where Ĥen is the electronic Hamiltonian that describes electron-nucleus interactions. In addition, Ĥp , Ĥenp , and Ĥd represent the photonic Hamiltonian, electronicnuclear-photonic interactions, and the dipole self-energy (DSE) term, respectively. The electronic-nuclear potential Ĥen , which describes the common molecular Hamiltonian (excluding the nu-clear kinetic energy) is described as follows Ĥen = Te + Vee + Ven + Vnn .