Infinite-order discrete-variable representation theory of rearrangement scattering

Abstract

We recently developed the infinite-order discrete-variable representation (IO-DVR) theory of quantum scattering, which has been proven to yield highly accurate results even for multidimensional rearrangement scattering systems. In this paper we illustrate this theory by considering a one-dimensional reaction path model in which the potential is taken to be an Eckart barrier. In another application, we consider a two-degree-of-freedom model for H + H-2 rearrangement collisions. This application is sufficiently complex that it is impractical to calculate the rearrangement scattering matrix by using the previous theory of Eisenberg et al., but with the IO-DVR theory, the problem is made easy. We demonstrate the convergence behavior of the IO-DVR theory with the size of the interaction region and the density of the DVR grid points. Also we find that the set of linear equations involved in this application is efficiently solved via an iterative method which exploits the sparsity of the relevant matrix.