Incorporating long-range electrostatics in neural network potentials via variational charge equilibration from shortsighted ingredients

We present a new approach to construct machine-learned interatomic potentials including long-range electrostatic interactions based on a charge equilibration scheme. This new approach can accurately describe the potential energy surface of systems with ionic and covalent interactions as well as systems with multiple charge states. Moreover, it can either be regressed against known atomic charge decompositions or trained without charge targets, without compromising the accuracy of energy and forces. We benchmark our approach against other state-of-the-art models and prove it to have equivalent performances on a set of simple reference systems while being less computationally expensive. Finally, we demonstrate the accuracy of our approach on complex systems: solid and liquid state sodium chloride. We attain accuracy in energy and forces better than the model based on local descriptors and show that our electrostatic approach can capture the density functional theory tail of the potential energy surface of the isolated Na-Cl dimer, which the local descriptor-based model fails to describe.