  Despite the fact that quantum mechanical principles do not allow the
establishment of an exact quantum analogue of the classical transition state
theory (TST), the development of a quantum TST (QTST) with a proper dynamical
justification, while recovering the TST in the classical limit, has been a long
standing theoretical challenge in chemical physics. One of the most recent
efforts of this kind was put forth by Hele and Althorpe (HA) [ J. Chem. Phys.
138 , 084108 (2013)], which can be specified for any cyclically invariant
dividing surface defined in the space of the imaginary time path integral. The
present work revisits the issue of the non-uniqueness of QTST and provides a
detailed theoretical analysis of HA-QTST for a general class of such path
integral dividing surfaces. While we confirm that HA-QTST reproduces the result
based on the ring polymer molecular dynamics (RPMD) rate theory for dividing
surfaces containing only a quadratic form of low frequency Fourier modes, we
find that it produces different results for those containing higher frequency
imaginary time paths which accommodate greater quantum fluctuations. This
result 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 in
general, and points to a new ambiguity of HA-QTST with respect to its
justification for general cyclically invariant dividing surfaces defined in the
space of imaginary time path integrals. Our analysis also offers new insights
into similar path integral based QTST approaches.
