Compensation Relationship in Thermodynamics of Gas-Phase Molecular Complexation

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.