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 systems. We build ACE potentials with descriptor sets truncated at body-orders $K=2,3,4$ trained on pure dimers, or on large datasets of different diversities but without any dimers. Potentials trained on a more diverse dataset fare better in validation and result in a nontrivial dimer curve, but still very far from the theoretical two-body interaction calculated by DFT. Moreover, dimer curves between descriptor sets clipped at different $K$ do not seem to converge to a universal function for a given dataset. We conclude that machine learning potentials employing atomic cluster expansions optimize losses at low $K$ but fail to generalize and converge properties described by two-body interactions.