Salts are involved in almost everything from biological and geological systems to industrial processes. They can exist in all phases, including in the form of a pure crystal, an aqueous solution, a melt, or even as a vapor of ion pairs. The behavior of ions in solution is specific and depends on the type of ion. However, many complications manifest as we extend beyond that i.e. the limit of infinite dilution (a single ion in water). The complications begin as these specific interactions depend on the type of counter ion, namely, depending on what counter ion is in solution, the ion behaves differently. Furthermore, these interactions are also dependent and change with concentration, limiting researchers' ability to develop an underlying model that can capture and predict their physics. The composition of solvent in the system and temperature both alter the effective dielectric of the system, adding an extra layer of complexity when attempting to investigate practical systems. In this work, utilizing the quasichemical framework, the different components of the hydration free energy were investigated. The hydration free energy was broken down into a short-range ion-specific contribution and a long-range ion-nonspecific contribution. Within the quasichemical approach, the hydration free energy of an ion is decomposed into a chemical term accounting for local, specific ion-water interactions within the coordination sphere and nonspecific contributions accounting for packing (cavity creation) and long-range interactions. The change in the chemical term with a change in the radius of the coordination sphere is the compressive force exerted by the bulk solvent medium on the surface of the coordination sphere. For the ions considered here, Na+, K+, F−, and Cl−, this compressive force becomes equal for equally charged ions of the same sign at short range, namely, at a coordination radii of about 3.5~{\AA} for cations and 4.2~{\AA} for anions. This includes waters just within the first hydration shell regardless of the sign of charge. For hypothetical ions, i.e. the same ions but with double the charge, Na2+, K2+, F2− and Cl2− ions, the results were similar with the compressive forces equating at r≈3.5 \AA for cations and r≈4.2 \AA for anions. These results show that ion-specific effects, which arise primarily due to differences in the local ion-water interactions, are short-ranged and are limited to the first hydration shell of an ion. Furthermore, investigating the reorganization of the solvent matrix in the presence of the ion indicates that while ion specificity is limited to the first hydration shell, the overall effect of the ion on the solvent matrix extends to the second shell and approaches zero by the third hydration shell. The long-range interactions of the ions, through the force curves, are found to be proportional to the Born hydration model. This finding rationalizes the success of certain approaches of electrolyte modeling such as the Unified Model\cite{djamali_unified_2009} and guides future work.

The Mean Ionic Activity Coefficient (MIAC) is of significant interest for practical systems investigations. Previous Molecular simulation studies of MIAC did not consider the effect of polarizability. In this work, we use the AMOEBA model that includes polarizability and describes van der Waals interactions with a Buffered 14-7 potential. We here calculate the MIAC for aqueous NaCl of varying concentrations up to near experimental saturation at 298.15 K and 1 atm. The free energy of hydration of NaCl was calculated by removing a single Na+ or Cl− from the solution and gradually switching off electrostatic interactions, followed by switching off Buffered 14-7 interaction. Simulating a charge non-neutral system inevitably involves accounting for neutralizing background potential which is accounted for in the free energy calculation. Investigating, system size effects within the AMOEBA model, simulations were performed at multiple system sizes per concentration, the results of which were extrapolated to obtain the free energy if the simulation box was infinite. No significant system size effect was found beyond the lowest concentration of m=0.019 mol/kg. Instead, we find that using the mean value of the free energy from the multiple system size simulation per concentration provided a better estimate of the MIAC. AMOEBA model correctly estimates the experimental MIAC up to the highest concentration simulated. We propose a different method of estimating Henry's law reference standard state free energy, the Self Consistent approach. This self-consistent method provides the ability to estimate the chemical potential if experimental data are lacking. The Individual Ionic Activity Coefficient (IIAC) was also calculated and compared with previously reported work using an empirical force field. Both Na+ and Cl− show some agreement with the empirical force field results, before deviating at higher concentrations.

Investigating both AMOEBA's capability to predict the free energy of hydration of higher valency ions and the temperature dependence of the hydration free energy, we study the Gadolinium ion. Free Energy Perturbation is utilized to calculate the hydration free energy of Gadolinium Chloride in water using the AMOEBA polarizable force field. The hydration free energy was calculated by gradually switching off electrostatic interactions, followed by switching off Buffered 14-7 interaction. Starting with a single ion in a water box or a charge non-neutral system inevitably involves accounting for neutralizing background potential which is accounted for in the free energy calculation. System size effects were accounted for through the Wigner correction. Good agreement of the hydration free energy and its temperature dependence from 298K to 473K at saturation conditions with experimental data reproduced through the unified model was achieved. Hydration free energy at 573K showed deviation from the experimental values by 23%, due to AMOEBA predicting a vapor instead of a liquid phase. Findings from this work indicate that calculations with a polarizable force field fitted from ab initio calculations can capture the thermodynamics of ion solvation and its temperature dependence with good agreement.