In a similar sense of defining the electronic Hamiltonian and corresponding eigenvalue equation for the matter, one can define a similar expression for the polaritonic system, Ĥpl ≡ ĤPF -TR , which includes all operators of molecules and cavity, except for the nuclear kinetic energy operator TR . As such, the polariton state is defined as the eigenstate of Ĥpl through the following eigenvalue problem (4) where Ĥpl ≡ ĤPF -TR is the polariton Hamiltonian, |Φ j (R)⟩ is the polariton eigenstate, and E j (R) is the polariton potential energy surface. As can be seen clearly, both |Φ j (R)⟩ and E j (R) parametrically depends on the nuclear configuration R. We denote |Φ 0 ⟩ as the ground state of polariton Hamiltonian.