给机器学习哈密顿量添加物理驱动的长程库仑修正，提升极性材料模拟精度。
Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians
- 基于变分分解推导原子轨道基下长程哈密顿量矩阵元
- 在锌氧、硒镉/锌硫等体系上误差降低2-3倍，消除阶梯状伪影
- 适合需要精确电场响应的异质结与超晶格研究者
机器学习电子哈密顿量相比密度泛函理论实现数量级加速，但现有模型忽略决定极性晶体和异质结构物理特性的长程库仑相互作用。本文通过静电能的变分分解，在非正交原子轨道基下推导出长程哈密顿量矩阵元的闭式表达，建立电子密度矩阵到有效原子电荷的变分一致映射。将该框架集成于HamGNN-LR模型中，采用双通道结构结合E(3)等变消息传递与倒空间Ewald求和。基准测试表明，基于物理的长程修正至关重要：纯数据驱动的注意力机制无法捕捉宏观静电势。在极性ZnO薄膜、CdSe/ZnS异质结和GaN/AlN超晶格上的测试显示，误差降低2至3倍，对远超训练尺寸的系统仍具强泛化能力，有效消除内置电场下短程模型常见的阶梯状伪影。
原文摘要 · Abstract (English)
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.
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