Prediction of Hydrogen-Bonding Interaction Free Energies with Two New Molecular Descriptors

This work is a continuation of our recent work on the prediction of hydrogen-bonding (HB) interaction enthalpies. In the present work, a simple method is proposed for the prediction of the HB interaction free energies. Quantum chemical (QC) calculations are combined with the Linear Solvation Energy Relationship (LSER) approach for the determination of novel QC-LSER molecular descriptors and the development of the method. Each hydrogen-bonded molecule is characterized by an acidity or proton donor capacity, αG, and/or a basicity or proton acceptor capacity, βG. These descriptors suffice for the prediction of HB interaction free energy when the interacting molecules possess one acidic and or one basic site. In this case of two interacting molecules, 1 and 2, their overall HB interaction free energy is cαG1βG2+βG1αG2, where c is a universal constant equal to (ln10)RT = 5.71 kJ/mol at 25 °C. This holds true over the full composition range, that is, regardless of which molecule is solute and which solvent. In the case of complex multi-sited molecules possessing more than one distant acidic site and/or more than one type of distant basic sites, two sets of αG and βG descriptors are needed, one for the molecule as solute in any solvent and one for the same molecule as the solvent of any solute. Descriptors αG and βG are reported for a number of common hydrogen-bonded molecules but they may be obtained for any other hydrogen-bonded molecule of interest from its molecular surface charge distribution already available or easily obtained via relatively cheap DFT/basis-set QC calculations. The new predictive scheme is validated against corresponding estimations of the widely used Abraham’s LSER model. The developments in the present work and the previous one are useful for solvation studies in chemical and biochemical systems and, particularly, for equation-of-state developments in molecular thermodynamics. The strengths and limitations of the new predictive method are critically discussed.