Effect of Medium Chirality on the Rate of Resonance Energy Transfer

Abstract

Resonance energy transfer (RET) between two chromophores in an absorptive and dispersive chiral medium is investigated using a quantum electrodynamical formulation. To accurately describe such an environment involves the introduction of electric displacement and auxiliary magnetic field operators that are solutions of the Drude-Born-Fedorov equations and the time-harmonic Maxwell equations. Perturbation theory within the electric and magnetic dipole approximation is used in the derivation of the probability amplitude for energy transfer. Expressions for the contributions to the RET rate arising from the pure electric dipole term, replacing one of the chiral chromophores by its corresponding enantiomer in the mixed electric-magnetic dipole term, and the pure magnetic dipole contribution are obtained. In the near-zone limit in a nonabsorptive medium, the medium chirality amplifies the pure electric dipole contribution to the rate relative to that in a racemic mixture and also increases the discriminatory contribution, but to a lesser extent relative to the pure electric dipole term. On the other hand, under the same conditions, the medium chirality does not affect the pure magnetic dipole contribution to the rate. Measurements of the rate could be used to obtain information on the magnitude of the chirality admittance or concentration of chiral species, by comparing with the rate in an environment comprised of a racemic mixture of the enantiomers. This method could allow for the analysis of macroscopically heterogeneous systems that are comprised of enantiomers and where the chromophores experiencing RET are located in regions of interest.