Beyond DFT electronic band structures via dual-space orbital learning
Minhyuk Kang, Beom Seok Kang, Nikolai Argatoff, Miguel Nouman, Danish Khan, William A. Goddard, Anima Anandkumar
Abstract
Accurate electronic band structures are essential for predicting material properties, but high-fidelity calculations are computationally demanding. We introduce O-kRystal, a dual-space orbital-learning framework that uses a lower-cost Perdew-Burke-Ernzerhof (PBE) calculation as both an energy baseline and a source of structured orbital information. Combining PBE band energies with real- and reciprocal-space orbital matrices, O-kRystal predicts higher-level corrections for individual electronic states as a function of crystal momentum and spin. For states within 5 eV of the band-edge midpoint, it predicts Heyd-Scuseria-Ernzerhof (HSE06) band energies with a mean absolute error of $0.171 \pm 0.009$ eV across nearly 6,000 three-dimensional materials spanning insulating, metallic, magnetic, and nonmagnetic systems. On a separate benchmark of six strongly correlated materials, it reduces the corresponding PBE band-energy MAE by 68.7% and resolves orbital-dependent changes in the relative placement of transition-metal d and ligand p states. Despite training only at high-symmetry points, it maintains comparable accuracy at unseen points along band paths and reconstructs HSE06 densities of states from dense Brillouin-zone predictions. Finally, training O-kRystal on $G_0W_0$ quasiparticle energies for two-dimensional materials demonstrates its applicability across levels of theory and the potential of orbital learning for higher-fidelity, momentum-resolved electronic-structure prediction beyond density functional theory.