  The atomic cluster expansion is a general polynomial expansion of the atomic
energy in multi-atom basis functions. Here we implement the atomic cluster
expansion in the performant C++ code \verb+PACE+ that is suitable for use in
large scale atomistic simulations. We briefly review the atomic cluster
expansion and give detailed expressions for energies and forces as well as
efficient algorithms for their evaluation. We demonstrate that the atomic
cluster expansion as implemented in \verb+PACE+ shifts a previously established
Pareto front for machine learning interatomic potentials towards faster and
more accurate calculations. Moreover, general purpose parameterizations are
presented for copper and silicon and evaluated in detail. We show that the new
Cu and Si potentials significantly improve on the best available potentials for
highly accurate large-scale atomistic simulations.
