which is ĤPF -TR -Ĥsb (see Eq. 192 for ĤPF ). The energy barrier along the minimum energy path for the twodimensional potential in Eq. 198 is unchanged in comparison to the original barrier ∆E ‡ of the bare molecule (barrier along R in E g (R)). When the dipole self-energy (DSE, which is ωc ℏ A 2 0 • µ 2 gg (R) in Eq. 198) is explicitly considered, E ‡ remains invariant to changes of the light-matter coupling strength or the photon frequency. This is because the light-matter interaction Hamiltonian (Eq. 192 and Eq. 198) has a complete square of (q c -q 0 c ) 2 , and the stationary point along the photonic coordinate q c is always q 0 c (R) = -2 ℏωc A 0 • µ gg (R) for all possible R (see Ref. 69 for details). As a result, ∆E ‡ is not changed for V (R, q c ), regardless of the magnitude of A 0 . Thus, k TST is also independent of ω c or A 0 for the Hamiltonian in Eq. 192. Note that it is crucial to include the dipole self-energy term ωc ℏ (A 0 µ gg (R)) 2 for describing light-matter interactions inside a Fabry-Pérot cavity, without this term the barrier height and consequently the k TST will be modified inside an optical cavity, which should be viewed as an artifact, 378 at least for the FP type of cavity. On the other hand, the shape of the dipole can also play a role in determining the dynamics of the molecule in the absence of the dipole self-energy (DSE) term. 155 However, these modifications will explicitly vanish when considering the DSE. We note that it has been argued for plasmonic cavities, the light-matter interaction Hamiltonian does not contain the DSE term. The work in Ref. 383 also pointed out an ambiguity in computing the DSE which originates from the truncation of the cavity modes. Ref. 81 resolved this ambiguity of truncating cavity modes in the long-wavelength limit and showed that it is appropriate to include the DSE term when considering a few energetically relevant cavity photon modes. Overall, the existence of the dipole self-energy (DSE) in the lightmatter Hamiltonian remains an ongoing debate. On the other hand, the ground state potential of the coupled molecule-cavity hybrid system has been shown to be modified, even in the presence of DSE, when including electronic excited states 101,103 but for high photon frequencies (in the UV regime) and is extensively discussed in Sec. 3.3.4. Thus, such theoretical treatments show neither resonance effect nor collective effect. In the next few sections, we will discuss theoretical works that have attempted to address these effects.