QED approaches that neglect the dipole self-energy operator altogether, which we term pRabi and Rabi-FCI approaches, respectively, to denote the analogy to the Rabi Hamiltonian. In these approaches, the only coupling between the electronic and photonic degrees of freedom arises through the bilinear coupling term. We compute the coupled LiH scan at the pRabi(500,2)/6-311G, pRabi(500,10)/6-311G, and Rabi-FCI-10/6-311G levels.