General Relationship Between Gibbs Energies and Enthalpies of Solvation, Vaporization, and Complexation for Molecular...

The Gibbs equation describes the relationship between the enthalpy (∆H), entropy (∆S), and Gibbs energy (∆G) changes in physicochemical processes: ∆G = ∆H - T∆S. It remains a cornerstone of chemical thermodynamics, yet it has features that need to be understood. The linear correlations between ∆S and ∆H (or ∆G and ∆H) are often found across various series of processes. These correlations do not follow from the laws of thermodynamics, thus meaning that there may be additional restrictions on the variation in the thermodynamic potentials. In this study, we attempted to establish the quantitative principles governing the ∆G vs. ∆H relationship across various processes involving non-covalent interactions at 298.15 K, from solvation and vaporization to molecular complexation and supramolecular recognition. The baseline for the analysis was the linear ∆G vs. ∆H correlation for solvation in non-associated solute-solvent systems, first noted by Barclay and Butler. The classification of the solute-solvent systems enabled quantification of the deviations associated with conformational flexibility, complexation and solvophobic effects upon solvation. These regularities necessarily meant that the ∆G vs. ∆H for solution- and gas-phase molecular complexation processes should be described by similar linear relationships, having the same slope as the Barclay-Butler baseline. Furthermore, this framework was applied to α-cyclodextrin host-guest systems. The validity of the established relationships was checked against more than 4500 experimental thermodynamic values. They enable the calculation of the enthalpy change from a single equilibrium constant measurement at 298.15 K, with the deviation comparable to an experimental uncertainty. The predictive power does not depend on the process (solvation, vaporization, and complexation), the phase it takes place in (gas, liquid), or the dominating interaction type (collective/pairwise, van der Waals forces/hydrogen bonding/charge transfer), highlighting the uniform character of the discussed relationships.