Reactive scattering using efficient time-dependent quantum mechanical wave packet methods on an L-shaped grid

Abstract

Most quantum mechanical time-dependent wave packet methods represent the wave packet on Cartesian grids. For reactive systems these grids can contain many points at which the wave function amplitude is negligible throughout the calculation. A significant fraction of the computational resources in a calculation may be used in calculating and storing values of the wave function at these grid points. This work describes a method which uses the Fourier transform method to calculate the kinetic energy of a wave function on a grid which covers only reactant and product regions of the potential. For a two-dimensional system this corresponds to the use of an L-shaped grid. The time propagation is performed using the Chebyshev propagation method. The method is demonstrated for a model problem treating dissociative adsorption and associative desorption of H2 from a flat surface. The amount of computational resources required for these calculations is much less than would be needed if the full rectangular grid was used.