Statistical theories of chemical reactions. Distributions in the transition region

TLDR

The distribution of states in the transition region for reactions with reactants in thermal equilibrium is examined. The authors argue that, when products are absent, the transition‑region distribution equals the equilibrium distribution minus product‑origin states, and introduce a conversion coefficient ξ to replace the usual transmission coefficient κ in transition‑state theory. They illustrate the phenomenon with classical trajectory calculations on three collinear systems with distinct potential energy surfaces and employ the ξ coefficient to correct the nonequilibrium distribution. The study finds a bobsled noneffect for purely classical reactants in equilibrium and demonstrates that the combined phase‑space/trajectory method is equivalent to the conventional trajectory method across the three examples.

Abstract

The distribution of states in the transition region is considered for chemical reactions occurring with reactants in thermal equilibrium. It is argued that when products are absent the distribution in the transition region is identical to an equilibrium distribution except that states originating from products are missing. The phenomenon is illustrated with classical trajectory calculations for three collinear systems with widely different potential energy surfaces: (a) intersecting rectangular channels of different elevation, (b) a smooth curve of parabolic cross section, and (c) a surface for the endothermic reaction H2+I → H + HI. For purely classical reactants in an equilibrium distribution a ``bobsled noneffect'' is found. The use of a conversion coefficient ξ in place of the usual transmission coefficient κ in transition state theory is shown to correct for the nonequilibrium distribution in the transition region. The equivalence of the combined phase space/trajectory method and the conventional trajectory method is demonstrated for the three examples.