Accurate calculation of the solvation free energy of single ions remains an important goal, involving development in the dielectric continuum solvation models, and statistical mechanics with explicit solvent and hybrid discrete–continuum methods. In the last case, many of the research studies involve a quasi-chemical approach using the monomer cycle or the cluster cycle to calculate the solvation free energy of single ions. In this work, a different cluster–continuum approach based on the cluster expansion method was tested for solvation of 16 cations and 32 anions in aqueous solution. The SMD model was used for the dielectric continuum part and three explicit water molecules were introduced in the region of the solute with the highest interaction energy. Harmonic frequency calculations and molecular dynamics sampling of configurations are not required. An empirical γ_N parameter for cations and another for anions is introduced. The method produces a substantial improvement of the SMD model with a mean absolute deviation of 2.3 kcal mol⁻¹ for cations and 2.9 kcal mol⁻¹ for anions. The analysis of the correlation between theoretical and experimental data produces a linear regression line with a slope of 1.09 for cations and 1.01 for anions. The good results of this approximated cluster expansion approach suggest that the method could be further improved by including more solvent molecules and sampling the configurations.

中文翻译：

---

单离子溶剂化自由能：一种基于簇扩展方法的新簇-连续体方法

准确计算单个离子的溶剂化自由能仍然是一个重要的目标，涉及介电连续溶剂化模型的发展，以及具有显式溶剂和混合离散连续体方法的统计力学。在最后一种情况下，许多研究涉及使用单体循环或簇循环来计算单个离子的溶剂化自由能的准化学方法。在这项工作中，基于簇扩展方法的不同簇-连续谱方法测试了水溶液中 16 个阳离子和 32 个阴离子的溶剂化。SMD模型用于介电连续体部分，在具有最高相互作用能的溶质区域引入了三个显式水分子。不需要谐波频率计算和分子动力学配置采样。一个经验引入了阳离子的γ _N参数和阴离子的另一个参数。该方法生产的SMD模型与2.3千卡mol的平均绝对偏差的显着改进^-1为阳离子和2.9千卡摩尔^-1为阴离子。理论数据和实验数据之间的相关性分析产生了一条线性回归线，阳离子的斜率为 1.09，阴离子的斜率为 1.01。这种近似簇扩展方法的良好结果表明，可以通过包含更多的溶剂分子和对配置进行采样来进一步改进该方法。