chromophores separated by relatively short distances (typically 5 nm or greater).…”

Quantum delocalization in photon-pair generation

“…(26). The numerical procedure, a lattice sum calculation, follows earlier approaches for calculating quantum amplitudes associated with molecular aggregates [84,85]. Here, we expand upon a preliminary, less computationally demanding treatment of SPDC, in which results were restricted to a single element of the coupling tensor [41].…”