A fundamental view of enthalpy–entropy compensation
In this paper, enthalpy–entropy compensation (EEC) during the association of two molecules is studied by minimising model systems with molecular mechanics (MM) or quantum mechanics (QM), calculating translational, rotational, and vibrational contributions to the enthalpy and entropy with standard statistical-mechanics methods, using the rigid-rotor harmonic-oscillator approach. We start with simple two-atom models, for which dispersion and electrostatics can be studied separately, showing that there is no fundamental difference between dispersion, electrostatics, or even covalent interactions. All three types of interactions give rise to EEC and a saturation of TΔS as ΔH becomes strongly negative. Next, homologous series of complexes dominated either by dispersion or hydrogen bonds are studied. We see no qualitative difference between results obtained at the MM or QM level, and for all complexes except two very weak, EEC is observed, owing to the loss of translational and rotational entropy, typically counteracted by the vibrational entropy. Within homologous series, linear relations between TΔS and ΔH with slopes of 0.1–1.7 are obtained with no clear difference between dispersive or hydrogen-bonded systems (but ∼0.01 for ionic and covalent interactions). These relations often reflect the increasing size of the complexes coming from the translational and rotational entropies, but at least for the hydrogen-bonded complexes, it is significantly enhanced also by the vibrational entropy (which depends on the strength of the interaction). Thus, for homologous series of molecules with repeated interactions studied in vacuum, EEC is a rule. However, if water molecules are added, the relation is blurred and it can be predicted that for a real binding reaction in water solution, both enthalpy–entropy compensation and anti-compensation can be observed, depending on the detailed interaction of the two molecules with water before and after binding, further complicated by dynamic effects.