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Liouville space hierarchical equation of motion (HEOM) method1-4 is recently developed to calculate the quantum rate dynamics.In our work,we apply HEOM equation to calculate the quantum reaction rate,to investigate whether a two-state spin-boson type of model5 is effective to replace the double well model6 to describe the proton dynamics.With exact numerical calculation,we note that proton transfer can be described by an effective spin-boson model for two-state tunneling in the case of low friction.Besides,we also compare these results with numerical result by the method of Fermi golden rule (FGR).