Effects of Donor-Acceptor Quantum Coherence and Non-Markovian Bath on the Distance Dependence of Resonance Energy Transfer

TL;DR

This paper addresses how donor-acceptor quantum coherence and non-Markovian baths influence the distance dependence of resonance energy transfer (RET). It develops a minimal transition-dipole coupling model $J(R)=J_0\left(\frac{R_0}{R}\right)^3$ embedded in independent, super-Ohmic baths and solves the dynamics using a polaron-transformed quantum master equation to compare coherent RET (CRET) with nonequilibrium FRET. The results show that coherence sharpens the distance dependence beyond the canonical $1/R^6$ scaling, while non-Markovian bath effects moderate this sensitivity, with an effective rate $k_{eff}=P_A(\infty)/\tau_{RET}$ capturing the main transfer timescale; the resulting changes in RET efficiency are modest unless donor lifetimes are very short or $J_0$ is large. The study highlights the need to account for coherence and bath memory effects when using RET as a nanoscale ruler at sub-nanometer distances and points to future work on more complex couplings and realistic excitation conditions.

Abstract

Accurate information on the distance dependence of resonance energy transfer (RET) is crucial for its utilization as a spectroscopic ruler \re{of} nanometer scale distances. In this regard, understanding the effects of donor-acceptor quantum coherence and non-Markovian bath, which become significant at short distances, has significant implications. The present work investigates this issue theoretically by comparing results from a theory of coherent RET (CRET) with a nonequilibrium version of Förster's RET (FRET) theory, both accounting for non-Markovian bath effects. Even for a model where the donor-acceptor electronic coupling is of transition dipole interaction form, it is shown that the RET rate in general deviates from the inverse sixth power distance dependence as opposed to the prediction of the original FRET. It is shown that the donor-acceptor quantum coherence makes the \re{distance} dependence steeper than the sixth power although detailed manner of enhancement is sensitive to specific values of parameters. On the other hand, the non-Markovian bath effects make the \re{distance} dependence more moderate than the sixth power for both CRET and nonueqilibrium FRET because finite time scale of the bath causes the rate to be smaller than the prediction of original FRET. While these effects are \re{demonstrated clearly} in the population dynamics at sub-picosecond time scales, their contributions to the conventional RET efficiency are relatively minor. This indicates that the actual detection of such effects through conventional RET efficiency measurement requires either high precision or utilization of a donor with fast spontaneous decay rate of excitation.

Figures (5)

• Figure 1: Excited $D$ populations for $\eta_D=\eta_A=2$, $\hbar \omega_c=1,000\ {\rm cm^{-1}}$ (Case I) for two different values of $E_D-E_A=800$ and $400\ {\rm cm^{-1}}$ (shown on the right on each row), at three values of $R/R_0$ (shown on the top). For all the cases, $J_0=5\ {\rm cm^{-1}}$ and $T=300\ {\rm K}$. Black solid lines represent results from CRET and red dashed lines from FRET.
• Figure 2: Excited $D$ populations for $\eta_D=\eta_A=5$ and $\hbar \omega_c=400\ {\rm cm^{-1}}$(Case II). Other parameters and conditions are the same as Fig. 1.
• Figure 3: Comparison of actual population dynamics based on either CRET or FRET with exponential dynamics corresponding to the effective rate, eq. \ref{['eq:k_eff']}, for $R/R_0=1/5$ and $E_D-E_A=400\ {\rm cm^{-1}}$.
• Figure 4: Upper Panels: Effective rates ($k_{eff}$) in logarithmic scale versus with $R/R_0$. Lower Panels: Effective rates multiplied by $(R/R_0)^6$ versus $R/R_0$.
• Figure 5: Efficiencies calculated by eq. \ref{['eq:eff-1']} based on both CRET and FRET. The ideal value of the efficiency based on FRET, eq. \ref{['eq:fret_eff']}, is shown as reference as well.