CHAPTER 20: Computation of Intrinsic RRKM and Non-RRKM Unimolecular Rate Constants

Rice–Ramsperger–Kassel–Marcus (RRKM) theory, for the constant energy unimolecular rate constant, assumes classical ergodic dynamics and a transition state separating the reactant and product. The assumption of RRKM theory is that a microcanonical ensemble of states is maintained as the reactant molecules decompose, so that the number of molecules versus time decays exponentially, i.e. N(t)=N(0)exp(−kt), where k is the RRKM rate constant. Intrinsic non-RRKM dynamics occurs when this microcanonical ensemble of states is not maintained and, as a result, N(t) becomes a multi-exponential without a single time-independent rate constant. At low energies the vibrational energy levels of the reactant molecule may be assigned quantum numbers but, for high energies near the unimolecular threshold, the levels may become intrinsically unassignable. From correspondences between classical and quantum mechanics, the unassignability of these levels is consistent with the classical ergodic dynamics assumed by RRKM theory. For dissociation reactions without a saddle point, e.g. CH₄ → H+CH₃, variational RRKM is required to locate the transition state and calculate the RRKM rate constant. Anharmonic corrections are often needed to calculate an accurate transition state sum of states and an accurate reactant density of the states for the RRKM rate constant. Intrinsic non-RRKM dynamics have been observed in both experiments and simulations. Quantum mechanically, the unimolecular reactant decomposes from resonances states whose spectra may be isolated or overlapping. The spectroscopic signatures of these resonances may be assignable or intrinsically unassignable.