Evaluating the London Dispersion Coefficients of Protein Force Fields Using the Exchange-Hole Dipole Moment Model

London dispersion is one of the fundamental interactions involved in protein folding and dynamics. The popular CHARMM36, Amber ff14sb, and OPLS-AA force fields represent these interactions through the C₆/ r⁶ term of the Lennard-Jones potential, where the C₆ parameters are assigned empirically. Here, dispersion coefficients of these three force fields are shown to be roughly 50% larger than values calculated using the quantum mechanically derived exchange-hole dipole moment (XDM) model. The CHARMM36 and Amber OL15 force fields for nucleic acids also exhibit this trend. The hydration energies of the side-chain models were calculated using REMD-TI for the CHARMM36, Amber ff14sb, and OPLS-AA force fields. These force fields predict side-chain hydration energies that are in generally good agreement with the experimental values, which suggests that the total strength of aqueous dispersion interactions is correct, despite C₆ coefficients that are considerably larger than XDM predicts. An analytical expression for the dispersion hydration energy using XDM coefficients shows that higher-order dispersion terms (i.e., C₈ and C₁₀) account for roughly 37.5% of the hydration energy of methane. This suggests that the C₆ dispersion coefficients used in contemporary force fields are elevated to account for the neglected higher-order terms.