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This research introduces eSpinor, a novel graph neural network architecture that incorporates SU(2)-equivariant spinor features to address the computational costs of modeling spin-orbit coupling in molecular magnetism. By leveraging gauge-covariant message passing initialized from approximate Hamiltonian eigenvectors, the model achieves superior predictions for zero-field splitting and electron-spin correlations compared to standard integer-rank equivariant surrogates. The study highlights how specific physical symmetries can serve as effective inductive biases, reducing parameter counts while maintaining accuracy across unseen ligands and solvents without retraining.
SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism
arXiv:2610.29111v1 Announce Type: cross Abstract: Predicting molecular magnetism often requires electronic-structure calculations with spin-orbit coupling (SOC), which are costly to repeat across many molecules. The underlying electronic states can transform as spinors, yet equivariant surrogates typically use only integer-rank features. Inspired by the spinor nature of these electronic states, we develop eSpinor, an SU(2)-equivariant graph neural network that propagates spinor features. We initialize spinor features from eigenvectors of an approximate SOC Hamiltonian and use gauge-covariant message passing with a gauge-invariant readout to make predictions independent of the arbitrary eigenbasis choice. On cobalt single-molecule magnet candidates, eSpinor improves zero-field-splitting predictions relative to NequIP, including for unseen ligands. For a dysprosium magnetic resonance imaging probe, eSpinor improves real electron-spin correlations over a Hamiltonian-informed baseline despite similar static crystal-field errors and fewer parameters, while accurately predicting low-field nuclear relaxation in water and after transfer to methanol without retraining. Overall, these results demonstrate that SU(2)-equivariant spinor message passing is a useful inductive bias for molecular magnetism. We also find that similar static tensor errors can yield different dynamical errors, motivating model selection based on accuracy for the intended physical observables.
Abstract:Predicting molecular magnetism often requires electronic-structure calculations with spin-orbit coupling (SOC), which are costly to repeat across many molecules. The underlying electronic states can transform as spinors, yet equivariant surrogates typically use only integer-rank features. Inspired by the spinor nature of these electronic states, we develop eSpinor, an SU(2)-equivariant graph neural network that propagates spinor features. We initialize spinor features from eigenvectors of an approximate SOC Hamiltonian and use gauge-covariant message passing with a gauge-invariant readout to make predictions independent of the arbitrary eigenbasis choice. On cobalt single-molecule magnet candidates, eSpinor improves zero-field-splitting predictions relative to NequIP, including for unseen ligands. For a dysprosium magnetic resonance imaging probe, eSpinor improves real electron-spin correlations over a Hamiltonian-informed baseline despite similar static crystal-field errors and fewer parameters, while accurately predicting low-field nuclear relaxation in water and after transfer to methanol without retraining. Overall, these results demonstrate that SU(2)-equivariant spinor message passing is a useful inductive bias for molecular magnetism. We also find that similar static tensor errors can yield different dynamical errors, motivating model selection based on accuracy for the intended physical observables.
Chemical Physics (physics.chem-ph); Machine Learning (cs.LG)
arXiv:2610.29111 [physics.chem-ph]
(or arXiv:2610.29111v1 [physics.chem-ph] for this version)
https://doi.org/10.48550/arXiv.2610.29111 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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