Further, the authors 157 also explain effects of the cavity coupling on the ground state of molecule, prior to perform ab initio polaritonic calculations. In this sc-QED framework, the authors used the coherent state basis (defined earlier in Sec. 3.2) which allows one to observe the size of the variance in the dipole with respect to the electronic ground state which is (∆μ) 2 (see discussion around Eq. 124). The size of the variance will give direct insight into the magnitude of the cavity effects on the ground state and can be calculated for the bare molecular system outside the cavity. This was computed for the sodium-halide species in the present example, which predicted the larger effects for the anionic (negatively charged) species that was later observed to be accurate after performing the explicit scQED procedure. In Ref. 102, the reactivity of a generic SN2 reaction between methyl chloride CH 3 Cl and ammonia NH 3 (which forms methylamine and hydrogen chloride) was explored from the viewpoint of molecular orbital (MO) theory. Here, the authors 102 portray a new ideology of MO theory inside the cavity, referred to as cavity MO theory. Using the self-consistently updated ground state MOs from a scQED-HF scheme, the authors make predictions regarding the thermodynamic driving force of the reaction based on the strongly participating MOs between reactive substituents. Fig. (ii) presents the main results of the work, where the transition state geometry of the reaction is shown along with the dominant MO, HOMO-5, with strongly overlapping orbitals between all participating species for coupling strengths λ = 0.0, 0.1, and 0.2 a.u. (left to right within each panel). Fig. 11d (i,iii) show the projections onto the substituents' MOs that largely contribute to the bonding process at each light-matter coupling strength. Notably, for the full molecule shown in (ii), the bonding of the nitrogen to the carbon gradually decreases with increasing coupling strength λ, effectively due to the localization of the nitrogen's lone pair to the nitrogen atom. Here, the presence of the cavity influences the relative contributions of the substituent MOs as shown for the (i) ammonia and (iii) methyl chloride. For the ammonia species, the contribution of the anti-bonding lone pair localized to the nitrogen is increased with increasing coupling strength λ. This is the main driving force for the reduction in the nitrogen-carbon bond at the transition state geometry found in Fig. (ii). The other effect found in (ii) is the weak conversion of the carbonchloride bonding character to anti-bonding character with increasing coupling strength. This is exemplified in (iii) which showcases two main contributing projected orbitals, HOMO-2 and HOMO-5, of the methyl chloride sub-system. HOMO-2 posses the bonding character between the chloride while HOMO-5 provides the antibonding character. As the coupling strength increases, the bonding orbital contribution decreases from 32% to 15% while the anti-bonding orbital increases from 5% to 9%. This accounts for the reduction in bonding character found in (ii). This work 102 exemplifies that molecular orbital theory still applies but needs to be further understood in the presence of a cavity. Through selfconsistent electronic-photonic structure theory (i.e., sc-QED ground state methods), one can more easily understand the response of the MOs due to the presence of the cavity. Performing a similar calculation via the pQED scheme, on the other hand, is not trivial for the analysis of the ground state MOs. In principle, it should be possible to reformulate Eq. 112 in the basis of MOs rather than electronically correlated excited Slater determinant states, carefully accounting for the occupation numbers of photon-dressed MOs.