Barrier recrossing dynamics and phenomenological rate equations from single-molecule perspective

The trajectory of a molecular system undergoing a reversible reaction A ⇌ B and crossing and recrossing a transition state separating the reactant and product consists of loops, i.e., excursions from the transition state to either side and back to the transition state. Motivated by recent experimental observations of loops, here, we discuss some of their statistical properties. In particular, we highlight that the transition-state rate is not only an upper bound on the true reaction rate but also a physical property of the loops. We further find that loops can be unambiguously divided into two sub-ensembles. Those consist of short loops, which are brief excursions from the transition state, and long loops that get trapped in the reactant or product wells before eventually returning to the barrier. Finally, we show that the loop time distribution contains information about both the reaction rate coefficients and their transition-state-theory counterparts.