Learning electron densities in condensed-phase space

The electron density is a fundamental quantity for modelling and understanding physical phenomena in materials. Not only is it the central quantity of theories like density-functional theory, but it also allows the calculation of a wide range of observables that are either directly or indirectly connected to it, like total energies, dipole moments, the electrostatic potential, work functions, and others. In this work, we present a model that is able to learn and predict the electronic density of diverse materials, ranging from liquids to solid semiconductors and metals. This is achieved by extending the framework presented by Fabrizio et al (Chem. Sci., 10, 9424, 2019) to work with periodic boundary conditions and numeric atom-centred orbitals in the FHI-aims code, where a resolution of the identity is used in order to obtain coefficients for the expansion of the periodic density. This density is learned using a Gaussian process regression model with local symmetry-adapted representations of the atomic structure, making our method both data-efficient and highly transferable. We discuss the applicability of this model for large-scale periodic systems and its transferability across the periodic table.