Avoiding long propagation times in wave packet calculations on scattering with resonances: A hybrid approach involving the Lanczos method

We investigate the usefulness of a hybrid method for scattering with resonances. Wave packet propagation is used to obtain the time-dependent wave function C(t) up to some time T at which direct scattering is over. Next, C(t) is extrapolated beyond T employing resonance eigenvalues and eigenfunctions obtained in a Lanczos procedure, using C(T) as starting vector to achieve faster convergence. The method is tested on one two-dimensional ~2D! and one four-dimensional ~4D! reactive scattering problem, affected by resonances of widths 0.1–5 meV. Compared to long time wave packet propagation, the hybrid method allows large reductions in the number of Hamiltonian operations NH required for obtaining converged reaction probabilities: A reduction factor of 24 was achieved for the 2D problem, and a factor of 6 for the 4D problem. © 1996 American Institute of Physics. @S0021-9606~96!02344-6#