Journal ArticleDOI
Quantum transition state theory: Perturbation expansion
TLDR
In this article, a perturbation theory expansion for the projection operator about the parabolic barrier limit and the classical limit was derived, and the expansion was applied to a symmetric and an asymmetric Eckart barrier.Abstract:
The exact quantum expression for the thermal rate of reaction is the trace of a product of two operators It may therefore be written exactly as a phase space integral over the Wigner phase space representations of the two operators The two are a projection operator onto the product’s space, which is difficult to compute, and the symmetrized thermal flux operator, which can be computed using Monte Carlo methods A quantum transition state theory was presented recently, in which the exact projection operator was replaced by its parabolic barrier limit Alternatively, the exact projection operator may be replaced by its classical limit Both approximations give thermodynamic estimates for the quantum rates In this paper, we derive a perturbation theory expansion for the projection operator about the parabolic barrier limit and the classical limit The correction terms are then used to evaluate the leading order corrections to the rate estimates based on the parabolic barrier or classical limits of the projection operator The expansion is applied to a symmetric and an asymmetric Eckart barrier The first two terms in the expansion give excellent results for temperatures above the crossover between quantum tunneling and thermal activation For deep tunneling and asymmetric systems, the use of variational transition state theory, the classical limit, and perturbation theory leads to significant improvement in the estimate of the tunneling rate Multidimensional extensions are presented and discussedread more
Citations
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Journal ArticleDOI
Chemical reaction rates from ring polymer molecular dynamics.
Ian Craig,David E. Manolopoulos +1 more
TL;DR: The ring-polymer molecular dynamics method can be adapted to calculate approximate Kubo-transformed flux-side correlation functions, and hence rate coefficients for condensed phase reactions, and it gives the exact quantum-mechanical rate constant for the transmission through a parabolic barrier.
Journal ArticleDOI
Reaction rate theory: What it was, where is it today, and where is it going?
Eli Pollak,Peter Talkner +1 more
TL;DR: Although classical rate theory reached a high level of maturity, its quantum analog leaves the theorist with serious challenges to this very day, the successes and challenges facing quantum rate theory are outlined.
Journal ArticleDOI
Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory.
TL;DR: It is demonstrated that the ring-polymer molecular dynamics (RPMD) method is equivalent to an automated and approximate implementation of the "Im F" version of semiclassical instanton theory when used to calculate reaction rates in the deep-tunneling regime.
Journal ArticleDOI
A refined ring polymer molecular dynamics theory of chemical reaction rates
Ian Craig,David E. Manolopoulos +1 more
TL;DR: The long-time limit of the new flux-side correlation function, and hence the fully converged RPMD reaction rate, is rigorously independent of the choice of the transition state dividing surface, which is especially significant because the optimum dividing surface can often be very difficult to determine for reactions in complex chemical systems.
Journal ArticleDOI
Spiers Memorial Lecture Quantum and semiclassical theory of chemical reaction rates
TL;DR: In this paper, the semiclassical (SC) initial value representation (IVR) is applied to models of unimolecular isomerization and electronic non-adiabatic transitions coupled to an infinite bath of harmonic oscillators.
References
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Journal ArticleDOI
On the Quantum Correction For Thermodynamic Equilibrium
TL;DR: In this article, the Boltzmann formula for the probability of a configuration is given in classical theory by means of a probability function, and the result discussed is developed for the correction term.
Book ChapterDOI
On the quantum correction for thermodynamic equilibrium
TL;DR: In this article, the Boltzmann formula for lower temperatures has been developed for a correction term, which can be developed into a power series of h. The formula is developed for this correction by means of a probability function and the result discussed.
Journal ArticleDOI
Reaction-rate theory: fifty years after Kramers
TL;DR: In this paper, the authors report, extend, and interpret much of our current understanding relating to theories of noise-activated escape, for which many of the notable contributions are originating from the communities both of physics and of physical chemistry.
Journal ArticleDOI
The Activated Complex in Chemical Reactions
TL;DR: In this paper, the probability of the activated state is calculated using ordinary statistical mechanics, and the probability multiplied by the rate of decomposition gives the specific rate of reaction, and necessary conditions for general statistical treatment to reduce to the usual kinetic treatment are given.