Paying attention to long-range electron correlation: a size-independent deep-learning approach to predicting molecules' electronic energies from one- and two-electron integrals

We propose a descriptor for molecular electronic structure that is based solely on the one- and two-electron integrals but is translationally, rotationally, and unitarily invariant. Then, directly exploiting size consistency, we train and fine tune a neural network to predict the energies of strongly-correlated systems, specifically hydrogen clusters. We use an attention mechanism to formulate a size-independent approach that uses and preserves size-consistency. Therefore, training on few-electron systems can guide predictions for systems with more electrons. Our results are more accurate than alternative geometry-based machine-learning models.