Free energy of cavity formation in solvent: Computational, methodological, and physical aspects

With molecular dynamics simulation techniques, the free energy of cavity formation in water is investigated and determined at 300 K and 1 atm. Different methods are compared: Widom particle insertion, thermodynamic integration, and perturbation. It is shown that the most efficient way to get accurate results is to apply Widom particle insertion for cavities up to a thermal radius of 0.25 nm followed by a thermodynamic integration with sampling at fixed thermal radii. In order to converge the result to 2.5% at one thermal radius a simulation period in the order of 100 ps is needed. The convergence behavior for thermal radii slightly above the van der Waals radius of a water molecule (0.31 nm) is poor and thus indicates instabilities in the water shell surrounding the cavity and that the free energy is a nonsmoothly increasing function of the thermal radius.