Charge Transfer Interactions in Quantum Mechanics and in Classical Force Fields

Charge transfer (CT) is the delocalization of electron density from a donor to an acceptor. It is a crucial component of noncovalent interactions that significantly influences hydrogen bonding, ion solvation, and the structure of aqueous and biomolecular systems. Because direct experimental measurement of CT is challenging, theoretical methods rooted in quantum mechanics (QM) are essential. However, defining CT uniquely within QM and separating it from polarization remains a major methodological hurdle. This review surveys the theoretical methodologies developed to quantify CT, focusing primarily on water and ion-water dimers. We systematically examine various energy decomposition analysis (EDA) schemes, spanning variational methods and perturbation-theory approaches like symmetry-adapted perturbation theory (SAPT). We discuss the recommended levels of theory and basis sets for reliable CT estimates, giving particular attention to basis set dependence and convergence. Furthermore, we explore how these insights inform explicit CT energy expressions for classical molecular mechanics (MM) and molecular dynamics (MD) simulations, and evaluate efforts to incorporate CT into polarizable force fields and emerging machine learning models. Across representative systems, CT typically accounts for 5 to 20% of the total interaction energy, with larger contributions in strongly interacting ion-water complexes. Finally, we highlight the inherently nonadditive nature of CT, which is vital for accurately modeling complex condensed-phase phenomena, and outline the ongoing challenges in constructing transferable, physically grounded CT models for large-scale molecular simulations.