Machine-Learned Electrostatic Potentials for Accurate Hydration Free Energy Calculations

Free energy calculations are widely used tools in computational chemistry, but their dependence on the assignment of partial charges during force field parametrization reduces their accuracy and reproducibility. In this work, we highlight the direct connection between the low accuracy of AM1-BCC charges on polar species and the poor accuracy of corresponding hydration free energy calculations. We then propose an XGBoost regressor trained on atomic descriptors to rapidly predict charges obtained with high-fidelity density functional theory calculations at PBE0-D3(BJ)/def2-TZVP level. The more accurate electrostatic description results in more reliable free energy calculations than those obtained with semiempirical AM1-BCC charges. Finally, we leverage this predictive model in combination with a 1 ns gas-phase molecular dynamics simulation to propose the Boltzmann Percentile method for assigning charges representative of the conformational ensemble of a molecule. Charges obtained with this method are robust to different input conformations, and the resulting free energies, calculated on a subset of the FreeSolv data set, show a root mean squared error of 1.69 kcal/mol against the 3.05 kcal/mol obtained with semiempirical charges as well as a significantly better ranking. We provide a trained model, easily integrable into traditional workflows, enabling free energy calculations at the same computational cost as AM1-BCC charges. These two aspects make it a realistic tool for enhancing already expensive free energy calculations, and more in general, molecular dynamics simulations in condensed phase.