Reaction kinetics in stochastic models. II

Abstract

Three distinct topics in the theory of stochastic models of chemical reaction kinetics are discussed. The first, treated in Sec. II, concerns the case of two or more simultaneous reactions, as typified by the mutual interconversion of three or more species. The formula that relates the rate constants to the microscopic transition rates is discussed. The same formula, alternatively interpreted, is then seen also to be the relation that one would use to derive experimental rate constants from the amplitudes and time constants that are the primary experimental data. The second topic is that treated in Sec. III, which is on a class of stochastic models for which the conventional steady-state approximation is essentially exact. The origins and implications of that circumstance are discussed. The third subject is that of Sec. IV, on a fundamental difference between three-center exchange reactions A+BC⇄AB+C and (bimolecular) isomerizations A⇄B. The difference is in certain dynamical features of the respective collision mechanisms, which in one case imply that an ``equilibrium'' approximation to the rate constant, such as that given by transition-state theory, would be a good approximation, and in the other case not.