When Reaction Geometry Is Periodic: Understanding and Learning Transition States

Learning transition-state (TS) geometries directly from reaction endpoints offers a route to accelerating reaction-pathway discovery, yet periodic systems pose distinct geometric challenges. Equivalent lattice representations alter endpoint displacements, local interactions can cross unit-cell boundaries, and reaction motion can be highly localized within extended structures. We characterize these effects across three periodic reaction benchmarks and introduce SurfReact-TS, a curated benchmark for constrained periodic surface reactions. Guided by this analysis, we develop PeriTS, a geometry-aware flow-matching framework that incorporates PBC-consistent endpoint conditioning, periodic interaction modeling, coordinate constraints, and reaction-focused learning. Across the three benchmarks, PeriTS or its matched One-shot counterpart achieves the lowest mean RMSD among the evaluated methods. Controlled studies further show that the value of iterative refinement depends strongly on the reaction regime, while increasing candidate breadth provides only modest gains in the settings studied. Selected-case DFT calculations provide complementary energy and force diagnostics. Overall, our results establish periodic TS prediction as a geometry-dependent learning problem in which representation, model design, and inference strategy should be adapted to the underlying reaction system.