We observed that including either only the photonic ground state (N cav v = 1) or the lowest two molecular vibrational states (N mol v = 2), the reaction rate k increases slightly and linearly with ω c . This increase stems from the change in the dipole self-energy term ω c η 2 c x 2 in Eq. ( ), which is necessary to have a gauge invariant Hamiltonian and crucial for an accurate description of light-matter interactions under the dipole gauge. The absence of a peak confirms that the zero-point energy effect of both the cavity photonic and the molecular DoF is irrelevant for the resonance structure in the cavity frequency-dependent rate profile. This finding aligns with Ref. 31, which demonstrates that, despite the improvement of the ring-polymer molecular dynamics over the classical treatment due to accounting for the zero-point energy effect, it is not sufficient for studying chemical reactions inside the cavity.