Wigner tunneling correction

This expression is called the Wigner tunneling correction factor, and is valid for a small degree of tunneling (high and/or broad barrier, hv high temperatures (hv correction factor is larger than one. 

The need to include quantum mechanical effects in reaction rate constants was realized early in the development of rate theories. Wigner [8] considered the lowest order terms in an -expansion of the phase-space probability distribution function around the saddle point, resulting in a separable approximation, in which bound modes are quantized and a correction is included for quantum motion along the reaction coordinate - the so-called Wigner tunneling correction. This separable approximation was adopted in the standard ad hoc procedure for quan-... 

ARRHENIUS EQUATION, TRANSITION STATE THEORY, AND THE WIGNER TUNNELING CORRECTION... 

The leading quantum correction to TST at high temperatures is the Wigner tunneling correction [28], that is, a multiplicative factor ... 

Including the Wigner tunneling correction (3.7), the kinetic isotope ratio becomes... 

At somewhat lower temperatures, when quantum effects start to play a role, the basic TST expression (3.29) can be improved in several ways First, classical partition functions 2r and can be replaced by their exact quantum analogues for a harmonic potential. (In fact, this is usually done automatically in TST.) Second, quantum tunneling can be included approximately via the Wigner tunneling correction (3.7) ... 

Methods used Arrhenius law, transition state theory, Wigner tunneling correction, quanrnm instanton approximation, and exact analytical solution... 

If information on the reaction path is available, as, for instance, in variational transition state theory, this can be used to calculate k [69,70]. In transition state theory, only the knowledge of the energy and its first and second derivatives at the reactant and transition state locations is needed and the barrier is typically approximated by a simple functional form. One possibility is to describe the reaction barrier by an Eckart potential [75] (also called a sech potential, depending on the literature source), k in Eq. (7.19) is defined as the ratio of transmitted quantum particles to classical particles and the resulting integral for the Eckart potential can be solved numerically. An approximate solution is the Wigner tunneling correction ... 

Rate expressions are recommended to be used as relative quantities only. PPL, phenethyl phenyl ether a-PPE", a-radical of PPL )8-PPE, )8-radical of PPL TST, transition state theory including anharmonic corrections TST, transition state theory including anharmonic corrections and Wigner tunneling correction SS, steady-state approximation for intermediate. 

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