title: Mixed quantum classical calculation of proton transfer reaction rates: from deep tunneling to over the barrier regimes.
abstract: We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of non-adiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the non-adiabatic transmission coefficients. It is found that the two-surface Landau-Zener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the Landau-Zener formula.
authors.affiliation: Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.
authors.forename: Weiwei
authors.initials: W
authors.lastname: Xie
authors.affiliation: Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Xu
authors.affiliation: Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.
authors.forename: Lili
authors.initials: L
authors.lastname: Zhu
authors.affiliation: Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Shi
mesh_terms: D001665:Binding Sites; D006859:Hydrogen / Q000737:chemistry*; D007700:Kinetics; D008956:Models, Chemical; D011522:Protons; D011789:Quantum Theory; D013816:Thermodynamics
chemical_list: D011522:Protons; D006859:Hydrogen