A harmonic transition state approximation for the duration of reactive events in complex molecular rearrangements

Motivated by recent experimental efforts to measure the time a molecular system spends in transit between the reactants and the products of a chemical reaction, here we study the properties of the distribution of such transit times for the case of conservative dynamics on a multidimensional energy landscape. Unlike reaction rates, transit times are not invariant with respect to the order parameter (a.k.a. the experimental signal) used to monitor the progress of a chemical reaction. Nevertheless, such order parameter dependence turns out to be relatively weak. Moreover, for several model systems we find that the probability distribution of transit times can be estimated analytically, with reasonable accuracy, by assuming that the order parameter coincides with the direction of the unstable normal mode at the transition state. Although this approximation tends to overestimate the actual mean transit time measured using other order parameters, it yields asymptotically correct long-time behavior of the transit time distribution, which is independent of the order parameter.