Wave-packet solution to the time-dependent arrangement-channel quantum-mechanics equations

Abstract

The time-dependent arrangement-channel quantum-mechanics (ACQM) equations are numerically solved for the collinear exchange reaction H+${\mathrm{H}}_{2}$. The method employs the fast-Fourier-transform scheme of Kosloff and Kosloff and an efficient time propagator involving a Chebyshev polynomial expansion due to Tal-Ezer and Kosloff. The time-dependent ACQM formalism, which is based on the use of the time-dependent arrangement-channel-component states as introduced by Kouri, Kruger, and Levin, involves a non-Hermitian matrix Hamiltonian in arrangement-channel space. We employ the channel-permuting array-coupling sequence of Baer, Kouri, Levin, and Tobocman. The remarkable property of the channel-component states that, below the dissociation threshold, only the component in channel j gives rise to outgoing waves in that arrangement channel, is explicitly seen in this time-dependent calculation. The calculated reaction probability is in reasonable agreement with the time-independent calculation result. The question of whether the numerically generated time-dependent solutions contain spurious solutions (which can arise in principle, due to the matrix nature of the Hamiltonian in arrangement-channel space) is discussed. It is found computationally that such spurious solutions do not create any difficulties in the calculation of reactive probabilities within the time-dependent ACQM formalism.