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 () to represent the unimolecular reaction of the excited molecule versus energy. RRKM theory assumes an exponential ()/(0) population for the excited molecule versus time, with decay given by RRKM microcanonical (), 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 (ω,) has brought this assumption into question. It was found that a biexponential ()/(0), for intrinsic non-RRKM dynamics, gives a Hinshelwood-Lindemann (ω,) curve very similar to that of RRKM theory, which assumes exponential dynamics. The RRKM (ω,) curve was brought into agreement with the biexponential (ω,) by multiplying ω in the RRKM expression for (ω,) by an energy transfer efficiency factor . Such scaling is often done in fitting Hinshelwood-Lindemann-RRKM thermal kinetics to experiment. This agreement between the RRKM and non-RRKM curves for (ω,) was only obtained previously by scaling and fitting. In the work presented here, it is shown that if ω in the RRKM (ω,) is scaled by a factor there is analytic agreement with the non-RRKM (ω,). The expression for the value of is derived.