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

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A quantum dynamical comparison of the electronic couplings derived from quantum electrodynamics and Förster theory: application to 2D molecular aggregates
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The objective of this study is to investigate under what circumstances Förster 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 Förster theory and those calculated from quantum electrodynamics. The quantum electrodynamics (QED) derived couplings contain medium- and far-zone terms that do not exist in Förster theory. The results of the simulations indicate that Förster 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 Förster 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 Förster 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.
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Transcript: English(auto-generated)
In this work we are looking at the process of electronic energy transfer. Specifically we are comparing the electronic couplings derived from molecular quantum electrodynamics and Forster theory that serve to regulate this process. Molecular quantum electrodynamics is the theory that treats both matter and light on equal quantum mechanical footings.
Within this context QED has provided a platform with which to describe electronic energy transfer through a unified theory which links regimes of EET that were once thought to be distinct mechanisms, that is near-zone non-radiative energy transfer and far-zone radiative energy transfer. The electromagnetic coupling tensor describes the spatial dependence
of the coupling that mediates EET. Highlighted are three distance dependencies. This is the near-zone contribution which dominates when the donor acceptor separation distance R is much less than the reduced wavelength of the mediating photon. And here we have the far-zone term. Within this theory we see a contribution from this intermediate zone
term which plays an important role when R is approximately equal to the reduced wavelength. These are the orientation factors that define the directionality of coupling. To undertake this investigation we carried out quantum dynamic simulations of exciton migration. The simulations are performed in the site basis and off-diagonal elements of the Hamiltonian correspond to
electronic couplings between molecules. The study focuses on comparing QED derived couplings with the classical Forster couplings. In this set of simulations we employ a 2D brick stone lattice of transition dipole moments which are represented by arrows. The parameters of the lattice are Rx and Ry. To investigate when the intermediate and far-zone terms
play an important role in EET we consider three different lattice parameters, namely 2, 5 and 10 nm. Here we have the coupling landscapes of the individual contributions to the tensor for the lattice parameters of 2 nm. Far zones on the left, intermediate zone in the centre and the near zone on the right. These landscapes can be understood
by considering the nature of the mediating photon. Using the Helmholtz theorem, any vector field can be separated into irritational and solenoidal components. For this work the Coulomb gauge is employed when describing electromagnetic fields and hence the irritational component disappears. The result of the transversality associated with the equation
in the box is that the electric and magnetic field vectors are orthogonal to k, the propagation vector. However, when the emitted photon is still close to the donor, its short path means it is strongly subject to quantum uncertainty in vector momentum, including direction, and hence transverse and longitudinal components contribute to the EET process. However,
in the far zone, behaviour is consistent with the fully transverse field. Due to the contributions of photon fields with longitudinal character in the near zone, coupling of type A can occur. In the far zone, the exclusively transverse electric fields only couple transition dipole moments whose orientation is shown in b. This explains the different coupling landscapes as described in the previous slide.
We now show a movie of the 100 femtosecond trajectory based on the QED derived coupling and lattice parameters of 2 nm. The exciton moves symmetrically away from the central molecule in a wave-like motion with the favour directions of energy transfer consistent with the coupling landscapes. It is more informative to look at plots of the differences in the
dynamics for the two coupling mechanisms. It is quite apparent that the population change that occurs in the central region of the lattice is the same for the two EET coupling models under investigation. Small differences in the spatial dependency of the energy transfer can be seen in some regions, particularly early times in the dynamics.
This difference is effectively washed out as time goes on. Now we look at the differences that occur when the lattice parameters are increased to 5 nm. Here we can see the difference in the spatiotemporal dynamics for QED and forced to derive couplings are more pronounced and long lived. These differences are now
even more evident in the case where the lattice parameters are increased to 10 nm. Our results show that as the lattice size is increased by means of changing the distances between the molecules that comprise the lattice, the intermediate and far zone contributions
to the coupling start to play important roles in the spatial and temporal exciton dynamics. Inclusion of these terms may then become important in accurately describing exciton dynamics in mesoscopic structures such as quantum dot arrays.