Beyond the Geometric Mean: A Monopole-Based Combining Rule for Hydrogen-Bonding Cross-Interactions

Abstract

Intermolecular interactions govern the condensed-phase properties of substances as well as the thermodynamic behavior and phase equilibria of solutions. A central challenge in the molecular thermodynamics of mixing is the estimation of cross-interaction energies (εAB) between unlike molecules from the pure-substance properties via combining rules─a task complicated by the vast number of possible mixtures and the experimental difficulty of directly measuring cross-interaction energies. Classical Berthelot geometric-mean combining rules, originally derived for exchangeable van der Waals interactions, are inadequate for specific donor–acceptor interactions such as hydrogen bonding. Hydrogen bonding is governed by two independent molecular characteristics: donor and acceptor abilities (α and β). Consequently, the self-association energy of a pure substance is expressed as the product αβ, following a Coulombic-type attraction principle. Crucially, hydrogen-bonding interactions between two unlike molecules A and B are intrinsically asymmetric and non-exchangeable (A → B ≠ B → A) since each molecule possesses its own distinct α and β parameters. To address this, we propose a new combining rule in which the cross-association energy is evaluated as the sum of two cross-products: αAβB + αBβA. This model treats hydrogen bonding as mediated by two opposing monopoles (single charges) rather than dipoles, which fundamentally distinguishes it from conventional single-energy-parameter approaches, where cross-association energies are derived directly from pure-component self-association energies. To implement the model, H-bonding strengths based on the dimensionless Kamlet–Taft H-bonding donor and acceptor parameters are converted into physically meaningful interaction energies. The resulting framework enables the prediction of mixture thermodynamic properties and enthalpies of mixing from pure-component parameters alone.