SU(2)-Equivariant Spinor Message Passing for Molecular Magnetism

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.