At the mean-field level, and in the coherent state representation, it is commonly understood that the DSE is the leading contribution to the cavity-induced changes to the ground state. In this representation, the direct electron-photon term is shifted away, leaving only a modified DSE term proportional to the dipole fluctuations ⟨(∆μ) 2 ⟩ GS in the ground state (GS) rather than the square of the dipole itself ⟨μ 2 ⟩ GS . In this work, we do not employ the coherent state representation, but we still expect the DSE to contain the physics of the ground state problem, to leading order. However, our approach goes well beyond the mean-field approach, incorporating, in principle, the exact electron-photon correlation by direct diagonalization in the adiabatic-Fock representation. In this case (Fig. ), it is clear that the DSE is directly related to the chemically relevant modifications to the ground state energies (to a first approximation), since the DSE contribution nearly quantitatively reproduces the changes to the TS barrier energy in all cases (i.e., other contributions largely cancel among each other). This also provides confirmation of the various meanfield QED-HF calculations as well as high-level approaches in the community exploring ground state cavitymodifications.