Beyond Partitioning: Using Force Field Science to Evaluate Electrostatics Models

Accurate models for electrostatic and induction interactions are fundamental for computational molecular science, including drug discovery, studies of biomolecular systems and materials design. Given a precise model of the entire charge distributions, the electrostatic interaction between molecules can be calculated accurately using Coulomb's law. Here, we evaluate partitioning methods for deriving charges from electron density as well as the popular method of fitting point charges for use in force field calculations to the electrostatic potential (ESP). For the data set used in this work, which consists of charged amino-acid side chain analogs, inorganic ions and water, the best of these methods yield a root-mean-square deviation (RMSD) of 17 kJ/mol. By combining positive point charges (PC) with Gaussian or Slater distributed negative charges, ESP-fitted models predict electrostatic interactions approximately 30% better than just point charges (RMSD 12 kJ/mol), similar to the Minimal Basis Iterative Stockholder (MBIS-S) method [Verstraelen, T. . <i>J. Chem. Theory Comput.</i> 2016, 12, 3894-3912.]that employs a PC and a Slater charge as well. Since interaction energies are perhaps the most important deliverable of force field calculations, it may be advantageous to train models directly to reproduce energy components from symmetry-adapted perturbation theory (SAPT) calculations, rather than taking a detour through monomer-based charge models. To this end, we employ machine learning using the Alexandria Chemistry Toolkit [van der Spoel, D. . <i>Digit. Discovery</i> 2025, 4, 1925-1935.] to generate parameters for multiple physics-based models that reproduce electrostatic and, optionally, induction interaction energies from SAPT calculations of compound dimers. For a nonpolarizable model combining a PC and a Gaussian distributed charge on the core, the RMSD drops to 3 kJ/mol thanks to direct training on dimer energy components. The approach outlined in this work consists of applying force field science to make apples-to-apples comparisons between models and machine learning to design physics-based force fields that yield interaction energies consistent with SAPT calculations. Together, these tools will enable rapid progress in force field development and enhance the predictive power of molecular simulations for applications in many fields of science.