We first examine the reaction mechanism for the molecule outside the cavity (dashed lines). By looking into the short-time dynamics (t ∈ [0, 1.5] ps), as shown in the bottom panel of Fig. , one can clearly see the rise of the |ν L population (red) during the first 1 ps, which then reaches a steady state. The rise of the |ν R population (green) follows the rise of the |ν L population due to its diabatic coupling with |ν L through ∆ (tunneling splitting between |ν 2 and |ν 3 ) and then reaches a steady population after 1 ps. Finally, the increase in |ν R population (blue) follows the increase in |ν R population. The high-lying excited vibrational states |ν 4 and |ν 5 are less populated (for both cavity-free and cavity-coupling cases), indicating a less important role in this system reaction dynamics at T = 300 K, due to their higher energy. As such, a qualitative understanding of the basic reaction mechanism for the molecule outside the cavity is |ν L → |ν L due to the phonon coupling (mediated by the Ĥν term in Eq. 4), and then |ν L → |ν R through the vibrationally excited states tunneling splitting ∆ , and finally |ν R → |ν R through vibration relaxation (again mediated by Ĥν ).