On the dimensionality dependence of the properties of reactive collisions

Abstract

Quasiclassical trajectory calculations have been carried out in 1D, 2D, and 3D on potential energy surfaces modeling H+Br₂ and H+HBr collisions with the reactants in the ground vibration–rotation state. Cross sections, reaction lengths, and reaction probabilities are reported as a function of relative translational energy. Using information theoretic concepts, the surprisal of the branching ratio Γ=k_a/k_e for the processes H+HBr→H₂+Br (k_a) and H′+HBr→H′Br+H(k_e) is studied in all three dimensions. The surprisal in 1D has a much different energy dependence than in 3D while the 2D surprisal follows the 3D surprisal more closely. The surprisals of the above two reactions and the H+Br₂→HBr+Br reaction are reported as a function of energy. While the surprisals all show the same qualitative energy dependence the 1D results generally increase much more rapidly with energy than do the 2D or 3D. Two methods for estimating the energy dependence of 3D reaction cross sections from 2D reaction lengths or 1D reaction probabilities are compared. The method which assumes the surprisal of the reaction probability is dimensionally invariant is shown to be preferable. Given that a reaction has occurred, the distributions of scattering angles, translational energy fractions, and reactive impact parameters are compared in various dimensionalities. From all of the results taken together, it is concluded that quite reasonable (in some cases quantitative) 3D estimates of reaction properties can be derived from 2D trajectory data and information theoretic concepts. Extrapolation from 1D to 3D is shown to be of generally marginal utility.