The Hydration Free Energy of Aqueous Na+ and Cl- at High Temperatures Predicted by ab Initio/Classical Free Energy Perturbation: 973 K with 0.535 g/cm3 and 573 K with 0.725 g/cm3

Abstract

The ab initio/classical free energy perturbation (ABC-FEP) method combines the free energy calculated from a classical simulation of an approximate model with the free energy of perturbing the approximate interactions to ab initio interaction energies. This method was used to calculate the hydration free energies of Na+ and Cl- at two high temperature state points (973 K with 0.535 g/cm3 and 573 K with 0.725 g/cm3). At 573 K with 0.725 g/cm3 our result for the sum of free energies for the two ions, G = −657 kJ/mol, is in good agreement (4 kJ/mol) with the well-known experimental value. The ab initio result at 973 K with 0.535 g/cm3 is G = −538 kJ/mol, in good agreement (7 kJ/mol) with semiempirical extrapolations from low-temperature experimental results. The accuracy of the ab initio methods and estimates of the sampling error indicate that this result is more reliable than previous predictions using either molecular dynamics simulations or empirically parametrized equations of state. Analysis of the results showed that Lennard-Jones plus charge models for ion−water interactions are not as accurate as models with exponents less than 6 and 12, because of short-range multibody interactions. Even the best smaller-exponent models for Na+(aq) do not accurately reproduce the ab initio energies, but the best model for Cl-(aq) is reasonably accurate. The short-range multibody interactions are not negligible and effective model parameters depend on density and temperature. The multibody interactions are particularly strong for Na+(aq) so that even if an accurate effective pairwise model can be found for one temperature, it will not be accurate at other temperatures. Fortunately, the ABC-FEP method allows accurate prediction of free energies including multibody effects that are neglected in the approximate models.