# Physics-Informed Long-Range Coulomb Correction for Machine-learning Hamiltonians

arXiv: https://arxiv.org/abs/2603.20007 · HTML: https://mlsanity.com/paper/2603.20007/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)
- [Euclidean Fast Attention -- Machine Learning Global Atomic Representations at Linear Cost](https://mlsanity.com/paper/2412.08541/) (2024)
- [Learning local equivariant representations for quantum operators](https://mlsanity.com/paper/2407.06053/) (2024)

## Abstract (arXiv)

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.