When the coupling strength increases, the polaritonic PES starts to change its curvatures and characters, which can be clearly seen from the color coding of the polariton PES. As we can see from Fig. (g c = 0.005) and Fig. (g c = 0.01), the gap between the 2 nd and the 3 rd polariton PES becomes larger and the state |e1 starts to mix with the JC subspace. The |g0 state, on the other hand, only slightly mixes with the other photon dressed states, even with the largest light-matter couplings we considered. The population dynamics for g c = 0.005 are presented in Fig. and Fig. . The main transitions occur between |e0 and |g1 . But now the |e1 state also shows finite oscillating population, which is mainly caused by the light-matter interaction due to the presence of the permanent dipole µ ee . When increasing the coupling strength to g c = 0.01, the main population transition now happens between |e0 and |e1 states, due to the permanent dipole µ ee that dominates the lightmatter coupling. For all cases, both Ehrenfest and FSSH approaches generate reasonably accurate polariton population dynamics, with FSSH slightly outperforming the Ehrenfest dynamics.