In this work, an approach to the calculation of hydrogen bonding enthalpies is proposed. It employs the correlation proposed by M.H. Abraham, establishing the connection between the equilibrium constant (K_HB) and acidity (${\alpha }_2^{\mathrm{H}}$) and basicity (${\beta }_2^{\mathrm{H}}$) parameters: log K_HB = 7.354 · ${\alpha }_2^H$ · ${\beta }_2^H$ − 1.099. Hydrogen bonding enthalpy (Δ_HBH) is found using the compensation relationship with Gibbs energy (Δ_HBG): Δ_HBG = 0.66 · Δ_HBH + 2.5 kJ·mol⁻¹. This relationship enables the calculation of the enthalpy, Gibbs energy and entropy of hydrogen bonding. The validity of this approach was tested against 122 experimental hydrogen bonding enthalpies values available from the literature. The root mean square deviation and average deviation equaled 1.6 kJ·mol⁻¹ and 0.5 kJ·mol⁻¹, respectively.

Solvent association and solute–solvent complexation are known to influence the relationship between the thermodynamic functions of solvation, known as the compensation relationship. Here, we accomplish a series of works devoted to the analysis of Gibbs energy–enthalpy relations in the systems with different capabilities of hydrogen bonding. The data on proton acceptors solvated in alcohols were collected, and the quantitative regularities in their solvation thermodynamics were established, depending on the binding degree in solution. The equations connecting the Gibbs energies and enthalpies of solvation in the systems with competition for hydrogen bonding sites were derived from the previously found correlation between the thermodynamic functions of complexation and solvation in simpler solutions. These equations enabled the successful prediction of the solvation enthalpies of 56 proton acceptors in alcohols (RMSD = 1.8 kJ·mol⁻¹). Together with the results of the previous works, the general linear equation connecting the Gibbs energies and enthalpies of solvation in various solute–solvent systems has been obtained. This finding led us to reshaping common understanding of the compensation relationship phenomenon.

The compensation relationship in thermodynamics is a linear correlation between enthalpy (ΔH) and entropy (ΔS) changes in a series of related systems. Over 90 years of research, its manifestations in numerous processes were observed (also in the form of Gibbs energy (ΔG) vs. enthalpy correlations), and much attention was paid to its origin. It is commonly accepted that the linear ΔH vs. ΔS correlations hold as long as the same interaction type or mechanism operates throughout. This saves space for using the compensation plots to characterize narrow series of processes but reduces its predictive capability in the general case. In this work, we applied Hess’s law to derive the relationship between ΔG and ΔH of gas-phase molecular complexation based on our previous studies of the compensation effect in solvation thermodynamics. This relation was then checked against the experimental data on 67 complexes in the ΔH range up to 70 kJ·mol−1. The scarce experimental data were supplemented with computations of the binding enthalpies of each complex using the coupled cluster method with complete basis set extrapolation. The root-mean-square deviation between the ab initio computed binding enthalpies and the values predicted from the experimental Gibbs energies was 2.7 kJ·mol−1. ΔG and ΔH of both collective and pairwise interactions governed by van der Waals forces, hydrogen bonding, and charge transfer appear to obey a common relationship, which might also be applicable in more complex processes, e.g., supramolecular recognition. The extent of the established relationships indicates that there may be more fundamental restraints on the thermodynamics of intermolecular interactions that we need to understand.