A force field of Li$^+$ , Na$^+$ , K$^+$, Mg$^{2+}$, Ca$^{2+}$, Cl$^-$, and SO$_4^{2-}$ in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

Abstract: In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li$^+$ , Na$^+$ , K$^+$, Mg$^{2+}$, Ca$^{2+}$ and the anions Cl$^-$, and SO$_4^{2-}$. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.

Evaluation of Ionic Force Field Based on TIP4P/2005 Water Model and Scaled Charges

The study presented delves into a non-polarizable force field development for ionic solutions involving Li$^{+}$, Na$^{+}$, K$^{+}$, Mg$^{2+}$, Ca$^{2+}$, Cl$^{-}$, and SO$_{4}^{2-}$ ions in water. Employing the TIP4P/2005 water model, the force field introduces scaled charges for ions to enhance solution property predictions. This approach follows the notion that scaling ion charges, 0.85 for monovalent and 1.7 for divalent ions, effectively accounts for polarization effects, especially when direct polarizability is absent.

Numerical Results and Observations

The force field, referred to as the Madrid-2019 model, demonstrates its capacity to accurately predict density and viscosity of ionic solutions up to high concentrations. Notably, the model aligns well with experimental density data across various molalities for many ionic solutions:

• Density and Structural Properties: The calculated densities are consistently within 1% of experimental values for most solutions, showcasing the model's precision. Sodium chloride solutions, for instance, report hydration numbers and RDF peak positions in accordance with experimental observations, but the charge scaling implies limitations for purely ionic systems.

• Viscosity and Diffusion Coefficients: Up to concentrations of 3 molal, the model provides satisfactory viscosity predictions, although deviations grow at even higher salt concentrations. The diffusion coefficient assessments conform reasonably with experimental results, underlining improved ionic mobility descriptions from scaled charges.

Importantly, the model prevents crystallization at simulated solubility limits, an issue seen in full charge models, suggesting better utility in solution phase studies.

Implications of Scaled Charges and Limitations

The Madrid-2019 model highlights several critical ramifications when using scaled ion charges:

1. Improvement in Solvated Environment Simulations: By employing scaled charges, the model mitigates the typical over-coordination issues arising with integer charge force fields, reflecting a more accurate ion-water interaction throughout varied conditions.

2. Charge Scaling and its Theoretical Justification: The adoption of scaled charges, while it rectifies certain aqueous phase invariabilities, sacrifices accuracy in the crystalline and molten states. This trade-off indicates a need for polarizable models to resolve inter-phase discrepancies effectively.

3. Potential in Mixture Simulations: The model's transferable attribute is evident in predicting ternary mixture densities accurately without additional parameter optimization, affirming its adaptability.

Conclusions and Future Prospects

The paper provides a compelling argument for implementing scaled charges in non-polarizable force fields, achieving practical enhancements in representing ionic solutions. Despite limitations—chiefly the underestimation of solid and molten densities—the force field opens potential for further inquiry into other scaling factors and combined polarizable models.

Further research could focus on accurately integrating charge transfer and polarization effects in more sophisticated models or exploring alternative scaling factors to bridge current disparity in solid-state predictions. This work sets a precedent for continued exploration towards versatile and accurate ionic force predicts within computational chemistry frameworks.