A quantum transition-state theory valid in the deep-tunneling regime
In plain words
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.
Precise statement
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 + H2 type reactions.
What would settle it
A derivation with error bounds verified against exact quantum rates for one-dimensional and multidimensional benchmark barriers.
Status in the literature
Uniqueness and exactness without recrossing were derived in 2013; no transition-state theory is known to be exact in deep tunneling through asymmetric barriers.