From the theoretical side, a clear mechanistic understanding of VSC-modified ground-state chemical reactivity remains elusive, despite the recent theoretical developments . In particular, there is no well-accepted mechanism or analytic rate theory . There are many previous attempts to apply the existing rate theories (such as transition state theory (TST), Grote-Hynes theory , quantum TST , Pollak-Grabert-Hänggi theory , and molecular dynamics simulations , etc.), with the conceptual hypothesis that the cavity mode can be viewed and treated as regular nuclear vibrations . However, none of them have successfully predicted the correct resonance condition or the sharp resonance peak of the rate constant distribution . The fact that the VSC-influenced dynamics is sensitive to the quantum frequency ω 0 also explains why the GH theory , the PGH the-ory , or q-TST rate theory can not correctly predict the resonance condition because these theories are often based on a partition function expression that effectively sums over all possible vibrational frequencies, and does not explicitly contain the information of ω 0 , or they are more sensitive to the curvature of the potential which is not directly related to the quantum optical frequency. This suggests that the analytic rate theory of VSC Chemistry if that exists, might have a completely new analytic form that one has not encountered before in the Theoretical Chemistry literature.