Finally, we decompose the energy contributions from the Hamiltonian and provide a discussion on the effects of the dipole self-energy on the polaritonic ground state. The DSE contribution to the TS barrier energy has identical trends with the energy of the total Hamiltonian. Thus, we conclude that the DSE is the leading order physics to the cavity-mediated ground state modifications, which is in agreement with many other works at the mean-field QED-HF level and beyond. We hope this work enables further study of ground state chemistry inside the cavity that includes (i) identification of the optimal cavity polarization direction for each reaction (ii) a quantitative benchmark against other approaches, and (iii) a detailed comparison of the cavity parameters with state-of-theart experimental cavity designs.