Efficient parametrization of the atomic cluster expansion

The atomic cluster expansion (ACE) provides a general, local, and complete representation of atomic energies. Here we present an efficient framework for parametrization of ACE models for elements, alloys, and molecules. To this end, we first introduce general requirements for a physically meaningful description of the atomic interaction, in addition to the usual equivariance requirements. We then demonstrate that ACE can be converged systematically with respect to two fundamental characteristics---the number and complexity of basis functions and the choice of nonlinear representation. The construction of ACE parametrizations is illustrated for several representative examples with different bond chemistries, including metallic copper, covalent carbon, and several multicomponent molecular and alloy systems. We discuss the Pareto front of optimal force to energy matching contributions in the loss function, the influence of regularization, the importance of consistent and reliable reference data, and the necessity of unbiased validation. Our ACE parametrization strategy is implemented in the freely available software package pacemaker that enables largely automated and GPU accelerated training. The resulting ACE models are shown to be superior or comparable to the best currently available ML potentials and can be readily used in large-scale atomistic simulations.