In Sec. II we describe the model Hamiltonian of interest along with the relevant parameters and the choice of initial states is motivated in Sec. III B. The classical and quantum isomerization probabilities in the VSC regime are compared in the presence of virtual photons and zero photons in the cavity in Sec. III B, illustrating the effect of different types of initial states on the isomerization dynamics. In Sec. III C we provide a classical phase space based understanding of the cavity-mediated effects and the correspondence to the quantum results in terms of the influence of different polariton eigenstates. Section IV concludes.