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. For the past 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 has been 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 a narrow series of processes but reduces their predictive capability in a general case. In this study, 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 at 298.15 K. This relation was then checked against the experimental data on binding equilibria of 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 at 298.15 K was 2.7 kJ mol^-1, indicating that the relationships derived can be used as a predictive tool. Together with our previous findings in solvation and solution-phase complexation thermodynamics, the present results imply that ΔG and ΔH of both collective and pairwise intermolecular interactions of different natures appear to obey a common relationship. Their application to more complex phenomena, e.g., supramolecular recognition, is of interest.