Cartesian atomic cluster expansion for machine learning interatomic potentials

TL;DR

The paper introduces CACE, a Cartesian-coordinate-based atomic density expansion for machine learning interatomic potentials, offering a complete, efficient, and rotationally invariant feature set that improves accuracy and generalizability.

Contribution

It proposes a novel Cartesian atomic cluster expansion framework that reduces redundancy and computational overhead compared to traditional spherical harmonic methods.

Findings

CACE achieves high accuracy across diverse systems.

It maintains stability and generalizability in complex materials.

The approach reduces computational complexity.

Abstract

Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks typically use spherical harmonics as angular basis functions, and then use Clebsch-Gordan contraction to maintain rotational symmetry, which may introduce redundancies in representations and computational overhead. We propose an alternative: a Cartesian-coordinates-based atomic density expansion. This approach provides a complete set of polynormially indepedent features of atomic environments while maintaining interaction body orders. Additionally, we integrate low-dimensional embeddings of various chemical elements and inter-atomic message passing. The resulting potential, named Cartesian Atomic Cluster Expansion (CACE), exhibits good accuracy, stability, and generalizability. We validate its performance in diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys.