In Ref. 378, it has also been shown that when the DSE term is included, the cavity can only slightly modify the ZPE and bond lengths, but no obvious effects on dissociation energies and inversion barriers. When the quantum effects is considered, the reaction barrier will slightly decrease as the coupling strength increases. In a follow-up work, 225 the authors further concluded that both the number of reactive channels and the tunneling probability will be reduced when the quantum effects are considered explicitly. It is also found that there is a coherent energy exchange between the system and cavity mode in the resonant case.