We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare AQP method to the widely used semiclassical propagator of Herman and Kluk by computing energy-resolved transmission probabilities for the Eckart barrier from the wave packet time-correlation functions. We find the results obtained with the Herman–Kluk propagator to be essentially equivalent to those of AQP method with a one-Gaussian density fit for several barrier widths.
Published in The Journal of Chemical Physics, Volume 118, Issue 2482, 2003.
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The following article appeared in
Garashchuk, S. & Rassolov, V. A. (2003). Semiclassical dynamics with quantum trajectories: Formulation and comparison with the semiclassical initial value representation propagator. The Journal of Chemical Physics, 118, 2482. http://dx.doi.org/10.1063/1.1535421
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