Convergence of Body-Orders in Linear Atomic Cluster Expansions

TL;DR

This paper investigates how linear atomic cluster expansion (ACE) potentials converge with respect to basis functions for Carbon and Silicon, highlighting the importance of tailored datasets and basis sets for stability and interpretability.

Contribution

It demonstrates the convergence behavior of ACE potentials with different basis truncations and emphasizes the need for tailored datasets and basis sets for accurate, stable, and interpretable potentials.

Findings

ACE potentials with diverse datasets struggle to reproduce dimer curves.

Removing self-interactions from ACE bases does not improve generalization.

Properly tailored datasets and bases show signs of convergence and stability.

Abstract

We study the convergence of a linear atomic cluster expansion (ACE) potential with respect to its basis functions, in terms of the effective two-body interactions of elemental Carbon and Silicon systems. We build ACE potentials with descriptor sets truncated at body-orders $K=2$ to $K=5$ trained on a diverse Carbon dataset and on Silicon dimers to pentamers. The potentials trained on diverse structures with standard ACE bases are not able to recover the correct dimer curves much less produce stable curves or solutions. While employing ACE bases removed of self-interactions still does not generalize to the DFT-expected results, properly tailored datasets and basis sets are able to show signs of convergence and stability in the curves and expansions, suggesting a method to build potentials with interpretable bases with respect to the cluster expansion.