Chemical Environments: Representations and Correlations

This lecture covers the representation of chemical environments using the Smooth Overlap of Atomic Positions (SOAP) kernel, which compares atomic densities based on relative positions of neighbors. It also discusses symmetrized density correlations and the use of tensor products to encode information. The lecture delves into the symmetries of atomic environments, the role of spherical harmonics, and the computation of invariant features. Additionally, it explores machine learning applications at the atomic scale, focusing on tensors and molecular polarizabilities.