where V is the quantization volume of the photon field, ε is the electric permittivity, and ê is the unit vector of the electric field polarization. Eq. 13 is composed of four main elements: the molecular Hamiltonian ĤM , the photonic Hamiltonian Ĥph , the light-matter interaction Ĥel-ph , and the dipole self-energy ĤDSE . Similarly to the molecular Hamiltonian, we wish to solve an eigenvalue problem without the nuclear kinetic energy operator TR , which we define the polaritonic Hamiltonian Ĥpl (analogously to the electronic Hamiltonian Ĥel ) as,