Two‐dimensional wavepacket dynamics with quantum hydrodynamics

Abstract

AbstractWyatt and coworkers introduced a new approach (Wyatt, Quantum Dynamics with Trajectories Introduction to Quantum Hydrodynamics, Springer, New York, 2005; Lopreore and Wyatt, Phys Rev Lett, 1999, 82, 5190; Wyatt et al., J Chem Phys, 2001, 114, 5113; Lopreore and Wyatt, J Chem Phys, 2002, 116, 1228; Trahan and Wyatt, J Chem Phys, 2003, 118, 4784; Trahan et al., J Chem Phys, 2005, 122, 164104; Babyuk and Wyatt, J Chem Phys, 2006, 125, 64112) which is based on quantum hydrodynamics to the quantum wavepacket dynamics and applied to several systems including tunneling and nonadiabatic transition. This approach is expected to overcome some disadvantages of the conventional wavepacket dynamics, such as order‐N problem and use of absorbing potential. We applied this method to two‐dimensional model of quantum tunneling system and compared the new approach with the conventional wavepacket simulation since the validity of this method to multidimensional systems is not well known. In the simulation, we adopted two different model potentials (Model I and Model II) and calculated time dependence of the probability density and the tunneling probability in both models, where we showed explicitly that the results of the quantum hydrodynamics are identical with those of the conventional method. Using the moving grid and the regridding algorithm in the quantum hydrodynamics, we can effectively avoid order‐N problem and use of the absorbing potential. In addition to these computational advantages, the flux vector is easily obtained by the quantum hydrodynamics and these vectors field helps us to intuitively understand detailed tunneling dynamics. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007