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Surprisingly, there exists a quantum flux-side time-correlation functionwhich has a non-zero short-time (t->0+) limit, and thus yields a rigorousquantum generalization of classical transition-state theory (TST). In this PartI of two articles, we introduce the new time-correlation function, and deriveits short-time limit. The new ingredient is a generalized Kubo transform whichallows the flux and side dividing surfaces to be the same function ofpath-integral space. Choosing this common dividing surface to be a single pointgives a short-time limit which is identical to an expression introduced onheuristic grounds by Wigner in 1932, but which does not give positive-definitequantum statistics, causing it to fail while still in the shallow-tunnellingregime. Choosing the dividing surface to be invariant to imaginary-timetranslation gives, uniquely, a short-time limit that gives the correctpositive- definite quantum statistics at all temperatures, and which isidentical to ring-polymer molecular dynamics (RPMD) TST. We find that theRPMD-TST rate is not a strict upper bound to the exact quantum rate, but a goodapproximation to one if real-time coherence effects are small. Part II willshow that the RPMD-TST rate is equal to the exact quantum rate in the absenceof recrossing.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

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