# Beyond DFT electronic band structures via dual-space orbital learning

arXiv: https://arxiv.org/abs/2610.19919 · HTML: https://mlsanity.com/paper/2610.19919/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 71 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory](https://mlsanity.com/paper/2608.23895/) (2026)
- [Graph Transformer Networks for Accurate Band Structure Prediction: An End-to-End Approach](https://mlsanity.com/paper/2411.16483/) (2024)

## Abstract (arXiv)

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 ± 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 G0W0 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.