Determination of aqueous solubility of NaCl in molecular dynamics simulation using the Kirkwood-Buff method

Electrolyte solutions are central to a wide range of scientific and industrial applications, with ions in solution affecting properties as diverse as ion diffusion, solvation structure, and chemical potentials. However, accurately predicting the solubility of salts such as sodium chloride (NaCl) in molecular dynamics (MD) simulations is challenging. Existing methods, such as the direct coexistence method and the chemical potential route, provide insights but often require extensive computational resources or face limitations in reproducibility. In this study, we present an alternative approach using Kirkwood-Buff (KB) theory combined with MD simulations to estimate the solubility of NaCl. This "KB method" requires the calculation of ion-ion and ion-water Kirkwood-Buff integrals at different electrolyte concentrations based on a reference electrolyte chemical potential, yielding concentration-dependent chemical potentials. We calculated the solubility of five state-of-the-art NaCl models and found a clear link between ion pairing and solubility at low and moderately high electrolyte concentrations. Our results suggest that force fields with a mean number of contact ion pairs per ion between 0.014 and 0.025 in 1.0 molal aqueous electrolyte solution might be a good choice, offering valuable insights for future model refinement. By evaluating the computational efficiency of the KB method, we highlight its potential as a reliable tool to calculate the solubility of the future ion models.