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Many-body descriptors are widely used to represent atomic environments in the construction of machine learned interatomic potentials and more broadly for fitting, classification and embedding tasks on atomic structures. It was generally believed that 3-body descriptors uniquely specify the environment of an atom, up to a rotation and permutation of like atoms. We produce several counterexamples to this belief, with the consequence that any classifier, regression or embedding model for atom-centred properties that uses 3 (or 4)-body features will incorrectly give identical results for different configurations. Writing global properties (such as total energies) as a sum of many atom-centred contributions mitigates, but does not eliminate, the impact of this fundamental deficiency -- explaining the success of current machine-learning force fields. We anticipate the issues that will arise as the desired accuracy increases, and suggest potential solutions.
Quantum-chemical processes in liquid environments impact broad areas of science, from molecular biology to geology to electrochemistry. While density-functional theory (DFT) has enabled efficient quantum-mechanical calculations which profoundly impac
Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict the propert
Rechargeable lithium ion batteries are an attractive alternative power source for a wide variety of applications. To optimize their performances, a complete description of the solvation properties of the ion in the electrolyte is crucial. A comprehen
A major goal of energy research is to use visible light to cleave water directly, without an applied voltage, into hydrogen and oxygen. Since the initial reports of the ultraviolet (UV) activity of TiO2 and SrTiO3 in the 1970s, researchers have pursu
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process re