Quantum Transition-State Theory

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.

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