Self-consistent Coulomb interactions for machine learning interatomic potentials

TL;DR

This paper develops a mathematical framework for incorporating long-range electrostatic effects into machine learning interatomic potentials, maintaining locality and transferability, with a practical example on water clusters.

Contribution

It introduces a general framework for including long-range Coulomb interactions in ML potentials while preserving locality and transferability.

Findings

Provides a theoretical basis for charge equilibration in ML potentials.

Explains the success of existing models with electrostatic effects.

Demonstrates a practical fitting scheme for water clusters.

Abstract

A ubiquitous approach to obtain transferable machine learning-based models of potential energy surfaces for atomistic systems is to decompose the total energy into a sum of local atom-centred contributions. However, in many systems non-negligible long-range electrostatic effects must be taken into account as well. We introduce a general mathematical framework to study how such long-range effects can be included in a way that (i) allows charge equilibration and (ii) retains the locality of the learnable atom-centred contributions to ensure transferability. Our results give partial explanations for the success of existing machine learned potentials that include equilibriation and provide perspectives how to design such schemes in a systematic way. To complement the rigorous theoretical results, we describe a practical scheme for fitting the energy and electron density of water clusters.