Enhancing Electrostatic Embedding for ML/MM Free Energy Calculations

Hybrid ML/MM approaches that combine machine learning (ML) potentials with molecular mechanics (MM) potentials offer a promising balance between computational cost and accuracy. Most ML/MM simulations reported to date employ mechanical embedding schemes, and rely on Lennard-Jones and Coulomb potentials to model intermolecular interactions between the ML and MM regions. A promising approach to improving ML/MM schemes is to use electrostatic embedding, where polarization effects on the ML region by the MM region are explicitly incorporated. The electrostatic machine learning embedding (EMLE) method has been developed for this purpose. Here, we compute absolute hydration free energies for a set of small organic molecules to derive robust methodologies for training EMLE models using quantum mechanical data. We establish protocols for fine-tuning the static and induced components of electrostatic interactions and evaluate the accuracy limits of fitting these components to first-principles calculations. We also introduce an empirical adjustment to enhance agreement with experimental results, strengthening the competitiveness of ML/MM simulations relative to state-of-the-art methods. Overall, our findings provide valuable insights into the challenges and opportunities of electrostatic embedding ML/MM simulations, and offer strategies for achieving robust modeling of classes of drug-like molecules where the accuracy of conventional MM force fields fall short.