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 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 shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

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Organic-walled microfossils provide the best insights into the composition and evolution of the biosphere through the first 80 percent of Earth history. The mechanism of microfossil preservation affects the quality of biological information retained and informs understanding of early Earth palaeo-environments. We here show that 1 billion-year-old microfossils from the non-marine Torridon Group are remarkably preserved by a combination of clay minerals and phosphate, with clay minerals providing the highest fidelity of preservation. Fe-rich clay mostly occurs in narrow zones in contact with cellular material and is interpreted as an early microbially-mediated phase enclosing and replacing the most labile biological material. K-rich clay occurs within and exterior to cell envelopes, forming where the supply of Fe had been exhausted. Clay minerals inter-finger with calcium phosphate that co-precipitated with the clays in the sub-oxic zone of the lake sediments. This type of preservation was favoured in sulfate-poor environments where Fe-silicate precipitation could outcompete Fe-sulfide formation. This work shows that clay minerals can provide an exceptionally high fidelity of microfossil preservation and extends the known geological range of this fossilization style by almost 500 Ma. It also suggests that the best-preserved microfossils of this time may be found in low-sulfate environments.

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The structural characterization of local atomic environments is essential in our understanding and design of materials with customized properties. Atomistic simulations have become a powerful tool to provide insight into the structural patterns and mechanisms that signify transformations between different crystalline and liquid phases, or the formation and dynamics of point and extended defects. The development and availability of methods that provide a reliable and accurate structural analysis of atomistic simulation data constitute an indispensable task that continues to be an active field of research in materials science.