where κ PGH is the transmission coefficient within the PGH theory and Y cl is the classical depopulation factor that accounts for the finite time for the reaction coordinate to reach thermal equilibrium in the energy diffusion-limited regime. In the spatial diffusion-limited regime, Y cl → 1. As a result, in the spatial diffusionlimited regime the classical rate predicted by the PGH theory becomes k → κ GH • k TST which is the same as in the GH theory. Using this theory, the cavityinduced enhancement of chemical rate was predicted in Ref. 363, which was also demonstrated using direct numerical simulations 375 based on the flux-side correlation function formalism (Eq. 200). It is found that when the cavity frequency, ω c , is in resonance with the reactant well frequency ω 0 , the cavity can considerably improve the thermalization of the molecular system in the energy diffusion-limited regime. This is directly reflected in the photon frequency dependence of the depopulation faction Y cl shown in sharper than the cavity suppression of chemical reactivity shown in Fig. in the spatial diffusion-limited regime. Ref. 363 further points out that the extent of the cavity chemical kinetics modification is also more substantial in the energy diffusion-limited regime than in the spatial diffusion-limited regime, which often results in an enhancement by a factor of 2-3 (with a A 0 = 0.01 as the light-matter coupling). In Ref. 375, the same effect of cavity-enhanced chemical reactivity was investigated for the cis-trans isomerization of the HONO molecule, as schematically illustrated in Fig. . With direct molecular dynamics simulations, it is observed that when cavity photon frequency is resonant to the O-N stretching mode at 900-1000 cm -1 the chemical kinetics is enhanced (Fig. ). This is because the O-N stretch is strongly coupled to the torsion coordinate, which is the reaction coordinate for this isomerization reaction. Using the same computational setup they also verified the predictions made in GH theory where the chemical rate is suppressed due to cavity coupling in the spatial diffusionlimited regime (see Sec.5.4).