Effects of Roaming Trajectories on the Transition State Theory Rates of a Reduced-Dimensional Model of Ketene Isomerization

Abstract

The rates of chemical reactions (or any activated process) are by definition determined by the flux of reactants (or initial states) that end up as products (or final states). The forward flux through any surface that divides reactants from products is a constant as long as only those trajectories that were reactants in the infinite past and products in the infinite future are included in the flux once and only once. Transition state theory (TST) ignores this last clause, thereby overestimating the rate if any of the trajectories recross the dividing surface. However, its advantage is that it replaces a dynamical calculation with a statistical integral over the TST geometry. The recent identification of roaming trajectories-those that persist for a long time as neither reactant nor product without ever visiting near the col on the energy landscape-apparently challenges the dogma that TST's only error lies in the omission of recrossing trajectories. This question is investigated using the isomerization reaction of ketene in which the experimental values are verified to be in reasonable agreement with both the exact and TST values. We have found two trajectories for the ketene isomerization that carry the signature of roaming, but their effect on the calculation of the reaction rate constant using classical transition state theory is small. Indeed, the existence of roaming trajectories is seen to impose a limitation on which dividing surfaces are appropriate for the calculation of either exact or approximate TST rates, but in this case, they do not unseat the existence of dividing surfaces that can be used safely to calculate TST rates.