Coupled channel distorted wave calculations for the three-dimensional H+H2 reaction

Abstract

A method for determining cross sections and other dynamical information based on the use of accurate coupled channel nonreactive wave functions in an evaluation of the distorted wave reactive scattering amplitude is developed for three‐dimensional atom–diatom reactive collisions and applied to the H+H₂ reaction. The nonreactive wave functions are obtained by using a truncated expansion in asymptotic vibration/rotation states to generate coupled channel equations in terms of the full Hamiltonian. Explicit reduction of the distorted wave scattering matrix expression to a real valued three‐dimensional integral is given and methods for simplifying the calculation through the use of parity decoupling, even/odd decoupling, and the coupled states approximation are introduced. The application to H+H₂ considers the Porter–Karplus potential surface. Comparison of reaction probabilities, opacity functions, differential and integral cross sections with corresponding results from exact quantum calculations indicates that the coupled channel distorted wave method is an excellent approximation as long as the total reaction probability for each partial wave is less than 0.1. This upper limit occurs at 0.60 eV total energy for H+H₂. Above that energy, convergence with basis set size is oscillatory after an initial plateau. The coupled states distorted wave method is also found to be an excellent approximation, with results which are indistinguishable in accuracy from coupled channel distorted wave results. Extension of these approaches to a nonperturbative evaluation of the scattering matrix elements is discussed.