The effective cavity modification of reaction Entropy ∆S ‡ and reaction Enthalpy ∆H ‡ are extracted from the chemical rate constant k, measured experimentally. Fig. presents ln(k/T ) as a function of 1/T under VSC and compares it to the non-cavity scenario. The modification of the slope of ln(k/T ) indicates that ∆H ‡ is being modified (see Eq. 191) under VSC, and the changing of the y-intercept indicates that the reaction Entropy ∆S ‡ is also modified (see Eq. 191) by VSC. The modification of ∆H ‡ and ∆S ‡ under VSC as a function of Rabi-splitting Ω R (due to the change of the concentration C = N/V in the experiment) is shown in Fig. and, respectively. This analysis indicates that the free-energy barrier ∆G ‡ = (∆H ‡ -T ∆S ‡ ) is being modified under VSC inside the cavity, which is shown in Fig. that presents ∆(∆G ‡ ) = ∆G ‡ c -∆G ‡ 0 as a function of Ω R with corresponding chemical rate constant shown in Fig. . Interestingly, the chemical rate modification in Fig. shows a non-linear relationship between Rabi-splitting Ω R and rate constant k. Therefore, while Rabi-splitting is directly increases with √ N , the modification of the chemical rate assumes a more complicated relationship. The full theoretical understanding and the physical origin of how cavity modifies ∆S ‡ , ∆H ‡ and ∆G ‡ remains unclear and is a subject of ongoing theoretical research. Note that if one hypothesizes that an unknown mechanism forces the upper or lower vibrational polariton states to be a gateway of VSC polaritonic chemical reaction, 370 then the activation energy change should shift linearly 371 with Ω R . The experimental results in Fig. , on the other hand, demonstrate a non-linearity of reaction barrier. Figs. 19 and 20 summarize the basic features of the observed VSC modifications on chemical rate constants. Recent experiments also suggest that the symmetry of the vibrational normal mode coupled to the cavity mode also plays a role in modifying chemical reactivity 372 and leads to the modification of stereo-selectivity. Although it is not clear if the symmetry plays a key role in all VSC reactivities or just these specific ones. Recent theoretical investigations primarily aim to explain the following key features of the VSC-modified (adiabatic) ground-state chemical reaction. (i) cavity frequency dependence of the VSC-modified chemical rate: It is suggested that when the photon frequency is close (so-called resonant photon frequency) to some characteristic molecular vibrational frequency the chemical reaction kinetics is strongly modified. Meanwhile, when the photon frequency is far from these molecular vibrational frequencies (so-called off-resonant photon frequency) the chemical kinetics reduces to that of the cavity-free case. (ii) The collective regime of the VSC-modified reactivities: experimental studies that demonstrate cavity-modified ground-state chemical reactivity by coupling an ensemble of molecules to cavity photon modes. The Rabi-splitting that is formed due to collective light-matter coupling between molecular vibrations and cavity quantized radiation mode scales with √ N , where N is the number of vibrational degrees of freedoms. It is suggested that the cavity modification of a chemical reaction also scales with √ N . It is worth mentioning that for thermally activated nonadiabatic reactions both collective and resonant modification of chemical kinetics has been theoretically observed. In the following, we review several recent theoretical and computational works that have attempted to provide insights into cavity-modified ground-state chemical kinetics. In Sec. 5.1, we introduce the model Hamiltonian for the simplest scenario, a single molecule coupled to a single cavity photon mode. Sec. 5.2 shows why onedimensional transition state theory (TST) predicts negative results of the VSC reactivities. Then in Sec. 200, we review the Grote-Hynes rate theory, and in Sec. 5.4 we apply this theory in the context of VSC, which shows the cavity frequency dependence of chemical reactivity. In Sec. 5.5 we review recent works that demonstrate that cavities can resonantly enhance ground state chemical reactivity if solvent-solute interactions are weak (such that the reaction is under the Kramers under-damped regime). In Sec. 5.6, we review theories that show how IR-frequency cavities can modify ground-state non-adiabatic electron transfer reactions by directly coupling to the charge transfer transition dipole. In spite of the fact that all experimentally documented VSC-modified reaction rate constants fall under the regime of collective coupling, in this section, we will only review theoretical works that operate in state chemistry under vibrational strong coupling ward trend of ∆(∆G ‡ ) with ative of the higher energy under VSC compared to etarded reactivity up to a and as reported earlier [3]. h the changes in the therthe Rabi splitting, their n the VSC induced ħΩ R . VSC is not only an energy surface leading to the hange in reaction mechaevolution of ∆H ‡ and ∆S ‡ interesting to see that the reaction, which could be formation and organisastep. ter ∆H ‡ mostly represents uirement for the formaly indicates the degree of r ambient conditions, the hrough a pentacoordinate ociative mechanism with er value of ∆H ‡ (30 ± 4 kJ value of T∆S ‡ (-54 ± 6 kJ ty experiments agree well and with a TS that is more reactant/intermediate-like as schematically displayed in Figure . Interestingly, the thermodynamic data show that the reaction proceeds through a more product-like TS as shown in Figure under VSC. The dissociative TS requires higher energy as it is more bond-breaking, and it is less strained because of the tetrahedral-like structure. This could mean that the intermediate generated under VSC is easier to form but more stable than the noncavity case either by a charge stabilisation or by anisotropic interactions induced by light-matter coupling. For example, mode selective chemistry experiments have shown that TS control of the reaction can be modulated by anisotropic forces either to enhance or suppress a particular reaction path [38]. In other words, the role of strong coupling could be more important in determining the position and structure of the TS as shown in recent experimental [6, 8] and theoretical studies [23, 24].