mlsanityData to 14 Oct 2026

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames

arXiv 2506.09398 ↗First posted 11 Jun 2025cs.LG physics.comp-phcited by 6

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Abstract (arXiv)

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set of new efficient and powerful SO(2)-equivariant operations and performing all off-diagonal feature updates and message passing within SO(2) local frames, thereby eliminating the need of SO(3) tensor products. Moreover, a continuous SO(2) tensor product is performed within the SO(2) local frame at each node to fuse node features, mimicking the symmetric contraction operation. Extensive experiments on the large QH9 and MD17 datasets demonstrate that our model achieves superior performance across a wide range of molecular structures and trajectories, highlighting its strong generalization capability. The proposed SO(2) operations on SO(2) local frames offer a promising direction for scalable and symmetry-aware learning of electronic structures. Our code will be released as part of the AIRS library https://github.com/divelab/AIRS.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 38 of its 61 references that are in the map. First posted on arXiv 11 Jun 2025.

Builds on

38 of 61 references.

References · 38

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26 more
  1. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  2. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physicscited by 11
  2. 2025Learning from the electronic structure of molecules across the periodic tablecited by 7
  3. 2026Transferable SCF-Acceleration through Solver-Aligned Initialization Learningcited by 3
  4. 2025Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materialscited by 2
  5. 2026Edge Cluster Expansion with Radial Rotary Attention for Interatomic Potentialscited by 2
  6. 2026Equivariant Flow Matching for Electron Density Predictioncited by 0