⟨FLI⟩ we average the FLIs of N tot = 50000 trajectories sampled from the classical density ρ cl (z 0 ) corresponding to the initial quantum polaritonic wavepacket. In Fig. (a) we show the variation of ⟨FLI⟩ with ω c for the case corresponding to Fig. ). Similar results are obtained for the other initial state shown in Fig. and for different choices for the cavity-system coupling strength. It is clear that the variation of ⟨FLI⟩ with ω c perfectly correlates with the variation of the classical ⟨P iso ⟩ seen in Fig. . The correlation can be seen in more detail in Fig. ) which shows the distribution of FLI corresponding to the initial quantum state in Fig. (a) for two cavity mode frequencies, ω c = 945.6 and 1229 cm -1 at η = 0.06. Note that both quantum and classical ⟨P iso ⟩ at these frequencies exhibit a maximum and minimum respectively. From Fig. (b) it is seen that at ω c = 945.6 cm -1 , apart from a narrow distribution centered at low FLI values, there is a broad distribution around large FLI values. However, FIG. . Classical Poincaré surface of sections for varying cavity frequencies at fixed coupling η = 0.06. (Top row) System (q, p) phase space corresponding to the reactant well with the sectioning condition xc = xc and pc > 0. (Bottom row) Photon (xc, pc) phase space with sectioning condition q = q-= -0.75 au and p > 0. The purple arrow indicates the appearance of a 1:1 cavity-system nonlinear resonance and the blue arrow shows the appearance of regular trajectories undergoing transition from the reactant well to the product well. The cavity frequencies and the corresponding average energies at which the sections are computed are indicated. The solid black line in each plot delineates the boundary of the energetically allowed region. See text for discussions.