Analysis of Coupling Schemes in Free Energy Simulations:  A Unified Description of Nonbonded Contributions to Solvation Free Energies

The solvation free energies evaluated from molecular simulations with explicit solvent models and integral equation methods are compared to the results obtained from macroscopic models. Different parameter coupling schemes commonly used in free-energy simulations are analyzed. For the electrostatic and van der Waals contribution to the free energies of solvation, the macroscopic models suggest coupling schemes that can significantly reduce the time required for free energy simulations. A comparison of Poisson−Boltzmann calculations for solvation free energies with the Born−Kirkwood−Onsager multipole expansion method indicates that the former is a significant improvement for quantitative calculations of polyatomic solutes. However, the multipole expansion is useful for obtaining qualitative insights concerning the dependence of the solvation free energy on the characteristics of the charge distribution. The integral equation results for hydrophobic solvation have a surface area dependence with a proportionality factor, the effective “surface tension”, that depends on the nature of the solute. The behavior of the solvation free energy in the limit of a vanishing hydrophobic solute is shown to lead to a small deviation from the simple surface area dependence.