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International Journal of Quantum Chemistry - Volume 115, Issue 16 - Machine Learning and Quantum Mechanics - Wiley Online Library

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The image represents the atomic neighbor density around a central atom (indicated by the white spot and the arrow), which is often used as the starting point for generating rotationally and permutationally invariant descriptors of the environment of an atom. In the Gaussian Approximation Potentials scheme reported by Albert P. Bartòk and Gábor Csányi on page 1051 (DOI:10.1002/qua.24927), This neighbor density is then expanded in spherical harmonics and a complete set of invariants are provided by the corresponding structure factors. The invariants can be used to construct a kernel, which measures the similarity between neighbor environments and forms the basis for all machine learning and regression methods.