Grassmannian Density Learning for Physically Consistent Kohn–Sham Electronic Structure Prediction
4 affiliations
- 1State Key Laboratory of Human-Machine Hybrid Augmented Intelligence
- 2Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University
- 3Zhongguancun Academy
- 4Zhongguancun Institute of Artificial Intelligence
Abstract
Deep-learning electronic-structure models show great potential to accelerate first-principles calculations, with broad implications for materials science, biology and drug discovery. Yet no consensus has emerged on which physical quantity should be modeled to represent electronic states. As two fundamental quantities that arise naturally in Kohn–Sham density functional theory, the Kohn–Sham Hamiltonian and electronic density have attracted the most attention. Hamiltonian prediction, however, devotes substantial modeling capacity to degrees of freedom that do not affect the occupied electronic subspace, whereas direct regression of density matrices or real-space densities removes this redundancy but cannot ensure that the prediction represents a physically admissible electronic state. Motivated by the fact that electronic states themselves reside on a constrained manifold, we observe that predicting coordinates directly on this manifold can simultaneously eliminate redundant degrees of freedom and preserve physical admissibility. Here we introduce GeoK, a framework that predicts compact occupied–virtual orbital-rotation generators as coordinates on the manifold of electronic states, thereby ensuring each prediction corresponds to a valid electronic state of the target molecular system. We further develop a neural-network architecture tailored to this geometric prediction task. Across in-distribution and out-of-distribution benchmarks, as well as downstream applications, GeoK consistently improves electronic-state prediction over the evaluated Hamiltonian and unconstrained densityregression baselines, while supporting robust deployment in downstream first-principles workflows. These results establish orbital-rotation generator prediction as a principled and reliable paradigm for intrinsic electronic-state modeling, opening a route towards more accurate and transferable deep-learning electronic-structure models.
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BibTeX
@misc{wang2026grassmannian,
title = {{Grassmannian Density Learning for Physically Consistent Kohn–Sham Electronic Structure Prediction}},
author = {Yifei Wang and Pei Liu and Yuheng He and Jingwen Fu and Yongqiang Ma and Miao Kang and Jianji Wang and He Zhang and Chang Liu and Nanning Zheng},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010691/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010691/v1},
note = {CC BY-NC-ND},
}
RIS
TY - UNPB
TI - Grassmannian Density Learning for Physically Consistent Kohn–Sham Electronic Structure Prediction
AU - Yifei Wang
AU - Pei Liu
AU - Yuheng He
AU - Jingwen Fu
AU - Yongqiang Ma
AU - Miao Kang
AU - Jianji Wang
AU - He Zhang
AU - Chang Liu
AU - Nanning Zheng
PY - 2026
DA - 2026/10/20
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010691/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010691/v1
AB - Deep-learning electronic-structure models show great potential to accelerate first-principles calculations, with broad implications for materials science, biology and drug discovery. Yet no consensus has emerged on which physical quantity should be modeled to represent electronic states. As two fundamental quantities that arise naturally in Kohn–Sham density functional theory, the Kohn–Sham Hamiltonian and electronic density have attracted the most attention. Hamiltonian prediction, however, devotes substantial modeling capacity to degrees of freedom that do not affect the occupied electronic subspace, whereas direct regression of density matrices or real-space densities removes this redundancy but cannot ensure that the prediction represents a physically admissible electronic state. Motivated by the fact that electronic states themselves reside on a constrained manifold, we observe that predicting coordinates directly on this manifold can simultaneously eliminate redundant degrees of freedom and preserve physical admissibility. Here we introduce GeoK, a framework that predicts compact occupied–virtual orbital-rotation generators as coordinates on the manifold of electronic states, thereby ensuring each prediction corresponds to a valid electronic state of the target molecular system. We further develop a neural-network architecture tailored to this geometric prediction task. Across in-distribution and out-of-distribution benchmarks, as well as downstream applications, GeoK consistently improves electronic-state prediction over the evaluated Hamiltonian and unconstrained densityregression baselines, while supporting robust deployment in downstream first-principles workflows. These results establish orbital-rotation generator prediction as a principled and reliable paradigm for intrinsic electronic-state modeling, opening a route towards more accurate and transferable deep-learning electronic-structure models.
ER -