  Recent experiments suggest that vibrational strong coupling (VSC) may
significantly modify ground-state chemical reactions and their rates even
without external pumping. The intrinsic mechanism of this "vacuum-field
catalysis" remains largely unclear. Generally, modifications of thermal
reactions in the ground electronic states can be caused by equilibrium or
non-equilibrium effects. The former are associated with modifications of the
reactant equilibrium distribution as expressed by the transition state theory
of chemical reaction rates, while the latter stem from the dynamics of reaching
and leaving transition configurations. Here, we examine the VSC effect in a
cavity environment on chemical rates as calculated by transition state theory.
Our approach is to examine the effect of coupling to cavity mode(s) on the
potential of mean force (PMF) associated with the reaction coordinate. Within
the context of classical nuclei and classical photons, we find that while the
PMF can be affected by the cavity environment, this effect is negligible for
the usual cavities used to examine VSC situations.
