Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network

Based on an analysis of the short-range chemical environment of each atom in a system, standard machine-learning-based approaches to the construction of interatomic potentials aim at determining directly the central quantity, which is the total energy. This prevents, for instance, an accurate description of the energetics of systems in which long-range charge transfer or ionization is important. We propose therefore not to target directly with machine-learning methods the total energy but an intermediate physical quantity, namely, the charge density, which then in turn allows us to determine the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chemical accuracy, i.e., errors of less than a millihartree per atom compared to the reference density functional results for a huge data set of configurations with large structural variety. The introduction of physically motivated quantities which are determined by the short-range atomic environment via a neural network also leads to an increased stability of the machine-learning process and transferability of the potential.