Density and Temperature Dependences of Hydration Free Energy of Na+ and Cl- at Supercritical Conditions Predicted by ab Initio/Classical Free Energy Perturbation

Abstract

The ab initio/classical free energy perturbation (ABC−FEP) method proposed previously by Wood et al. [J. Chem. Phys. 1999, 110, 1329] combines the free energy calculated from a classical simulation of an approximate model with the free energy of perturbing the approximate solute−solvent interactions to ab initio interaction energies. This method was used to calculate the hydration free energies of Na+ and Cl- at a variety of high-temperature state points (973 K with 0.0101, 0.0935, 0.2796 g/cm3 and 723 K with 0.0098, 0.0897, 0.5113 g/cm3). The classical simulations were done with an approximate model, previously derived by fitting ab initio results at 973 K and 0.535 g/cm3. These were followed by perturbation to a QM/MM model in which the interactions of Na+ with H2O and Cl- with H2O are calculated by an ab initio method, while the interactions of H2O with H2O are calculated by the fluctuating charge TIP4P−FQ model. The pairwise ion−water interaction energies are obtained at the MP2/6-311++G(3df,3pd) level and multibody interactions at the B3LYP/6-311++G(3df,3pd) level for Na+ and B3LYP/aug-cc-pVDZ level for Cl-. Estimates of the accuracy of the ab initio methods and of the sampling errors indicate that these results are more reliable than previous predictions and can be used as benchmarks to assess the accuracy of molecular dynamics simulations or empirically parametrized equations of state. Extrapolations using various semiempirical models were not very accurate at the state points studied. The model of Tanger and Pitzer, which interpolates between gas-phase mass spectroscopic results and high-density predictions, was very accurate. Born models failed at the low-density state points, while compressible continuum models were much better. Interpolation or extrapolation of the present results indicates that previous simulations of two different Lennard−Jones plus charge models have substantial errors at most state points. The approximate models used in the present work performed reasonably well at all state points, with differences from the ABC−FEP corrected results ranging from 0 to 22 kJ/mol.