Analytic Rate Theory. Under the thermally activated initial condition, the reaction coordinate R 0 undergoes a barrier-crossing process, reaches the transition state, and finally relaxes to the product configuration. This is the well-accepted classical mechanism that can be properly described by transition state theory. Quantum mechanically, the same process is described as the thermally activated vibrational excitation on the reactant side |ν L ⟩ → |ν ′ L ⟩, (2) vibrational excited states transition |ν ′ L ⟩ → |ν ′ R ⟩, and (3) vibrational relaxation on the product side |ν ′ R ⟩ → |ν R ⟩. The population dynamics from the HEOM exact simulations (see Supplementary Note 2 and 3) indicate that the reaction mechanism can be described as follows