Quantum TransitionState Theory
Abstract
This dissertation unifies one of the central methods of classical rate calculation, `TransitionState Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum TransitionState Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transitionstate theory (RPMDTST), 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 pathintegral space to obtain a quantum fluxside timecorrelation function with a nonzero $t\to 0_+$ 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 positivedefinite Boltzmann statistics and therefore the preeminent method for computation of thermal quantum rates in direct reactions.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 arXiv:
 arXiv:1408.0996
 Bibcode:
 2014arXiv1408.0996H
 Keywords:

 Physics  Chemical Physics
 EPrint:
 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