The Inference Report

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.

Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities. We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies. Penalizing it requires no self-consistent-field solution during training. Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.

We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.

Although machine learning potentials (MLPs) generalize across configurational and chemical compound spaces, their accuracy is commonly believed to be limited by their training methods, with improvements beyond this limit achieved so far only by refitting to experimental observables. In this Perspective, we argue that MLPs can also be made more accurate than their training methods non-empirically by generalizing across a third space, that of quantum-chemical methods. We propose routes to method-transferable MLPs that predict at unseen methods, with working implementations in both density-functional and wavefunction-based theories showing that they can be more accurate than any of their training methods. Aiming beyond the accuracy of the training methods could also make universal MLPs more accurate than single-method models, even when the method-transferable MLPs remain less accurate than those QM methods. Method-transferable MLPs will shape the construction of training datasets and the evaluation of models, pushing the accuracy limits of chemical simulations.

Machine learning methods are increasingly used to predict chemical properties directly from the molecular structure to bypass the often prohibitive cost of quantum mechanical calculations. Recent work has shown that including the ground-state electron density as input to the machine learning model can improve accuracy in this setting. This work employs the recent surrogate functional framework originally developed for orbital-free density functional theory and extends it to predicting molecular properties. We show that passing the ground-state density as input to the model, while simultaneously enforcing it to be the minimum of the surrogate functional, surpasses state-of-the-art performance for six out of seven extensive properties of the QM9 dataset. Additionally, the approach shows improved generalization to larger molecules taken from the QM40 dataset. On all extensive properties of both datasets, our approach outperforms models that are informed by the ground-state density but do not enforce the surrogate functional constraints.

Elucidating molecular structures from spectra is a foundational problem in chemical and materials characterization, yet remains challenging due to spectral ambiguity and the vast molecular space. Although recent diffusion-based generators show strong promise for spectra-conditioned elucidation, existing methods struggle to learn robust spectra-structure relationships from limited paired data when relying solely on global spectral representation. Moreover, the repeated full sampling inference strategy incurs substantial computation overhead. To address these limitations, we propose \textbf{MAST}, a \textbf{M}otif-\textbf{A}ugmented diffusion framework with \textbf{S}earch \textbf{T}ree, for joint 2D-3D spectroscopic molecular structure elucidation. MAST introduces explicit, interpretable \emph{motif priors} as intermediate evidences throughout denoising, reducing conditional ambiguity and facilitating spectra-conditioned optimization. We further cast diffusion sampling as \emph{reward-guided tree search} to prioritize high-reward denoising trajectories, yielding a compact set of spectra-consistent candidates under limited budgets. On the QM9S multi-spectra benchmark, MAST achieves \textbf{94.89\%} exact recovery and improves 3D fidelity, while preserving high chemical validity and stability. Code is available at https://github.com/Jia040223/MAST.