Classical Wigner Method with an Effective Quantum Force

Abstract: In this work, I will present an effective way to study the dynamics in phase space and obtain the rate constants. Our method is based on the Classical Wigner (CW) model, which is an approximate method for including quantum mechanical effects into molecular simulations. The Classical Wigner model propagates each trajectory independently under a classical force. It becomes poorer when the temperature decreases, because it can not describe the dynamical interference effects. The mechanism of the CW model needs to be improved. We manage to solve this problem by using a parameter denoted 0, which is the characteristic distance between forward and backward Feynman paths that enter the expression of the correlation function[1]. We use this parameter to construct an effective force to substitute for the classical force. This new method still keeps the simplicity of the CW model and improves the accuracy. The new method is named Classical Wigner method with an effective quantum force (CWEQF). This new force has the ability to approximately contain the quantum effects in the dynamics. Also, we have a new way to interpret the tunneling effects, especially for the quasi-bound situation. Thus, we are able to describe a consistent mechanism for the quantum leak out effect exemplified for a cubic potential. Then we implement the CWEQF on the two-dimensional H + H2 reaction to obtain the rate constant. All the applications return consistently improved results compared to the ordinary CW model. There is still room for us to improve this method. However, from the pedagogical point of view, this method is really a good candidate to understand the quantum effect in phase space.