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. The population dynamics of |e1 starts to grow at an earlier time, due to the permanent dipole µ ee that couples |e0 state to the |e1 state, whereas the electronic NAC d eg still contribute to the later time population transfer to the |g0 state. Through out all coupling strength investigated here, both Ehrenfest and FSSH approaches provide a reasonable accuracy for the population dynamics for the |g1 and |e0 states at a short time, with less satisfied accuracy at a longer time, compared to the case of SM1 coupled to the cavity in Fig. .