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.
- Pub Date:
- August 2014
- Physics - Chemical Physics
- Doctoral (PhD) dissertation, 90 pages, 12 figures. Two chapters of the original dissertation, containing research which is yet to be published, have been omitted from this version of the dissertation deposited online. The central message and logical argument of the dissertation is unaffected, and the author intends to make the complete dissertation available as soon as practicable