Energy- and Time-Dependent Branching to Competing Paths in Coupled Unimolecular Dissociations of Chlorotoluene Radical Cations

The energy- and time-dependent branching to the competing dissociation paths are studied by theory for coupled unimolecular dissociations of the o-, m-, and p-chlorotoluene radical cations to C7H7+ (benzylium and tropylium). There are four different paths to C7H7+, three to the benzylium ion and one to the tropylium ion, and all of them are coupled together. The branching to the multiple paths leads to the multiexponential decay of reactant with the branching ratio depending on both internal energy and time. To gain insights into the multipath branching, we study the detailed kinetics as a function of time and internal energy on the basis of ab inito/RRKM calculations. The number of reaction steps to C7H7+ is counted for each path. Of the three isomers, the meta mostly goes through the coupling, whereas the para proceeds with little or no coupling. In the beginning, some reactants with high internal energy decay fast to the benzylium ion without any coupling and others rearrange to the other isomers. Later on all three isomers dissociate to the products via long-lived intermediates. Thus, the reactant shows a multiexponential decay and the branching ratio varies with time as the average internal energy decreases with time. The reciprocal of the effective lifetime is taken as the rate constant. The resulting rate-energy curves are in line with experiments. The present results suggest that the coupling between the stable isomers is thermodynamically controlled, whereas the branching to the product is kinetically controlled.