Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space

摘要

Despite the fact that quantum mechanical principles do not allow theestablishment of an exact quantum analogue of the classical transition statetheory (TST), the development of a quantum TST (QTST) with a proper dynamicaljustification, while recovering the TST in the classical limit, has been a longstanding theoretical challenge in chemical physics. One of the most recentefforts of this kind was put forth by Hele and Althorpe (HA) [ J. Chem. Phys.138 , 084108 (2013)], which can be specified for any cyclically invariantdividing surface defined in the space of the imaginary time path integral. Thepresent work revisits the issue of the non-uniqueness of QTST and provides adetailed theoretical analysis of HA-QTST for a general class of such pathintegral dividing surfaces. While we confirm that HA-QTST reproduces the resultbased on the ring polymer molecular dynamics (RPMD) rate theory for dividingsurfaces containing only a quadratic form of low frequency Fourier modes, wefind that it produces different results for those containing higher frequencyimaginary time paths which accommodate greater quantum fluctuations. Thisresult confirms the assessment made in our previous work [J. Chem. Phys. 144,084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST ingeneral, and points to a new ambiguity of HA-QTST with respect to itsjustification for general cyclically invariant dividing surfaces defined in thespace of imaginary time path integrals. Our analysis also offers new insightsinto similar path integral based QTST approaches.