Expressions for the singular flux operator eigenfunctions and eigenvalues are given in terms of the Dirac -function representable as a localized Gaussian wavepacket. This functional form enables computation of the cumulative reaction probability NE 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 NE 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. NE 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 Journal of Chemical Physics, Volume 131, Issue 16, 2009.
© 2009 by American Institute of Physics