Generalized Resonance Energy Transfer Theory: Applications to Vibrational Energy Flow in Optical Cavities

Abstract

A general rate theory for resonance energy transfer (gRET) is formulated to incorporate any degrees of freedom (e.g., rotation, vibration, exciton, and polariton) as well as coherently coupled composite donor or acceptor states. The compact rate expression allows us to establish useful relationships: (i) detailed balance condition when the donor and acceptor are at the same temperature; (ii) proportionality to the product of dipole correlation tensors, which is not necessarily equivalent to spectral overlap; (iii) scaling with the effective coherent size, i.e., the number of coherently coupled molecules or modes; (iv) decomposition of collective rate in homogeneous systems into the monomer and coherence contributions such that the ratio of the two defines the quantum enhancement factor F; (v) spatial and orientational dependences as derived from the interaction potential. For the special case of exciton transfer, the general rate formalism reduces to FRET or its multichromophoric extension. When applied to cavity-assisted vibrational energy transfer between molecules or within a molecule, the general rate expression provides an intuitive explanation of intriguing phenomena such as cooperativity, resonance, and nonlinearity in the collective vibrational strong coupling (VSC) regime, as demonstrated in recent simulations. The relevance of gRET to cavity-catalyzed reactions and intramolecular vibrational redistribution is discussed and will lead to further theoretical developments.

Understanding the Energy Gap Law under Vibrational Strong Coupling

“…These differences have been detailed by Nitzan and a useful guide on the saddle point method may be found in Morse and Feshbach . More recently, an evaluation of such rate expressions through a path-integral approach and the general case of VSC-mediated resonance energy transfer have also been considered by the Cao group.…”

“…These differences have been detailed by Nitzan 44 and a useful guide on the saddle point method may be found in Morse and Feshbach. 45 More recently, an evaluation of such rate expressions through a path-integral approach 46 and the general case of VSC-mediated resonance energy transfer 47 have also been considered by the Cao group. Returning to eq 16, one way to move forward is to bring all three summations into the integral and perform a single saddle point approximation (see Supplementary Note 3) to obtain and τ = τ 0 is the extremum of Re f (τ).…”

Gas-phase detection of oxirene

“…Upon formation through isomerization of ketene (H 2 CCO, 2 ), oxirene ( 1 ) is stabilized in the matrix via resonances with the vibrational modes of the matrix molecule (methanol). The transfer rate of newly formed vibrationally excited molecules [oxirene ( 1 )] in the matrix (methanol) maximizes when the vibrational frequencies of the donor [oxirene ( 1 )] and acceptor molecules (methanol) are at resonance, i.e., have identical frequencies ( 47 ). This is the case for the oxirene-methanol system as demonstrated in Fig.…”

Vibropolaritonic Reaction Rates in the Collective Strong Coupling Regime: Pollak–Grabert–Hänggi Theory

“…51,60 (f) Finally, our model and calculations do not show cavity enhancement effects of friction due to spatial delocalization of eigenstates. 42 We expect these effects to only increase reaction rates by a moderate amount (as discussed in the Supporting Information S2.3 of ref 61). Furthermore, these effects will only arise if there are additional near-field electrostatic interactions among molecules, which have been ignored in this model in light of how weak they are in the vibrational regime.…”

“…This sparked a series of works that considered additional effects such as anharmonicities, − multiple cavity modes, , intermode energy redistributions, − and disorders. , A summary of these theoretical results will be presented in an upcoming perspective . Note that considerable efforts have also been devoted to the second class of transitions − and will not be discussed here.…”