Convergence of Body-Orders in Linear Atomic Cluster Expansions

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.