Quantum mechanical reactive scattering via exchange kernels: Infinite order exchange on a grid

A general methodology is described for carrying out quantum mechanical reactive scattering calculations. The approach is based on Miller’s [J. Chem. Phys. 50, 407 (1969)] formulation of quantum reactive scattering in which rearrangement processes (i.e., chemical reactions) are characterized by nonlocal exchange interactions that couple different arrangements. The specific approach described here requires that nonreactive coupled channel calculations first be carried out separately in the various arrangements—this is a relatively standard inelastic scattering problem—and the non-local exchange interactions are then discretized on a grid in (translational) coordinate space; straightforward linear algebra calculations then lead to the scattering matrix. (Discretizing the exchange kernels on a grid is suggested because exchange is very short range.) The attractiveness of the overall method is its straightforwardness, generality, and special suitability for the vector-processing character of modern supercomputers. Application to a standard test problem (the collinear H+H2 reaction) shows that it is numerically stable over a wide range of collision energies.