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Its quantum version, built on ring polymers (chains of beads that represent a quantum particle), is unique and exact in some limits but can fail when tunneling dominates.","posed_since":"","precise":"Ring-polymer molecular dynamics transition-state theory (RPMD-TST) is the unique $t\\to 0+$ limit of a quantum flux-side time-correlation function and is exact when no recrossing of the dividing surface or its ring-polymer generalizations occurs (Hele and Althorpe, J. Chem. Phys. 2013, https://doi.org/10.1063/1.4792697). Below the crossover temperature $T_{x}=\\hbar\\omega_{b}/(2\\pi)$ ($\\omega_{b}=\\text{barrier frequency},\\ k_{B}=1$) it deviates from exact quantum rates for asymmetric barriers. Derive a rate theory without real-time dynamics whose error vanishes both without recrossing and in the semiclassical instanton limit, or rigorous bounds on the RPMD-TST error versus $T/T_{x}$ and barrier asymmetry, tested on Eckart barriers and H + $\\mathrm{H_2}$ type reactions.","problem_ref":"cf23395c4413a851b5c27819720124f706f9d259827d30dfc62d9633efb9ae17","references":"","settled_by":"A derivation with error bounds verified against exact quantum rates for one-dimensional and multidimensional benchmark barriers.","status_note":"Uniqueness and exactness without recrossing were derived in 2013; no transition-state theory is known to be exact in deep tunneling through asymmetric barriers.","title":"A quantum transition-state theory valid in the deep-tunneling 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