Noise-Induced Förster Resonant Energy Transfer between Orthogonal Dipoles in Photoexcited Molecules

We show that Förster resonance energy transfer (FRET) in an orthogonally arranged donor-acceptor pair can be induced by environmental noise, although direct transfer is prohibited. Environmental fluctuations break the strict orthogonal dipole arrangement and cause effective fluctuating excitonic interactions. Using a scaling argument, we show that interaction fluctuations are coupled to those of the energy levels and are strong enough to induce large FRET rates. This mechanism also explains the temperature dependence observed in a recent experiment on a perylene bisimide dyad and predicts a modified distance dependence as compared to standard Förster theory.

Figure 1

(a) Orthogonal arrangement of two electronic transition dipole moments, ${\overrightarrow{\mu }}_1$, ${\overrightarrow{\mu }}_2$ with connecting vector ${\overrightarrow{n}}_{12}$. The fluctuations $\delta {\overrightarrow{\mu }}_i\perp {\overrightarrow{\mu }}_i$. (b) Chemical structure of the perylene bisimide dyad [4, 5]. (c) Combined view of the transition density between the ground and the first $\pi {\pi }^{\star }$ state of donor and acceptor corresponding to the respective $S_0-S_1$ transitions.

Figure 2

(Main) Noise-induced FRET time $\tau$ versus the orientational reorganization energy ${\lambda }_{\varphi }$ for several inverse bath correlation times ${\omega }_c$. Temperature is $T=300\mathrm{K}$. The horizontal lines indicate the measured FRET times in PBD. (Inset) 3D plot of $\tau$ versus ${\lambda }_{\varphi }$ and ${\omega }_c$.

Figure 3

(Main) FRET times $\tau$ (data: violet dots, fits: lines) obtained from transient pump-probe measurements of PBDs in chloroform vs donor-acceptor distances. The left (blue) and right (red) hatched ellipse represent the donor and acceptor, respectively, of the dyad, while the spacer is depicted with its structural formula. (Inset) Time evolution of the absorbance changes caused by the photoinduced FRET at the probe wavelength of 580 nm (acceptor stimulated emission). The absorbance changes are normalized with the amplitude of the energy acceptor excited state lifetime ($\sim 4\mathrm{ns}$) obtained from the global fit.

Figure 4

Temperature dependence of the FRET times. The black crosses mark experimental data [5], while the blue line reflects noise induced FRET times. The red line shows the temperature dependence resulting from a 3-phonon process.