Pathway dependence of the efficiency of calculating free energy and entropy of solute-solute association in water

In this study we investigate two alternative pathways to compute the free energy and the entropy of small molecule association (ΔFassoc and ΔSassoc) in water. The first route (direct pathway) uses thermodynamic integration as function of the distance R between the solutes. The mean force and the mean covariance of the force with the energy in solution are calculated from molecular dynamics simulation followed by integration of these quantities with respect to the reaction coordinate R. The alternative approach examined (solvation pathway) would first remove the solutes from the solution using thermodynamic integration as function of a solvation coupling parameter λ, change the solute-solute distance in vacuo and then solvate back the solute pair at the new separation distance. The system studied was a pair of CH4 molecules in water. We investigate the influence of the CH4-water interaction strength on the obtained ΔFassoc and ΔSassoc values by changing van der Waals and Coulomb interaction and evaluated the accuracy and efficiency for the two pathways. We find that the direct route seems more suitable for the calculation of free energies of hydrophobic solutes while the solvation pathway performs better when calculating entropy changes for solutes that have a stronger interaction with the solvent.