{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"9b03c9a4787c28b879ec940ca6f28daddba33de8689419d52bb28349b8045167","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b","cf23395c4413a851b5c27819720124f706f9d259827d30dfc62d9633efb9ae17"],"salt":"8af4f03894cafaecac8575a746e515822047eb3929c16b9661930547bfa2540e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"chem.reaction-dynamics.quantum-tst-deep-tunneling","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Transition-state theory estimates a reaction rate from the flow across the top of the energy barrier without following full trajectories. 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 regime","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"89ca3626ba5d2178d4f3d1ce6310bf296149375e1345ed4656eaee1b30d2c43f","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"6546507b8204568f60e785943bc4aaa80415c8e86f7e33217a52c2eaca794944","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"FMt86CfcBiaUi4aGsevN_keaYGWfQbj0xSCQ6HnVUZlNBTnkC3ytle6FI_Y1N21onL7svPtZGRG7mS5JDIE_BA"},"schema":"pubphys.envelope/1"},"record_hash":"89ca3626ba5d2178d4f3d1ce6310bf296149375e1345ed4656eaee1b30d2c43f","leaf_index":2682}