A second point emphasized by Fischer et al , is that the cavity-mediated dynamical localization is nonmonotonic with respect to η and in the VSC regime the dependence of P iso on (η, ω c ) is rather complex. Consequently, for the initial state with q i = -0.9, but with a η value different from the one shown in Fig. (a), the maximum suppression in the isomerization probability occurs for ω c ̸ = ω R . In Fig. ) one can clearly observe this effect -the cavity frequency ω c = ω min c for which ⟨P iso ⟩ is maximally suppressed can be blueshifted from ω R by hundred wavenumbers or more. Given that ω R is nearly independent of the coupling strength η for the model system of interest, the observations in Fig. (b) are puzzling. Although one might be tempted to ascribe this effect to anharmonicity, in Sec. III C it will be shown that ω min c is related to the appearance of certain features in the classical phase space.