# Beyond Partitioning: Using Force Field Science to Evaluate Electrostatics Models

## TL;DR

The paper explores better ways to model electrostatic interactions in molecular simulations using advanced charge modeling and machine learning.

## Contribution

A novel approach combining machine learning and physics-based models to directly reproduce electrostatic and induction energies from SAPT calculations.

## Key findings

- ESP-fitted models with Gaussian or Slater charges improve electrostatic predictions by 30% over point charges.
- Direct training on SAPT energy components reduces RMSD to 3 kJ/mol for nonpolarizable models.
- The approach enables apples-to-apples comparisons between electrostatic models using force field science.

## Abstract

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
[

VerstraelenT.,

. J. Chem. Theory Comput.
2016, 12, 3894–3912.]27385073
10.1021/acs.jctc.6b00456that
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 SpoelD.,

. Digit. Discovery
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.