Damping and higher multipole effects in the quantum electrodynamical model for electronic energy transfer in the condensed phase

Abstract

The interplay between electronic coupling, spectral linewidth, and rate of electronic energy transfer between chromophores is examined in the context of a quantum electrodynamical ͑QED͒ model. The QED framework properly allows us to identify the partitioning between the near and far zone mechanisms for transfer of energy between chromophores dispersed in condensed phase ͑liquid or solid͒ host media. The extent to which coupling is modified by the medium is investigated. A general QED treatment of higher multipole contributions to the coupling between transition moments is also derived, whence interactions involving electric dipole, quadrupole and octopole as well as magnetic dipole and quadrupole interactions are examined explicitly. A new formulation is presented wherein expressions for the multipolar coupling tensors are obtained in terms of spherical Bessel functions, providing a clear, compact representation of the retarded coupling interaction and its distance-dependence. The irreducible tensor formulation of the coupling is discussed, highlighting features concerning the exact form of the orientation factors that have often in the past escaped notice. The detailed method of implementing a rotational averaging of the resultant interaction tensors is demonstrated, finally leading to a novel and concise representation for multipolar couplings of arbitrary order. The coupling between bacteriochlorophyll a chromophores is discussed as an example.

On the interactions between molecules in an off-resonant laser beam: Evaluating the response to energy migration and optically induced pair forces

“…The following second-order RET matrix element is determined from the first term of Eq. ͑8͒, its full derivation being already well documented, 32,33,36 leading to the following result:…”

Mechanistic principles and applications of resonance energy transfer

“…In general, the coupling is effected by the lowest orders of multipole, electric or magnetic, that can support the necessary donor and acceptor transitions. In the Förster range, the distance dependence exhibits the form R -(P+Q+1) for the coupling of two transition electric multipoles EP-EQ, or two magnetic multipoles MP-MQ; whilst for the coupling of an electric with a magnetic multipole, EP-MQ, the distance dependence is R -(P + Q) (59,60). For example, the coupling of an electric dipole decay with an electric quadrupole excitation, E1-E2, has an R -4 distance dependence within the Förster range.…”

Resonance Energy Transfer: Theoretical Foundations and Developing Applications

“…(14.15) require substantial manipulation for evaluation by any of several standard techniques, detailed in the original papers and subsequent reviews. 27 Implementing the necessary tensor calculus, the result emerges in a form concisely expressible as follows: 17) using the convention of implied summation over repeated vector and tensor indices i and j. In Eq.…”

“…In the Förster range, the distance dependence exhibits the form R -(P+Q+1) for the coupling of two transition electric multipoles EP-EQ, or two magnetic multipoles MP-MQ; while for the coupling of an electric multipole with a magnetic multipole, EP-MQ, the distance dependence is R -(P+Q) . 17,18 For example, the coupling of an electric dipole decay with an electric quadrupole excitation, E1-E2, has an R -4 distance dependence within the Förster range. However, it should be kept in mind that each unit increase in multipolar order, and each substitution of an electric transition by a magnetic counterpart, lowers the strength of the coupling by a factor of the order of 10 -2 to 10 -3…”