Coupled Unimolecular Dissociation Kinetics of Bromotoluene Radical Cations

Abstract

The unimolecular dissociations of <i>o</i>-, <i>m</i>-, and <i>p</i>-bromotoluene radical cations to C₇H₇⁺ (benzylium and tropylium) are examined by considering the coupling of the three isomers in the dissociation pathways. The potential energy surface obtained from ab initio calculations suggests the interconversion of isomers through methylene and hydrogen migrations on the ring. The rate equations for each isomer are combined together to form a rate matrix for coupled reactions. The rate matrix contains the microcanonical rate constants for all elementary steps, which are calculated using Rice–Ramsperger–Kassel–Marcus theory based on the molecular parameters obtained from density functional theory. The unimolecular dissociation rates for coupled reactions are determined by numerically solving the matrix equation. As a result of reaction coupling, the product branching ratio becomes time-dependent and the reaction rates of three isomers become parallel to one another as the energy increases, although their initial rates differently vary with energy. The calculated rate–energy curves fall below the time-resolved photodissociation data in the energy range 2.2–2.7 eV but are in line with the photoelectron photoion coincidence data in the energy range 2.7–3.5 eV. The discrepancy between experiment and theory in the low-energy region is ascribed to the uncertainties of the potential energy surface as well as the contribution of the radiative relaxation rate that has not been taken into account in the theoretical calculations. The rate–energy curves are then used to calculate the thermal reaction rate constants, and the Arrhenius parameters are determined in the temperature range 700–1300 K. Comparison of the activation energy and entropy obtained from the Arrhenius plot with the calculated enthalpy and entropy changes between the reactant and the highest-lying transition state suggests that a series of [1,2] H-atom migrations occurring near the entrance comprise the rate-determining steps and the subsequent [1,2] H-atom migrations play an important role in increasing the activation energy and decreasing the entropy by reducing the net flux to the exit