Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory

Surprisingly, there exists a quantum flux-side time-correlation function which has a non-zero t -> 0(+) limit and thus yields a rigorous quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function and derive its t -> 0(+) limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Choosing this function to be a single point gives a t -> 0(+) limit which is identical to an expression introduced on heuristic grounds by Wigner in 1932; however, this expression does not give positive-definite quantum statistics, causing it to fail while still in the shallow-tunnelling regime. Positive-definite quantum statistics is obtained only if the dividing surface is invariant to imaginary-time translation, in which case the t -> 0(+) limit is identical to ring-polymer molecular dynamics (RPMD) TST. The RPMD-TST rate is not a strict upper bound to the exact quantum rate, but is a good approximation to one if real-time coherence effects are small. Part II will show that the RPMD-TST rate is equal to the exact quantum rate in the absence of recrossing. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4792697]