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

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.