Transition state theory with Tsallis statistics

We discuss the rate of an elementary chemical reaction. We use the reaction path and especially its saddle point on the potential energy surface. The reaction path connects reactant and product of a reaction over the transition state (TS). Usually, the TS is assumed near or at the single saddle point of the reaction path. By means of comparison of the statistics of states at the reactant and at the TS, one can estimate the reaction rate by the Eyring theory. We propose to use the Tsallis statistics at the TS, a statistics of seldom accidents. Thus, we propose to generalize the well-known Boltzmann-Gibbs statistics, which is the limiting case of the Tsallis statistics. We use features of this nonextensive thermostatistics. The basic properties of the statistics are used to derive (approximated) partition functions, and they are applied on reaction rates. The approximation includes a factorization of the partition functions. The theory is applied to HCN isomerization to HNC, and to the reaction H(2) + CN --> H + HCN. It allows an accordance with experimental estimations of the reaction rates.