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Considerations of symmetry underpin the mathematical representations of the atomic configurations that are used by machine learning models to predict properties of various molecular structures. Though these models generally rely on a description of atom-centered environments, many of the quantities that are relevant for quantum mechanical calculations – notably the single-particle Hamiltonian Ĥ matrix when written in an atomic-orbital basis – aren’t associated with a single center, but rather with two or more atoms in the structure. In the paper “Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties,” recently published in the Journal of Chemical Physics, NCCR MARVEL researchers discuss a family of structural descriptors that generalize atom-centered density correlation features to the N-centers case and show how it can be applied to efficiently learn the matrix elements of Ĥ. These N-centers features are fully equivariant in terms of both translations and rotations as well as in terms of permutations of the indices associated with the atoms and are therefore suitable for use in constructing symmetry-adapted machine-learning models of new classes of properties of molecules and materials.