Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Diracδ-function representable as a localized Gaussian wavepacket. This functional form enables computation of the cumulative reaction probability N(E) from the wavepacket time-correlation functions. The Gaussian based form of the flux eigenfunctions, which is not tied to a finite basis of a quantum-mechanical calculation, is particularly useful for approximate calculation of N(E) with the trajectory based wavepacket propagation techniques. Numerical illustration is given for the Eckart barrier using the conventional quantum-mechanical propagation and the quantum trajectory dynamics with the approximate quantum potential. N(E) converges with respect to the Gaussian width parameter, and the convergence is faster at low energy. The approximate trajectory calculation overestimates tunneling in the low energy regime, but gives a significant improvement over the parabolic estimate of the tunneling probability.
Published in The Journal of Chemical Physics, Volume 131, Issue 164108, 2009.
Copyright 2009 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
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Garashchuk, S. & Vazhappilly, T. (2009). Wavepacket approach to the cumulative reaction probability within the flux operator formalism. The Journal of Chemical Physics, 131, 164108. http://dx.doi.org/10.1063/1.3251333
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