Quantum reactive scattering via the S-matrix version of the Kohn variational principle: Differential and integral cross sections for D+H ₂ → HD+H

A comprehensive survey of the quantum scattering methodology that results from applying the S-matrix version of the Kohn variational principle to the reactive scattering formulation given by Miller [J. Chem. Phys. 50, 407 (1969)] is presented. Results of calculations using this approach are reported for the reaction D + H₂ → HD + H. The 3-d calculations include total angular momentum values from J = 0 up to 31 in order to obtain converged integral and differential cross sections over a wide range of energy (0.4-1.35 eV total energy). Results are given for reaction probabilities for individual values of J, integral and differential cross sections for a number of energies, and state-to-state rate constants (i.e., a Boltzmann average over translational energy), and comparisons are made to a variety of different experimental results. A particularly interesting qualitative feature which is observed in the calculations is that the energy dependence of the differential cross section in the backward direction (θ = 180°) shows a resonance structure (due to a short-lived DH₂ collision complex) which is very similar to that in the J = 0 reaction probability. This resonance structure does not appear in the energy dependence of the integral cross section, being averaged out by the sum over J.