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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.22669 |
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| _version_ | 1866913109299429376 |
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| author | Wu, Jiankun Fan, Jinming Qian, Chao Zhou, Shaodong |
| author_facet | Wu, Jiankun Fan, Jinming Qian, Chao Zhou, Shaodong |
| contents | Ab initio calculations are fundamentally bottlenecked for large systems by the steep computational scaling of solving self-consistent field (SCF) equations. While machine learning offers potential accelerations, existing methods often compromise physical rigor or rely on basis-dependent, non-transferable representations. Here, we introduce DeepHartree, a Poisson-coupled neural field that accelerates linear combination of atomic orbitals (LCAO) density functional theory (DFT). By coupling an E(3)-equivariant neural network with the Poisson equation through automatic differentiation and mitigating nuclear singularities via delta-learning, DeepHartree simultaneously predicts mutually consistent real-space electron densities and Hartree potentials. This resolves the Coulomb bottleneck by substituting $\mathcal{O}(N^4)$ analytical integrals with GPU-accelerated, near-linear $\mathcal{O}(N)$ numerical inference. Trained solely on small molecules, DeepHartree enables scalable density functional theory through a two-level transferability: for SCF convergence acceleration, it achieves robust zero-shot transferability across diverse basis sets, functionals, and systems up to 168 atoms; for predicting other density-related physical quantities, it retains zero-shot capability on small molecules while enabling precise predictions for larger systems via efficient few-shot fine-tuning. Our model accelerates standard SCF protocols by reducing iterations by up to 40.9% via high-fidelity initial density matrices, and its rigorous long-range asymptotics provide a zero-cost physical uncertainty metric prior to grid evaluation. By grounding deep learning in Poisson-coupled neural fields, DeepHartree accelerates demanding tasks -- such as near-coupled-cluster dynamic infrared simulations -- by orders of magnitude, establishing a scalable paradigm for density functional theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | DeepHartree: A Poisson-Coupled Neural Field for Scalable Density Functional Theory Wu, Jiankun Fan, Jinming Qian, Chao Zhou, Shaodong Chemical Physics Ab initio calculations are fundamentally bottlenecked for large systems by the steep computational scaling of solving self-consistent field (SCF) equations. While machine learning offers potential accelerations, existing methods often compromise physical rigor or rely on basis-dependent, non-transferable representations. Here, we introduce DeepHartree, a Poisson-coupled neural field that accelerates linear combination of atomic orbitals (LCAO) density functional theory (DFT). By coupling an E(3)-equivariant neural network with the Poisson equation through automatic differentiation and mitigating nuclear singularities via delta-learning, DeepHartree simultaneously predicts mutually consistent real-space electron densities and Hartree potentials. This resolves the Coulomb bottleneck by substituting $\mathcal{O}(N^4)$ analytical integrals with GPU-accelerated, near-linear $\mathcal{O}(N)$ numerical inference. Trained solely on small molecules, DeepHartree enables scalable density functional theory through a two-level transferability: for SCF convergence acceleration, it achieves robust zero-shot transferability across diverse basis sets, functionals, and systems up to 168 atoms; for predicting other density-related physical quantities, it retains zero-shot capability on small molecules while enabling precise predictions for larger systems via efficient few-shot fine-tuning. Our model accelerates standard SCF protocols by reducing iterations by up to 40.9% via high-fidelity initial density matrices, and its rigorous long-range asymptotics provide a zero-cost physical uncertainty metric prior to grid evaluation. By grounding deep learning in Poisson-coupled neural fields, DeepHartree accelerates demanding tasks -- such as near-coupled-cluster dynamic infrared simulations -- by orders of magnitude, establishing a scalable paradigm for density functional theory. |
| title | DeepHartree: A Poisson-Coupled Neural Field for Scalable Density Functional Theory |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2604.22669 |