On the uniqueness of t->0+ quantum transition-state theory

TL;DR

This paper demonstrates that the quantum transition-state theory (QTST) derived from the t->0+ limit of flux-side correlation functions is unique and equivalent to RPMD-TST, with all other forms failing to produce positive-definite quantum statistics.

Contribution

It provides strong evidence that RPMD-TST is the only valid QTST in the t->0+ limit, introducing a generalized correlation function encompassing all known forms.

Findings

RPMD-TST is the unique QTST with positive-definite quantum statistics.

Other flux-side correlation functions yield non-positive-definite or zero limits.

The generalized correlation function includes all known flux-side functions as special cases.

Abstract

It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t->0+ limit of a (new form of) quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here we provide evidence which suggests very strongly that this QTST (= RPMD-TST) is unique, in the sense that the t->0+ limit of any other flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. We introduce a generalized flux-side time-correlation function which includes all other (known) flux-side time-correlation functions as special limiting cases. We find that the only non-zero t->0+ limit of this function that contains positive-definite quantum statistics is RPMD-TST.