Scattering matrix in reactive collision theory: From resonances to rate constants

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.