Two bridge-particle-mediated RET between chiral molecules

Abstract

The problem of resonance energy transfer between a pair of chiral molecules mediated by two electrically polarizable bridging particles is solved using molecular quantum electrodynamics theory. In this framework, a single virtual photon propagates between any two-coupled entities and is responsible for the conveyance of excitation energy from the emitter to the absorber. Electric dipole and quadrupole, and magnetic dipole couplings linear in the Maxwell fields are employed for donor and acceptor, while each mediator scatters two virtual photons and responds quadratically to the electric displacement field via its electric dipole polarizability. This enables fourth-order diagrammatic perturbation theory to be used to compute the probability amplitude for the process. Individual multipole moment contributions to the Fermi golden rule rate are then extracted for oriented and isotropic systems. Discriminatory transfer rates arise when either the donor or the acceptor are electric–magnetic dipole and the other has a pure multipole moment, or when both are chiral, with mixed electric dipole–quadrupole contributions vanishing in the fluid phase. The bridge-mediated transfer rate is found to be a maximum for a collinear geometry. Moreover, a multi-level model of the mediator is necessary for energy migration. Asymptotically limiting rates for arbitrary and collinear geometries are also obtained for one center purely electric dipolar and the other purely quadrupolar, or both donor and absorber purely quadrupolar. Understanding is gained of radiationless and radiative transfer mechanisms between chiral moieties in a dielectric medium.