Localized electronic density around a Ca2 + cation and two water molecules in bulk water, reconstructed from their respective Wannier orbitals. The dark and light isodensity surfaces include 90% and 95% of the corresponding densities, respectively.
Repulsion potential between water and alkaline cations (a) and alkaline earth cations (b), in units of the thermal energy β−1 = k B T.
Force (in a.u.) acting on the Ca2 + ion. The prediction of the classical force field (lines) for the three components F x , F y , and F z are compared to the DFT result (×), for 100 configurations composed of 32 water molecules and 1 Ca2 +.
Ion-oxygen radial distribution functions for the aqueous cations.
Comparison between simulated and experimental EXAFS (Ref. 63) signal for aqueous Ca2 +. The agreement is very good both for the amplitude, which reflects the number of neighbours, and frequency of the oscillations, related to their position.
(a) Snapshot of CaCl2 cristal. (b) Snapshot of MgCl2 cristal. Both structures are stable during the simulations. Cl− in cyan, Mg2 + in red, and Ca2 + in green.
Comparison between simulated and experimental F XX (Q) from Ref. 90 for a concentrated NaCl solution (one NaCl pair for 17 water molecules).
Comparison between simulated and experimental F XX (Q) from Ref. 90 for a concentrated KCl solution (one NaCl pair for 17 water molecules).
Parameters of the Dang-Chang water model.
Polarizability α and magnitude of the induced dipole of each ion . The latter is 1.18 D for water.
Parameters for the cation-water interactions. As for water-water interactions, repulsion and dispersion involve the oxygen atom, while electrostatic interactions involve the additional M site. The damping parameter b D for the dispersion interaction for the monovalent ions is chosen equal to that of the corresponding cation-chloride interaction (see text and Table V). The electrostatic damping is between the water dipole and cation charge.
Parameters for the chloride-water interactions. The dipole damping is between the Cl− and the water charges. For the reasons already explained, there is no damping of the dispersion.
Parameters for the ion-ion interactions.
χ2 for the forces on the ions and the dipoles of water and the ions.
χ2 in crystals, for the forces on the cations and anions, and the dipoles of anions.
χ2 in crystals, for the forces on the cations and anions, with the polarizable Dang-Chang models.
Structural properties: position of the first maximum in radial distribution function and coordination number. The experimental values are taken from Refs. 63 and 69–71, and 73.
Differences in Gibbs free energy of hydration: simulated and experimental values. The experimental values for the monovalent ions are taken from Refs. 79–84 and those for divalent ions from Refs. 81 and 83, and 84.
Ratio between the ions and water diffusion coefficients. The experimental values for the ions are taken from Ref. 88, the one for the water from Ref. 89.
Density of the crystals at 1 bar and 300 K. The experimental values are taken from Ref. 88. Note that the correct crystal structures (separated in the table) are preserved during the simulations.
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