An alternative derivation of ring-polymer molecular dynamics transition-state theory

TL;DR

This paper clarifies that the $t o 0_+$ limit of ring-polymer molecular dynamics transition-state theory (RPMD-TST) is equivalent to a quantum transition-state theory, correcting a recent reinterpretation by Jang and Voth.

Contribution

The authors demonstrate that the recent rederivation by Jang and Voth actually confirms RPMD-TST as the $t o 0_+$ quantum transition-state theory.

Findings

The $t o 0_+$ limit of RPMD-TST is confirmed to be a quantum transition-state theory.

Jang and Voth's rederivation aligns with RPMD-TST, not the centroid-density approximation.

Clarifies the theoretical foundation of RPMD-TST in quantum rate theory.

Abstract

In a previous article [J. Chem. Phys. 138, 084108 (2013)], we showed that the $t\to 0_+$ limit of ring-polymer molecular dynamics (RPMD) rate-theory is also the $t\to 0_+$ limit of a new type of quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD transition-state theory (RPMD-TST) is a $t\to 0_+$ quantum transition-state theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this quantum $t\to 0_+$ limit, and claimed that it gives instead the centroid-density approximation. Here we show that the $t\to 0_+$ limit derived by Jang and Voth is in fact RPMD-TST.