Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918400057409536 |
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| author | Zhong, Yang Li, Xiwen Gong, Xingao Xiang, Hongjun |
| author_facet | Zhong, Yang Li, Xiwen Gong, Xingao Xiang, Hongjun |
| contents | Machine-learning electronic Hamiltonians achieve orders-of-magnitude speedups over density-functional theory, yet current models omit long-range Coulomb interactions that govern physics in polar crystals and heterostructures. We derive closed-form long-range Hamiltonian matrix elements in a nonorthogonal atomic-orbital basis through variational decomposition of the electrostatic energy, deriving a variationally consistent mapping from the electron density matrix to effective atomic charges. We implement this framework in HamGNN-LR, a dual-channel architecture combining E(3)-equivariant message passing with reciprocal-space Ewald summation. Benchmarks demonstrate that physics-based long-range corrections are essential: purely data-driven attention mechanisms fail to capture macroscopic electrostatic potentials. Benchmarks on polar ZnO slabs, CdSe/ZnS heterostructures, and GaN/AlN superlattices show two- to threefold error reductions and robust transferability to systems far beyond training sizes, eliminating the characteristic staircase artifacts that plague short-range models in the presence of built-in electric fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20007 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians Zhong, Yang Li, Xiwen Gong, Xingao Xiang, Hongjun Computational Physics Materials Science Artificial Intelligence Machine-learning electronic Hamiltonians achieve orders-of-magnitude speedups over density-functional theory, yet current models omit long-range Coulomb interactions that govern physics in polar crystals and heterostructures. We derive closed-form long-range Hamiltonian matrix elements in a nonorthogonal atomic-orbital basis through variational decomposition of the electrostatic energy, deriving a variationally consistent mapping from the electron density matrix to effective atomic charges. We implement this framework in HamGNN-LR, a dual-channel architecture combining E(3)-equivariant message passing with reciprocal-space Ewald summation. Benchmarks demonstrate that physics-based long-range corrections are essential: purely data-driven attention mechanisms fail to capture macroscopic electrostatic potentials. Benchmarks on polar ZnO slabs, CdSe/ZnS heterostructures, and GaN/AlN superlattices show two- to threefold error reductions and robust transferability to systems far beyond training sizes, eliminating the characteristic staircase artifacts that plague short-range models in the presence of built-in electric fields. |
| title | Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians |
| topic | Computational Physics Materials Science Artificial Intelligence |
| url | https://arxiv.org/abs/2603.20007 |