Time-dependent reactive scattering in the presence of narrow resonances: Avoiding long propagation times

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Abstract
Time-dependent scattering is extended to systems possessing narrow resonances. At short times the wave function is integrated directly, and at late times the wave function is expanded in terms of the slowly decaying (complex) resonance eigenfunctions of the Hamiltonian, Ψ(X,t)≂Σn ane−iεnt−Γ nt/2Φn(X). The slowly decaying eigenfunctions are easily found via a short-time filterization approach adapted from bound-state studies, in which a random wave packet is filtered at various energies and the resulting vectors are then diagonalized. The method is exemplified for collinear reactions of H+H2, where it halves the propagation time.