Accuracy of Discrete-Continuum Solvation Model for Cations: A Benchmark Study

Metal ions play important roles in chemistry, biochemistry, and material sciences. Accurately modeling ion solvation is crucial for simulating ion-containing systems. There are different models for ion solvation in computational chemistry, such as the explicit model, continuum model, and discrete-continuum model. Compared to the explicit model and continuum model, the discrete-continuum model of solvation is a hybrid solvation model in which the first solvation shell is described explicitly, and the remainder of the bulk liquid is characterized by a continuum model, which provides an excellent balance between accuracy and computational costs. This work serves as a systematic benchmark of the discrete-continuum model for the solvation of cations with +2, +3, and +4 charges. The calculated hydration free energies (HFEs) of ions were compared to those obtained by the SMD continuum model alone and the available experimental data. The discrete-continuum model showed improved performance over the continuum model alone via a smaller overall error and more consistent performance. Experimentally observed trends, such as the Irving-Williams series, are generally reproduced. In contrast, greater overall error was obtained for Ln³⁺ ions, and the HFE trend along the Ln³⁺ series was more difficult to reproduce, indicating these ions are challenging to model by the discrete-continuum model and continuum model. Overall, the discrete-continuum model is recommended to calculate the HFEs of cations when experimental data are not available.