Comparison of Exponential and Biexponential Models of the Unimolecular Decomposition Probability for the Hinshelwood–Lindemann Mechanism

The traditional understanding is that the Hinshelwood–Lindemann mechanism for thermal unimolecular reactions, and the resulting unimolecular rate constant versus temperature and collision frequency ω (i.e., pressure), requires the Rice–Ramsperger–Kassel–Marcus (RRKM) rate constant k ( E ) to represent the unimolecular reaction of the excited molecule versus energy. RRKM theory assumes an exponential N ( t )/ N (0) population for the excited molecule versus time, with decay given by RRKM microcanonical k ( E ), and agreement between experimental and Hinshelwood–Lindemann thermal kinetics is then deemed to identify the unimolecular reactant as a RRKM molecule. However, recent calculations of the Hinshelwood–Lindemann rate constant k uni (ω, E ) has brought this assumption into question. It was found that a biexponential N ( t )/ N (0), for intrinsic non-RRKM dynamics, gives a Hinshelwood–Lindemann k uni (ω, E ) curve very similar to that of RRKM theory, which assumes exponential dynamics. The RRKM k uni (ω, E ) curve was brought into agreement with the biexponential k uni (ω, E ) by multiplying ω in the RRKM expression for k uni (ω, E ) by an energy transfer efficiency factor β c . Such scaling is often done in fitting Hinshelwood–Lindemann–RRKM thermal kinetics to experiment. This agreement between the RRKM and non-RRKM curves for k uni (ω, E ) was only obtained previously by scaling and fitting. In the work presented here, it is shown that if ω in the RRKM k uni (ω, E ) is scaled by a β c factor there is analytic agreement with the non-RRKM k uni (ω, E ). The expression for the value of β c is derived.