Further corroboration for the involvement of the 1:1 nonlinear resonance in the phase space comes from inspecting Fig. ) which shows the vibropolariton eigenspectrum as a function of the cavity frequency. At ω c = ω R ≈ 1182 cm -1 one can observe avoided crossing between certain states. For example, states k = 11 and k = 13 are involved in an avoided crossing. Similarly, states k = 17 and k = 19 are involved in an avoided crossing. Note that the states k = 13 and k = 19 have a strong photon like character. Given the well known semiclassical connections between near-degeneracy of states at avoided crossings and classical resonances, it is expected that the involved states signal facile energy flow between the system and the cavity mode. Thus, the strong suppression of ⟨P iso ⟩ for the initial state q i = -0.9 au in Fig. (a) for ω c ≈ ω R is an example of a dynamical resonance effect, consistent with the interpretation given in the earlier work .