Fig. also presents the change of the effective free energy barrier ∆(∆G ‡ ) (red), directly calculated from the rate constant ratio k/k 0 obtained from HEOM simulations (red dots) and FGR (red line). One can interpret the rate constant changes as the change of the effective free energy barrier ∆(∆G ‡ ) through ∆(∆G ‡ ) = ∆G ‡ -∆G ‡ 0 = -k B T ln (k/k 0 ). Note that this is not an actual change in the free-energy barrier, but rather an effective measure of the purely kinetic effect. Here, one can see a non-linear relation of ∆(∆G ‡ ) with Ω R that agrees with what has been observed experimentally (e.g., Fig. in Ref. 4). Preliminary experimental investigations suggest a non-linear trend between ∆(∆G ‡ ) and Ω R , and future experimental investigations should focus on measuring more data points to determine the fundamental scaling relations.