On the theory of unimolecular reactions: Application of mean first passage time to reaction rates

Abstract

We apply the theory of first passage times to the process of collision free unimolecular decomposition of large molecules at a given total energy. The theory is intermediate between the dynamical and statistical theories. We find that the rate of decomposition is given in terms of a series, the leading term of which has the form used in the RRKM theory. We analyze the conditions for which this term is dominant, and find that when the molecule is large or the total energy is low or the rate of decomposition is small, our expression coincides with the phase space approach. We show that the separation of time scales (energy redistribution vs decomposition) is large when the same conditions are met. Our analysis reduces to the Montroll–Shuler model for the decomposition of a diatomic molecule in a bath of inert atoms, in the appropriate limits.