The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical reactivity. It was developed by Rice and Ramsperger in 1927 and Kassel in 1928 (RRK theory ) and generalized (into the RRKM theory) in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable the computation of simple estimates of the unimolecular reaction rates from a few characteristics of the potential energy surface.

Assumption

Assume that the molecule consists of harmonic oscillators, which are connected and can exchange energy with each other.

Derivation

Assume that A* is an excited molecule: where P stands for product, and A‡ for the critical atomic configuration with the maximum energy E0 along the reaction coordinate. The unimolecular rate constant is obtained as follows: where k(E,J) is the microcanonical transition state theory rate constant, is the sum of states for the active degrees of freedom in the transition state, J is the quantum number of angular momentum, \omega is the collision frequency between A^* molecule and bath molecules, Q_r and Q_v are the molecular vibrational and external rotational partition functions.