An Orbital-based Geometric Deep Learning Framework for Periodic Materials

Orbital-based deep learning has achieved notable success in molecular systems by integrating quantum mechanical information into geometric deep learning. In this study, we introduce OrbNet-Crystal, which extends the OrbNet-Equi framework from molecular systems to periodic crystal graphs. Our approach derives orbital features from lower-level semi-empirical quantum mechanical calculations, converts reciprocal-space orbital features into real-space orbital features via inverse Fourier transforms, and embeds them into SE(3)-equivariant graph neural networks for periodic materials. We evaluate OrbNet-Crystal on the Computational 2D Materials Database for band gap prediction at multiple electronic-structure levels of theory. Using semi-empirical orbital features, OrbNet-Crystal achieves strong accuracy across all targets, both for direct prediction and delta-learning across multiple levels of theory. Furthermore, we show that transfer learning substantially improves performance for data-scarce, higher-level theory targets. Overall, this work establishes the first orbital-based deep learning paradigm for crystalline systems and demonstrates the potential of orbital features for transferable, multi-fidelity learning in solid-state materials discovery.