We now move to another recent direction, where the ground state of a molecular system can be significantly modified by coupling to a cavity photon mode with a photon frequency beyond the infrared (IR). From the technical perspective of electronic structure theory, this appears to be a simpler problem because ground states (even for polaritons) are often easier to obtain compared to excited states. Meanwhile, an intuitive understanding of cavity modification of the molecular ground state is not available when using simple quantum optics models. In fact, the JC model predicts that the ground state is simply |g, 0⟩ irrespective of the cavity coupling strength λ or the cavity photon frequency ω c and is therefore completely decoupled from the manifold of excited adiabatic-Fock basis states. Of course, the JC model Hamiltonian is known to explicitly break down, especially for large coupling strengths (see Fig. and Fig. ). Therefore, the investigations focused on the ground state properties of a polaritonic system necessarily belong to a regime beyond the JC model. This failure of the JC model also indicates that the cavity modification to the molecular ground state operates in the ultra-strong coupling regime (USC) or beyond. Further, this is also an interesting direction where new chemical reactivity could occur in the ground state of the hybrid system, which is not well-understood and may require one to "re-learn" molecular orbital theory in the presence of the cavity. In this case, there is no semblance of the Rabi splitting (Eq. 6), since the electronic state in question (i.e., the ground state) is far away in energy from the cavity frequency (e.g., ∼ 1-10 eV) as we will see in the following examples. However, the dipole self-energy, which couples electronic states through dipole interactions mediated by the cavity, will still have a drastic effect, especially at large coupling strengths. To be clear, the cavity frequency in these examples is far away from those of the vibrational strong coupling (VSC) cases, which have cavity frequencies on the order of ∼0.1 eV (see Sec. 5 for more details of VSC) lying in the IR regime. Additionally, the difficulties of such calculations are significantly simplified because they only require a ground state electronic-photonic structure method for the scQED scheme (e.g., QED-HF, QED-DFT, QED-CC, etc., see Sec. 3.2) and are therefore computationally simpler than those previously discussed simulations in this section that required the explicit calculation of excited polaritonic states. In contrast, performing pQED calculations require the calculation of excited states, since these ground state modification reviewed in this section are induced by off-resonance couplings between the molecular ground state and other electronic states (through DSE) or other light-matter dressed states (through light-matter coupling term). Of course, the pQED Hamiltonian will provide the same results as the scQED approaches in the infinite basis limit.