Where 〈… 〉 represents the ensemble average, V the volume of the simulation cell. The simplest numerical scheme for approximating the integral in Equation is by integrating over an evenly spaced grid of insertion points. A regular grid for xs with a mesh spacing of about 1 bohr was chosen. A successful insertion was defined as an insertion that gives a non-zero exp �-∆𝑈𝑈 𝑘𝑘 𝐵𝐵 𝑇𝑇 �, evaluated from the Lennard-Jones potential. The solute-water cross parameters were deduced from the Lorentz-Berthelot mixing rules, where 𝜀𝜀 𝑖𝑖𝑖𝑖 = � 𝜀𝜀 𝑖𝑖𝑖𝑖 𝜀𝜀 𝑖𝑖𝑖𝑖 , and 𝜎𝜎 𝑖𝑖𝑖𝑖 = (𝜎𝜎 𝑖𝑖𝑖𝑖 + 𝜎𝜎 𝑖𝑖𝑖𝑖 )/2. At least 1000 particle insertions were performed for every other snapshot of each NPT simulation trajectory (i.e., 20 ps between snapshots, 1,000 snapshots total). As the Class II models COMPASS and PCFF use a 9-6 functional form for the Lennard-Jones interactions, 12-6 parameters were extrapolated for the solute-solvent interactions from energy vs. distance plots of the 9-6 functional. For the PCFF model, the values were 3.155 Å for sigma and 0.274 kcal/mol for epsilon for the oxygen, and 0.96 Å for sigma and 0.013 kcal/mol for epsilon for the hydrogen. For the COMPASS model, the values were 3.355 Å for sigma and 0.0.08 kcal/mol for epsilon for the oxygen, and 0.95 Å for sigma and 0.008 kcal/mol for epsilon for the hydrogen.