A transition state theory of nonadiabatic unimolecular reactions controlled by a conical intersection. Application to the C2H+4 ion

We propose an extension of the RRKM method to nonadiabatic reactions. The basic ideas were suggested by Zahr, Preston, and Miller in the simpler case of a spin-orbit interaction for which the coupling matrix element remains constant over the configuration space. These ideas have been adapted to the more complicated case of a conical interaction. The rate constant is then expressed as a product of a RRKM rate term times an average probability of staying in a given electronic state which is evaluated from the Landau–Zener–Nikitin linear model. The method is applied to the dissociation of the C2H+4 ion, whose reaction mechanisms have been previously determined by ab initio calculations, and for which convincing experimental observations suggest that the system can be represented by a microcanonical ensemble. The relevant rate constants are calculated as a function of energy and fragmentation yields derived therefrom. This gives rise to a mass spectrum calculated from first principles. Agreement with experiment is satisfactory.