Fig. further presents the change of the effective free energy barrier ∆(∆G ‡ ), directly calculated from the rate constant ratio k/k 0 obtained from HEOM simulations. To account for the "effective change" of the Gibbs free energy barrier ∆(∆G ‡ ), we consider the simple rate equation k = A • exp(-β∆G ‡ ), with the outside the cavity case as k 0 = A • exp(-β∆G ‡ 0 ), as is commonly assumed by experimental analysis. The prefactor A is assumed to be the same with or without the cavity. The change of the effective free energy barrier compared to the bare molecular reaction (with k 0 and ∆G ‡ 0 ) is then