Figure 2
From: On the curvature in logarithmic plots of rate coefficients for chemical reactions
Plots of the total vibrational energy in a cluster versus the cluster size d c , the energy per vibrational degree of freedom, and the cumulative binomial distribution functions for one active mode (green) and a active modes (blue). The reduced reaction barrier is taken from the hydride transfer catalyzed by Escherichia coli dihydrofolate reductase in 17% methanol. (a) Total energy in units of kT for a cluster solute-solvent of size 10 ≤ d c ≤ 80 Å according to the Debye model. (b) Ratio of the vibrational energy given by (13) in a water cluster over its number of vibrational degrees of freedom. (c-d) Cumulative binomial distribution functions as a function of d c for p = 1/s v (green) and p = a/s v (blue).* The reduced reaction barrier is taken from the hydride transfer catalyzed by Escherichia coli dihydrofolate reductase in 17% methanol with α = 200 and β = 105. * Note that in (d) the blue curve lies above the green curve only for d c approximately above 20 Å, indicating the presence of a threshold size for the cooperative effect to take over.