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

Timothy J H Hele; Stuart C Althorpe

doi:10.1063/1.4819077

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

J Chem Phys. 2013 Aug 28;139(8):084116. doi: 10.1063/1.4819077.

Authors

Timothy J H Hele¹, Stuart C Althorpe

Affiliation

¹ Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

PMID: 24006983
DOI: 10.1063/1.4819077

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.