Abstract
Molecular quantum electrodynamics (QED) theory is employed to calculate the rate of resonance energy transfer (RET) between a donor, D, described by an electric dipole and quadrupole, and magnetic dipole coupling, and an identical acceptor molecule, A, that is mediated by a third body, T, which is otherwise inert. A single virtual photon propagates between D and T, and between T and A. Time-dependent perturbation theory is used to compute the matrix element, from which the transfer rate is evaluated using the Fermi golden rule. This extends previous studies that were limited to the electric dipole approximation only and admits the possibility of the exchange of excitation between a chiral emitter and absorber. Rate terms are computed for specific pure and mixed multipole-dependent contributions of D and A for both an oriented arrangement of the three particles and for the freely tumbling situation. Mixed multipole moment contributions, such as those involving electric–magnetic dipole or electric dipole–quadrupole coupling at one center, do not survive random orientational averaging. Interestingly, the mixed electric–magnetic dipole D and A rate term is non-vanishing and discriminatory, exhibiting a dependence on the chirality of the emitter and absorber, and is entirely retarded. It vanishes, however, if D and A are oriented perpendicularly to one another. Near- and far-zone asymptotes of isotropic contributions to the rate are also evaluated, demonstrating radiationless short-range transfer and inverse-square radiative exchange at very large separations.
Highlights
Molecular quantum electrodynamics (QED) theory is employed to calculate the rate of resonance energy transfer (RET) between a donor, D, described by an electric dipole and quadrupole, and magnetic dipole coupling, and an identical acceptor molecule, A, that is mediated by a third body, T, which is otherwise inert
The problem of RET mediated by a passive, polarizable third body has been tackled within the framework of molecular QED theory
Previous work [29,30,31,32], which was limited to the electric dipole approximation being made for the emitter and receiver particles, has been extended to include the effects of magnetic dipole and electric quadrupole interaction terms
Summary
Located at R D , and the second, A, positioned at R A , playing the role of acceptor entity. Employing it will help to simplify the computation of the matrix element by reducing the number of Feynman-like diagrams that have to be drawn and summed over, which is beneficial when solving higherorder processes This type of coupling Hamiltonian has been used to similar good effect in the evaluation of the Casimir–van der Waals dispersion potential, which is attributed to two virtual photon exchanges [46,47,48,49], and its radiation-induced analog [50,51]. Note that the leading elecwhere the shorthand notation Vijk ijk m0 tric dipole–dipole term appears as the first term in Equation (24), just as in Equation (21) This completes the evaluation of the matrix element for RET between an electric dipole, quadrupole, and magnetic dipole donor and acceptor molecule mediated by a third molecule. Specific contributions to the transfer rate are extracted in the sections that follow
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