Nonlinear scaling schemes for Lennard-Jones interactions in free energy calculations.

Alchemical free energy calculations provide a means for the accurate determination of free energies from atomistic simulations and are increasingly used as a tool for computational studies of protein-ligand interactions. Much attention has been placed on efficient ways to deal with the "endpoint singularity" effect that can cause simulation instabilities when changing the number of atoms. In this study we compare the performance of linear and several nonlinear transformation methods, among them separation shifted "soft core" scaling, for a popular test system, the hydration free energy of an amino acid side chain. All the nonlinear methods yield similar results if extensive sampling is performed, but soft core scaling provides smooth lambda curves that are best suited for commonly used numerical integration schemes. Additionally, results from a more flexible solute, hexane, will also be discussed.