To begin with, we focus on the ⟨P iso ⟩ behavior shown in Fig. (a) for the initial state with q i = -0.9 au. The ⟨FLI⟩ computation shown in Fig. (a) shows a decrease in the extent of chaos for ω 10 ≲ ω c ≲ ω R , and this is also approximately the range where both quantum and classical ⟨P iso ⟩ get suppressed. In Fig. the reactant well SOS for specific cavity frequencies and the corresponding average total energies are shown. Note that Fig. shows both the reactive mode and photon mode phase spaces for comparison. One can clearly see the chaos-order-chaos transition with increasing ω c and a significant amount of regularity in the phase space for ω c ≈ ω R = 1182 cm -1 . In particular, already at ω c = ω 10 two specific features appear prominently in the phase space. The first one (indicated in purple in Fig. ) is a regular island that corresponds to a 1:1 nonlinear resonance between the reactive mode frequency and the cavity frequency. Using actionangle representation of the Hamiltonian it can be shown that the size of the resonance region scales as √ ω c for a fixed η value. Thus, with increasing ω c the 1:1 resonance island grows in size until further increase leads to overlaps with the other resonances leading to chaos . A fairly detailed analysis of the classical rates in terms of reactive flux based on overlaps of specific low order resonances is possible. However, we do not attempt this in the present work. The second feature (blue color in Fig. ) also corresponds to regular dynamics but distinct from the resonant trajectory. In fact, these tori are born out of bifurcation, and trajectories from this region connect the reactant and the product wells . In this work we do not go into the details of the bifurcations of various periodic orbits. However, note that it is possible to analyze the system in far more detail from the perspective of phase space reactive transport based on the periodic orbits and their associated stable and unstable manifolds.