Quantum Transition-State Theory

TL;DR

This paper derives a rigorous quantum transition-state theory (QTST) by unifying classical TST with quantum mechanics, validating RPMD-TST as an exact quantum rate method under certain conditions.

Contribution

It establishes QTST as equivalent to RPMD-TST and proves its validity and uniqueness for computing thermal quantum rates in direct reactions.

Findings

QTST is identical to RPMD-TST and validated as an exact quantum rate method.

Proves QTST's validity in the absence of recrossing by exact quantum dynamics.

Argues QTST is the only positive-definite quantum rate theory for direct reactions.

Abstract

This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transition-state theory (RPMD-TST), which was previously considered a heuristic method, and whose results we thereby validate. The key step in deriving a QTST is alignment of the flux and side dividing surfaces in path-integral space to obtain a quantum flux-side time-correlation function with a non-zero $t\to 0_+$ limit. We then prove that this produces the exact quantum rate in the absence of recrossing by the exact quantum dynamics, fulfilling the requirements of a QTST. Furthermore, strong evidence is presented that this is the only QTST with positive-definite Boltzmann statistics and therefore the pre-eminent method for computation of thermal quantum rates in direct reactions.