Unimolecular reaction rates and products quantum states distribution

7 Unimolecular reaction rates and products quantum states distribution 

The field of unimolecular reaction rates had an interesting history beginning around 1920, when chemists attempted to understand how a unimolecular decomposition N2Os could occur thermally and still be first-order, A — products, even though the collisions which cause the reaction are second-order (A + A— products). The explanation, one may recall, was given by Lindemann [59], i.e., that collisions can produce a vibrationally excited molecule A, which has a finite lifetime and can form either products (A — products), or be deactivated by a collision (A + A— A + A). At sufficiently high pressures of A, such a scheme involving a finite lifetime produces a thermal equilibrium population of this A. The reaction rate is proportional to A, which would then be proportional to A and so the reaction would be first-order. At low pressures, the collisions of A to form A are inadequate to maintain an equilibrium population of A, because of the losses due to reaction. Ultimately, the reaction rate at low pressures was predicted to become the bimolecular collisional rate for formation of A and, hence, second-order. 

The development of a theory of unimolecular reactions proceeded rapidly in the mid-1920s, initiated by Hinshelwood with an A whose collision-free lifetime for reaction was approximated by an energy-independent one. The analysis was much elaborated by Rice and Ramsperger [60] and Kassel [61], known later as the RRK theory, where now the lifetime was, as it is in modern times, energy-dependent [62]. These theoretical works of the 1920s stimulated many measurements of the unimolecular rates of dissociation of organic compounds as a function of the gas pressure. Within a few years, however, this entire field collapsed or, more precisely, evolved into a new field It was shown experimentally that the unimolecular reactions , assumed originally to consist of only one chemical step, in- 

As a post-doctoral researcher in E.W.R. Steacie s laboratory in the National Research Council of Canada in the late 1940s, I was involved in experiments on several such free radical reaction steps [64, 65] and the data prompted me to wonder about their theoretical interpretation. A second post-doctoral under the tutelage of Oscar Rice led to the formulation in 1951-1952 of what later became known as the RRKM theory [62, 66-68]. Here, I blended the statistical ideas of the RRK theory of the 1920s with the concepts of the TS theory of the mid 1930s. 

In the RRKM theory, the microcanonical rate constant k(E, J) at a given E and total angular momentum quantum number / is given by [62, 68], 

---