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.