Single-ion solvation free energy: A new cluster–continuum approach based on the cluster expansion method

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 γN 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.