Description of Bound Reactive Dynamics within the Approximate Quantum Trajectory Framework

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The quantum trajectory framework incorporates quantum effects on dynamics through the quantum potential acting on a trajectory ensemble in addition to the classical potential. A global quadratic approximation to the quantum potential makes the method practical in many dimensions and captures dominant quantum effects in semiclassical systems. In this paper the approach is further developed to describe the “double well” dynamics—a prototype of the proton transfer reactions—which exhibits the “hard” quantum effect of tunneling. Accurate description is achieved by combining the approximate quantum trajectory dynamics with the population amplitudes in the reactant and product wells. The quantum trajectory dynamics is defined by the asymptotic classical potentials. The population amplitudes represented in a small basis describe transfer between the wells. The method is exact if the reactant/product potentials are quadratic and the basis size is sufficiently large. In the semiclassical regime the trajectory dynamics is approximate and the basis size can be as small as two functions. The approach is fully compatible with the trajectory description of multidimensional systems capturing quantum tunneling along the reactive coordinate and zero-point energy flow among all degrees of freedom.