Models that combine quantum mechanics (QM) with machine learning (ML) benefit from accuracy and transferability of QM as well as from the computational efficiency of ML. Such QM/ML models have mostly been used either for prediction of molecular properties across systems, e.g., atomization energies, or, for investigation of single systems, e.g., interpolation of potential energy surfaces. We present a model to predict physical observables of atoms in molecules, across chemical compound space, scaling linearly in system size. For proof of principle, we focus on 1H and 13C nuclear magnetic resonance chemical shifts, 1s core ionization energies, and forces on atoms, calculated using density functional theory. Our model uses local, atom-centered coordinate systems to represent an atom in its environment, where non-scalar properties like forces are represented using the same coordinate system. Kernel ridge regression is used, with hyperparameters chosen based on physical considerations. We benchmark our approach on quantum chemistry results for 9k small organic molecules. We demonstrate linear scaling on a set of doped linear polyethylene molecules of increasing size.
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