A practical approach to Hohenberg-Kohn maps based on many-body correlations: learning the electronic density

Abstract: High throughput screening of materials for technologically relevant areas, like identification of better catalysts, electronic materials, ceramics for high temperature applications and drug discovery, is an emerging topic of research. To facilitate this, density functional theory based (DFT) calculations are routinely used to calculate the electronic structure of a wide variety of materials. However, DFT calculations are expensive and the computing cost scales as the cube of the number of electrons present in the system. Thus, it is desirable to generate surrogate models that can mitigate these issues. To this end, we present a two step procedure to predict total energies of large three-dimensional systems (with periodic boundary conditions) with chemical accuracy (1kcal/mol) per atom using a small data set, meaning that such models can be trained on-the-fly. Our procedure is based on the idea of the Hohenberg-Kohn map proposed by Brockherde et al. (Nat. Commun, 8, 872 (2017)) and involves two training models: one, to predict the ground state charge density, $\rho(r)$, directly from the atomic structure, and another to predict the total energy from $\rho(r)$. To predict $\rho(r)$, we use many-body correlation descriptors to accurately describe the neighborhood of a grid point and to predict the total energy we use amplitudes of these many-body correlation descriptors. Utilizing the amplitudes of the many-body descriptors allows for uniquely identifying a structure while accounting for constraints, such as translational invariance; additionally, such a formulation is independent of the charge density grid.