with Ω R being the Rabi frequency and d 1 -0 + ≡ ⟨1 -|d(q)|0 + ⟩ being the transition dipole element associated with the 0 + → 1 -bright transition of the molecular system. Note that the dipole self energy H DSE is included in the Hamiltonian. Moreover, effects of dissipation and cavity losses are ignored, resulting in a conservative two degrees of freedom system. The parameters for the isomerization model system are taken from the earlier work and given in Table . ) correspond to the initial cavity state with virtual photons and zero photons respectively. The contours of the potential energy surface eq. 2 are also shown.