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

Equivariant graph neural networks for ab initio atomistic prediction use integer-rank irreducible representations of SO(3). Magnetic anisotropy sits outside that framework. It determines whether a complex can act as a single-molecule magnet or a qubit, arises from spin-orbit states with half-integer angular momentum, and needs days of multireference calculation to resolve. Existing models contract these states to integer rank before learning, which discards the states the anisotropy is a property of and leaves it to be relearned from geometry. Our model, eSpinor, propagates them as half-integer irreps of SU(2) instead. Doing so exposes a gauge freedom, since geometry fixes each Kramers pair only up to a unitary rotation no continuous convention removes. We therefore require every operation to commute with that rotation rather than fix a basis, which admits exactly three couplings and gives SU(2)-equivariant, gauge-covariant features and gauge-invariant predictions. By propagating the spinor we cut the zero-field-splitting error on transition-metal complexes by 29%, and on a lanthanide trajectory we match an SO(3) network trained on twice as many labels. At matched size, a model that instead contracts the same states to integer rank cuts that error by only 8%, so the gain rests on the SU(2) inductive bias rather than the added information.