Fig. presents the results of dissociation of the MgH + molecule coupled to the cavity. The comparison between the scQED-CIS approach (at the level of configuration interaction singles) and pQED-CIS are performed, where a three-state Pauli-Fierz model was used including the |g, 0⟩, |g, 1⟩, and |e, 0⟩ states for the pQED-CIS (where the energies, permanent dipoles, and single transition dipole were taken from bare CIS calculations). In other words, only one electronically excited state and one excited Fock state were used. This is the "minimum basis" for constructing the pQED Hamiltonian and one should enlarge the basis for achieving more accurate results at large light-matter coupling strengths. The agreement between the pQED-CIS and scQED-CIS are not perfect, and the deviations can be seen near the minima of the upper polariton (blue). Even with the minimal basis, the pQED Hamiltonian performs well for these parameters, and the deviation may be due to the simplicity of the excited state manifold (i.e., minimal basis) or rather the exclusion of dipole coupling and dipole self-energy contributions from higher-energy excitations (not included in the pQED simulation) for the choice of coupling strength used (see discussion regarding Fig. ). In Fig. , the bond length of the MgH + molecule (coupled inside an cavity) was fixed while the light-matter coupling strength was increased. Here, at low coupling strengths λ < 0.01 a.u., the pQED-CIS Hamiltonian perfectly matches the scQED-CIS results. At large couplings λ > 0.01 a.u., the pQED-CIS deviates from the scQED-CIS results, indicating that the minimal basis of |g, 0⟩, |g, 1⟩, and |e, 0⟩ is no longer good enough to converge the interaction and/or DSE terms that require additional electronic or photonic states.