Density-Based Long-Range Electrostatic Descriptors for Machine Learning Force Fields

TL;DR

This paper introduces a long-range electrostatic descriptor for machine learning force fields that preserves symmetry and improves accuracy for ionic materials, bridging the gap between short-range descriptors and long-range electrostatics.

Contribution

The paper proposes a novel atomic density-based descriptor capable of incorporating long-range electrostatic interactions into ML force fields, compatible with existing schemes.

Findings

Improves force prediction accuracy for liquid NaCl by 2-3 times over short-range descriptors.

Achieves errors below 0.1% in electrostatic toy models.

Less effective for solid zirconia compared to message-passing networks.

Abstract

This study presents a long-range descriptor for machine learning force fields (MLFFs) that maintains translational and rotational symmetry, similar to short-range descriptors while being able to incorporate long-range electrostatic interactions. The proposed descriptor is based on an atomic density representation and is structurally similar to classical short-range atom-centered descriptors, making it straightforward to integrate into machine learning schemes. The effectiveness of our model is demonstrated through comparative analysis with the long-distance equivariant (LODE) descriptor. In a toy model with purely electrostatic interactions, our model achieves errors below 0.1%, worse than LODE but still very good. For real materials, we perform tests for liquid NaCl, rock salt NaCl, and solid zirconia. For NaCl, the present descriptors improve on short-range density descriptors, reducing errors by a factor of two to three and coming close to message-passing networks. However, for solid zirconia, no improvements are observed with the present approach, while message-passing networks reduce the error by almost a factor of two to three. Possible shortcomings of the present model are briefly discussed.