Real-time interpretation of neutron vibrational spectra with symmetry-equivariant Hessian matrix prediction

The vibrational behavior of molecules serves as a crucial fingerprint of their structure, chemical state, and surrounding environment. Neutron vibrational spectroscopy provides comprehensive measurements of vibrational modes without selection rule restrictions. However, analyzing and interpreting the resulting spectra remains a computationally formidable task. Here, we introduce a symmetry-aware neural network that directly predicts Hessian matrices from molecular structures, thereby enabling rapid vibrational spectral reconstruction. Unlike traditional approaches that focus on eigenvalue prediction, the Hessian matrix provides richer, more fundamental information with broader applications and superior extrapolation. This approach also paves the way for predicting other properties, such as reaction pathways. Trained on small molecules, our model achieves spectroscopic-level accuracy, allowing real-time, unambiguous peak assignment. Moreover, it maintains high accuracy for larger molecules, demonstrating strong transferability. This adaptability unlocks new capabilities, including on-the-fly spectral interpretation for future autonomous laboratories, and offers insights into molecular design for targeted chemical pathways.