SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism
Abstract
Predicting molecular magnetic properties often requires costly electronic-structure calculations that account for spin-orbit coupling. Inspired by the spinor nature of the underlying electronic states, we introduce eSpinor, an SU(2)-equivariant graph neural network that propagates spinor features alongside the integer-rank tensors used in conventional equivariant models. We initialize spinors from eigenvectors of an approximate Hamiltonian that includes spin-orbit coupling. The network preserves their rotation laws and makes predictions independent of arbitrary eigenbasis choices. Comparisons with geometry-only and Hamiltonian-informed baselines assess the benefit of this architecture beyond supplying electronic information. On cobalt single-molecule magnet candidates, eSpinor improves magnetic anisotropy predictions, including for unseen ligands. It also improves excitation-energy predictions for dysprosium candidates with unseen ligands, extending the benefit to rotationally invariant scalar targets. For a dysprosium magnetic resonance imaging probe, it predicts real electron-spin correlations and low-field nuclear relaxation rates more accurately despite static crystal-field errors similar to the Hamiltonian-informed baseline. This dynamical advantage extends from water to methanol without retraining. These results support spinor message passing as a useful inductive bias for molecular magnetism in the tested systems and show why model selection should be guided by accuracy on the intended physical observables.
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BibTeX
@misc{sheng2026su2equivariant,
title = {{SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism}},
author = {Erh-Wei Sheng and Beom Seok Kang and Yuchao Lin and Danish Khan and Anima Anandkumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29111},
eprint = {2610.29111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29111},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism
AU - Erh-Wei Sheng
AU - Beom Seok Kang
AU - Yuchao Lin
AU - Danish Khan
AU - Anima Anandkumar
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.29111
UR - https://arxiv.org/abs/2610.29111
AB - Predicting molecular magnetic properties often requires costly electronic-structure calculations that account for spin-orbit coupling. Inspired by the spinor nature of the underlying electronic states, we introduce eSpinor, an SU(2)-equivariant graph neural network that propagates spinor features alongside the integer-rank tensors used in conventional equivariant models. We initialize spinors from eigenvectors of an approximate Hamiltonian that includes spin-orbit coupling. The network preserves their rotation laws and makes predictions independent of arbitrary eigenbasis choices. Comparisons with geometry-only and Hamiltonian-informed baselines assess the benefit of this architecture beyond supplying electronic information. On cobalt single-molecule magnet candidates, eSpinor improves magnetic anisotropy predictions, including for unseen ligands. It also improves excitation-energy predictions for dysprosium candidates with unseen ligands, extending the benefit to rotationally invariant scalar targets. For a dysprosium magnetic resonance imaging probe, it predicts real electron-spin correlations and low-field nuclear relaxation rates more accurately despite static crystal-field errors similar to the Hamiltonian-informed baseline. This dynamical advantage extends from water to methanol without retraining. These results support spinor message passing as a useful inductive bias for molecular magnetism in the tested systems and show why model selection should be guided by accuracy on the intended physical observables.
ER -