Wavepacket propagation for reactive scattering using real L 2 eigenfunctions with damping

Abstract

A wavepacket propagation method for reactive scattering using real L² eigenstates is proposed and tested. The wavepacket propagation is carried out by explicit time evolution of a basis of real L² eigenstates. The wavepacket is damped at each time step to avoid unphysical reflections at the grid edges and then re-expanded in terms of the real eigenstates. Most of the computational effort is associated with the calculation of eigenstates, while the propagation in the real L² basis and analysis are relatively inexpensive. In addition, once the L² basis is available the wavepacket propagation for any initial state can be done very efficiently. Propagation by complex L² eigenstates is also briefly reviewed. In this approach no explicit time propagation is required since the time-to-energy wavepacket transformation is analytical for any given potential. Applications of both methods for a one-dimensional Eckart potential show excellent agreement with exact results for the energy dependence of the reaction probability. The real L² approach is also applied to three-dimensional D+H₂ for zero total angular momentum. Reaction probabilities for H₂(v=0, j=0–5), summed over final DH states, as well as the cumulative reaction probability are presented over a wide energy range and compared to previous accurate results.