A single arrangement variational method for reactive scattering: Total and state-resolved reaction probabilities

Abstract

A detailed discussion of an approximate, variational approach to atom–molecule reactive scattering is presented. This approach reduces the formally three arrangement atom–diatomic molecule reactive scattering problem to one of a single arrangement without the use of negative imaginary potentials at the exit channel boundaries. The method is based on applying the Kohn variational principle for the log-derivative matrix to a representation of the scattering wave function that spans just the reactant arrangement. For many reactive systems, the method yields impressively accurate results for total reaction probabilities from a specific initial state. In such cases, it is also possible to extract fairly accurate state-resolved reaction probabilities from the results of the variational calculation. The mathematical and practical aspects of accomplishing this are presented. We evaluate the advantages and the limitations of the method by numerical computations on the collinear H+H2 (and isotopes) and F+H2, and the three dimensional (J=0) F+H2 reactions.