具有物理信息的长程库仑修正的机器学习哈密顿量
Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians
AI总结：
本文提出一种结合E(3)等变消息传递与倒数空间Ewald求和的双通道架构，通过变分分解静电能推导出非正交原子轨道基下的长程哈密顿量矩阵元，验证了物理信息长程修正对极性晶体和异质结构的重要性。
摘要：
机器学习电子哈密顿量在密度泛函理论上实现了数量级的加速，但当前模型忽略了长程库仑相互作用，这些相互作用支配着极性晶体和异质结构的物理行为。我们通过变分分解静电能，推导出非正交原子轨道基下的闭合形式长程哈密顿量矩阵元，推导出从电子密度矩阵到有效原子电荷的变分一致映射。我们实现了这一框架在HamGNN-LR中，该框架结合E(3)等变消息传递与倒数空间Ewald求和。测试表明，基于物理的长程修正是必要的：纯数据驱动的注意力机制无法捕捉宏观静电势。在极性ZnO片、CdSe/ZnS异质结构和GaN/AlN超晶格上的测试显示，长程修正减少了两到三倍的误差，并在远超训练规模的系统中表现出稳健的可迁移性，消除了内置电场下短程模型中特有的阶梯状伪影。
英文摘要：
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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