# Learning from the electronic structure of molecules across the periodic table

arXiv: https://arxiv.org/abs/2510.00224 · HTML: https://mlsanity.com/paper/2510.00224/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 54 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNs](https://mlsanity.com/paper/2302.03655/) (2023)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [Learning Smooth and Expressive Interatomic Potentials for Physical Property Prediction](https://mlsanity.com/paper/2502.12147/) (2025)
- [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)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [Latent Ewald summation for machine learning of long-range interactions](https://mlsanity.com/paper/2408.15165/) (2024)
- [The dark side of the forces: assessing non-conservative force models for atomistic machine learning](https://mlsanity.com/paper/2412.11569/) (2024)
- [Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems](https://mlsanity.com/paper/2502.19227/) (2025)
- [An ab initio foundation model of wavefunctions that accurately describes chemical bond breaking](https://mlsanity.com/paper/2506.19960/) (2025)
- [Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity](https://mlsanity.com/paper/2502.01171/) (2025)
- [High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction](https://mlsanity.com/paper/2505.18817/) (2025)
- [Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames](https://mlsanity.com/paper/2506.09398/) (2025)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [Energy & Force Regression on DFT Trajectories is Not Enough for Universal Machine Learning Interatomic Potentials](https://mlsanity.com/paper/2502.03660/) (2025)

## Built on by (most cited first, 7 of 7)

- [Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory](https://mlsanity.com/paper/2608.23895/) (2026)
- [Enhancing molecular dynamics with equivariant machine-learned densities](https://mlsanity.com/paper/2604.24563/) (2026)
- [Multitask learning with semiempirical orbital charges enables sample-efficient MLIPs](https://mlsanity.com/paper/2605.24073/) (2026)
- [MALOQ: Massively Accelerated Learning of Operators for Quantum Transport](https://mlsanity.com/paper/2606.28911/) (2026)
- [Coupled-cluster molecular properties across the main group that extrapolate beyond training size](https://mlsanity.com/paper/2608.18346/) (2026)
- [Complete Neural Electronic Initialization Accelerates Materials DFT](https://mlsanity.com/paper/2609.21759/) (2026)
- [Physics-Aligned Electronic Ground-State Learning Improves Generalization](https://mlsanity.com/paper/2610.10298/) (2026)

## Abstract (arXiv)

Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of accompanying data in the Hamiltonian matrix H behind these datasets has so far gone unused for this purpose. Here, we provide a recipe for integrating the orbital interaction data within H towards training pipelines for atomic-level properties. We first introduce HELM ("Hamiltonian-trained Electronic-structure Learning for Molecules"), a state-of-the-art Hamiltonian prediction model which bridges the gap between Hamiltonian prediction and universal MLIPs by scaling to H of structures with 100+ atoms, high elemental diversity, and large basis sets including diffuse functions. To accompany HELM, we release a curated Hamiltonian matrix dataset, 'OMol_CSH_58k', with unprecedented elemental diversity (58 elements), molecular size (up to 150 atoms), and basis set (def2-TZVPD). Finally, we introduce 'Hamiltonian pretraining' as a method to extract meaningful descriptors of atomic environments even from a limited number atomic structures, and repurpose this shared embedding space to improve performance on energy-prediction in low-data regimes. Our results highlight the use of electronic interactions as a rich and transferable data source for representing chemical space.