To overcome the high computational expense of conventional quantum chemistry techniques and the limited incorporation of physical constraints in machine learning models, we present SphereDiff-TS: a diffusion-based method for predicting 3D transition state (TS) structures using a spherical coordinate system with flexible boundary and dynamic radius constraints. Evaluated against true transition states, the model achieves chemical accuracy in both geometry (median RMSD: 0.048 Å; median of 0.022 Å on selected cross-system cases) and energy (median absolute error: 0.55 kcal/mol; 0.328 kcal/mol on the same cases). Moreover, comparative analysis with the literature-reported structures confirms that the model accurately reproduces barrier heights, with deviations generally below 1.5 kcal/mol. These results highlight the potential of SphereDiff-TS as a robust computational tool for exploring reaction mechanisms and aiding in computer-driven reaction design.
Zhao et al. (2026) studied this question.