Hildebrand Solubility Parameters Revisited - Cohesive Energy or Electrophilicity Densities?

We present certain concepts and expressions from conceptual density functional theory (DFT) for calculating Hildebrand solubility parameters. The original form of the Hildebrand solubility parameter is used to qualitatively estimate solubilities for various apolar and aprotic substances and solvents and is based on the square root of the cohesive energy density. Our revised expression allows the replacement of cohesive energy densities with electrophilicity densities that are numerically accessible through simple DFT calculations. As an extension, the reformulated expression offers a deeper interpretation of the main contributions and particularly emphasizes the importance of charge-transfer mechanisms. All calculated values of the Hildebrand parameters for a large set of common solvents are compared to experimental values and show good agreement for non- or moderately polar aprotic solvents. The observed deviations for more polar and protic solvents define robust limits where the Hildebrand approach is valid.