Application of the spectral element method to the solution of the multichannel Schr\"odinger equation

Abstract

We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates are described by either purely diabatic or locally diabatic (diabatic-by-sector) bases. Bound levels and scattering matrix elements are determined with spectral accuracy using relatively small numbers of points. The scattering problem is cast as a linear system solved using state-of-the-art sparse matrix non iterative packages. Boundary conditions can be imposed so to compute a single column of the matrix solution. A comparison with log-derivative propagators customarily used in molecular physics is performed. The same discretization scheme can also be applied to bound levels that are computed using direct scalable sparse-matrix solvers.