Chemical basis sets and average-atom formalism for interatomic potentials

Interatomic potentials are central tools in the atomistic modeling of a wide variety of materials. The atomic cluster expansion (ACE) parameterizes such potentials from \textit{ab initio} data, conventionally encoding the chemical degrees of freedom with a unit vector representation that yields chemically stratified models. The consequences of the alternative chemical representations used in on-lattice configurational cluster expansions remain unexplored. Here we revisit the multicomponent ACE for an arbitrary chemical site basis, and we establish an exact analytical mapping between a fitted linear ACE and the average-atom potential that describes a perfectly random alloy. We then benchmark potentials built on the occupational, Chebyshev, and conventional ACE bases against solute binding and vacancy formation energies in Mg-Nd, and against the mixing enthalpies of the Mo-Nb and Cr-W solid solutions. When training data are scarce, the occupational basis offers the best control over targeted material properties, whereas the conventional and Chebyshev bases can fail qualitatively. In the large-data limit the three bases perform identically. The occupational basis likewise yields the most reliable average-atom description of disordered alloy thermodynamics. The chemical basis is therefore a design choice that governs data efficiency, and its explicit treatment opens a route to average-atom potentials for the thermodynamic, mechanical, and kinetic properties of concentrated and high-entropy alloys.

The datasets contain the crystal structure data used to test the different chemical representations of the ACE and the average-atom ACE. The data include: symmetry-distinct orderings on Mg-Nd, Mo-Nb, and Cr-W; several bulk Mg structures (hcp, bcc, stable and generalized stacking faults); several Nd point defect structures; and several symmetry-distinct vacancies in various Mg-Nd phases.