We now turn our attention to the other two initial states whose polariton weights are shown in Fig. and for which Fig. (a) indicates enhanced isomerization probabilities due to the cavity-system coupling. The results in Fig. (a) clearly show that states k = 3, 4 dominantly contribute to the dynamics of the initial state with q i = -0.439 au. From Fig. it is apparent that these states are delocalized along the interwell orbit. The phase space densities of these states are localized around q ≈ 0 and hence, given the sectioning condition, localized around the saddle. Therefore, the enhanced cavitymediated isomerization for these initial vibropolariton wavepackets comes from the fact that the dominantly contributing polaritons have mainly a matter-like character. Similar coordinate and phase space features are associated with the states k = 7, 8 and hence more matterlike in character (see Supplementary Fig. for the phase space Husimi representations of the 8 th and 12 th polaritonic states projected onto the cavity phase space). Note that the nature of the dominantly contributing states for q i = -0.9 au and q i = -0.439 au are distinctly different despite their initial average system energies ⟨H S ⟩ being nearly the same. On the other hand, Fig. (a) indicates that there are nearly eight polaritons k and k = 9, 10 that contribute equally to the initial state with q i = -0.602 au. In this case the states k = 1, 2 belonging to the X 0 manifold are also important. The corresponding coordinate and phase space densities of the dominant polariton states that contribute to the dynamics are shown in Fig. , indicating that both matter-like and photon-like states are involved. Consequently, the dynamics associated with this initial state is fairly complicated.