Linear Free-Energy Relationships and Solvation Thermodynamics: The Thermodynamic Basis of LFER Linearity

The Abraham solvation parameter model, known alternatively as the Linear Solvation Energy Relationships (LSER) model, is widely used in numerous applications in the broader chemical, biochemical, and environmental sector with remarkable success. So far, there is no explanation at the fundamental thermodynamic level for the very linearity of this model. This is, however, essential for the evaluation and exchange of thermodynamic quantities between models and databases. The present work offers such an explanation by combining the equation-of-state solvation thermodynamics with the statistical thermodynamics of hydrogen bonding. It shows what this linearity entails and in what way it is interpreted and handled so far. In addition, it proposes new ways of extending it for estimations over a broad range of external conditions and, eventually, in predicting solvent LFER coefficients from the corresponding molecular descriptors, which are known for thousands of compounds. This would enhance significantly the predictive capacity of the model in practical applications, such as solvent screening, solute partitioning, activity coefficients at infinite dilution, or hydration/solvation energies. Various examples of calculations are reported. A critical discussion of perspectives and challenging emerging issues are also presented.