where we have made use of the orthogonality of the vacuum Fock states, ⟨n |m ⟩ = δ nm . For example, one may be interested in the polaritonic transition density 39;71;37 ρ M 0j (r) (see Eq. 21) or the polaritonic difference density 40;17;41 ∆ρ (r) = ρ M j jξ j j of the molecule inside the cavity. With the pQED approach, textbook organic reactions can be studied. Several theoretical studies have recently shown that the cavity can completely switch selectivity of well-known chemical reactions. If successful, cavity QED could revolutionize fundamental knowledge of organic chemistry. One such reaction is the electrophilic bromination of nitrobenzene shown in Fig. . This is a textbook reaction, where only the meta-substitution product is possible, and the ortho-substituted (or para-substituted) product is not observed experimentally. This has been wellexplained due to the stability of the catatonic active complex PhNO 2 -Br + , for example, using the resonance structure or using ab initio calculations. By coupling this reaction to an optical cavity which mixes the character of the ground and excited electronic states, it was observed that one can fundamentally change the selectivity of this reaction, making the ortho-substituted product possible. Fig. presents the relative energy difference between the meta-substituted and the ortho-substituted catatonic active complex PhNO 2 -Br + , where the blue region of the figure indicates where the meta-substitution is more stable, and red region of the figure indicates where the ortho-substitution is more stable. Fig. presents the ground state density difference (∆ρ (r), defined below Eq. 26 using Eq. 21) for the meta-and ortho-substituted intermediate coupled inside the cavity and outside the cavity. This density difference aids in the understanding of the cavity QED effects on modified relative energies of the intermediate species. This observable has a close connection with the intuitive resonance structure arguments, since the difference density shows how the electronic distribution is modified by the presence of the cavity. As such, coupling to the cavity cavity enables ortho-substituted nitro-benzene, thus making impossible reactions possible. Additionally, Ref. 17 predicts that the experimental condition for this change requires the cavity frequency of ω c = 1.8 eV and the filed intensity of 2 -10 V/nm, both of which can be accomplished with the state-of-the-art plasmonic cavity designs.