Title: Streamlined Prediction of SO(3)-Equivariant Hamiltonian Matrices Using SO(2) Local Frames

Abstract:

Accelerating electronic structure calculations through the prediction of Hamiltonian matrices is a critical objective in the fields of physics, chemistry, and materials science. Building on the intrinsic connection between the off-diagonal blocks of the Hamiltonian matrix and SO(2) local frames, we introduce QHNetV2, a novel and highly efficient neural network architecture. This model delivers global SO(3) equivariance while bypassing the computationally expensive SO(3) Clebsch-Gordan tensor products. We accomplish this by implementing a suite of new, robust SO(2)-equivariant operations and conducting all off-diagonal feature updates and message passing within SO(2) local frames, which effectively removes the requirement for SO(3) tensor products. Additionally, we employ a continuous SO(2) tensor product within each node’s local frame to fuse node features, a process that emulates symmetric contraction operations. Our extensive evaluations on the large-scale QH9 and MD17 datasets reveal that the proposed model delivers exceptional performance across diverse molecular structures and trajectories, underscoring its robust generalization capabilities. The introduction of SO(2) operations on SO(2) local frames presents a promising pathway toward scalable, symmetry-aware learning of electronic structures. The source code will be made available as part of the AIRS library: https://github.com/divelab/AIRS.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC