Stochastic theories of the activated complex and the activated collision: The RNA example

We propose a common rigorous foundation to the classical collision theory and that of the classical activated complex. Based on the notion of activated complex, this foundation relies on a stochastic approach showing up the different influence factors of a chemical reaction. The thermodynamic formulation is obtained here by assuming the exponential statistical distribution within each stable chemical state. The general model we obtain yields two stochastic formulations called the stochastic transition state theory (denoted STST) and the stochastic activated collision theory (denoted SACT) respectively, depending on whether the rate of the reaction is of the same scale as, either the rate of passing over the potential energy barrier, for the STST, or the rate of reaching the activated complex state (which is a generalization of the collision rate), for the SACT. The modeling is first done in the case of a closed small system undergoing stochastic changes of chemical state and then, by extension, in the frame of classical chemical kinetics. Some properties of these two theories are studied. Furthermore the formulation is applied to the stochastic example of RNA structure changes and to the classical simple example of a reaction between two atoms A and B to form the diatomic molecule AB.