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.
@article{arxiv.2406.10915,
title = {Self-consistent Coulomb interactions for machine learning interatomic potentials},
author = {Jack Thomas and William J. Baldwin and Gábor Csányi and Christoph Ortner},
journal= {arXiv preprint arXiv:2406.10915},
year = {2024}
}