RRKMTheorie

RRKM theory, named after Rice, Ramsperger, Kassel, and Marcus, is a statistical framework for unimolecular reaction rates in gas‑phase chemistry. It describes the rate of a molecule with a fixed total internal energy E dissociating or isomerizing via a high‑energy transition state, assuming rapid intramolecular energy redistribution (IVR) among vibrational modes.

In its microcanonical form, the RRKM rate constant k(E) is given by k(E) = N‡(E − E0) / [h ρ(E)], where E0 is the activation energy (the barrier height), ρ(E) is the density of states of the reactant at energy E, and N‡(E − E0) is the sum of states of the activated complex (transition state) with energy up to E − E0. The expression reflects the idea that reaction proceeds when enough energy lies in the transition state, with the rate determined by the ratio of available transition-state states to reactant states.

Thermal rate constants k(T) are obtained by averaging k(E) over the vibrational energy distribution at temperature T, typically through integration over the Boltzmann distribution with appropriate partition functions or densities of states. Practical implementations use harmonic oscillator and rigid rotor approximations to compute ρ(E) and N‡(E).

RRKM theory extends earlier RRK theory by incorporating a quantum-statistical treatment of state densities and by treating the transition state explicitly. Marcus contributed to its development by clarifying the role of the activated complex’s density of states. The theory is widely applied to gas‑phase unimolecular dissociations, isomerizations, and photodissociations, especially for polyatomic molecules with dense energy spectra, while its assumptions (ergodicity, IVR, weak coupling to environments) define its domain of validity.