Wigner correction

The first order term is known as the Wigner correction. ... 

It has been previously noted that the first quantum correction to the classical high temperature limit for an isotope effect on an equilibrium constant is interesting. Each vibrational frequency makes a contribution c[>(u) to RPFR and this contribution can be expanded in powers of u with the first non-vanishing term proportional to u2/24, the so called first quantum correction. Similarly, for rates one introduces the first quantum correction for the reduced partition function ratios, includes the Wigner correction for k /k2 and makes use of relations like Equation 4.103 for small x and small y, to find a value for the rate constant isotope effect (omitting the noninteresting symmetry number term)... 

The Wigner correction for tunneling depends only on the imaginary frequency fflj, X for the unbound mode at the saddle point [8]... 

The pyrolysis mechanism of PPE and its derivatives given in Scheme 7.2 consist of bimolecular and unimolecular reactions. Applying transition state theory, we calculate the rate constants for the hydrogen abstraction reactions using Eq. (7.19) and the rate constants for reactions 1 and 3-5 using Eq. (7.21). The Wigner correction (Eq. (7.20)) is utilized to approximate quantum effects and the molecular partition functions are defined through Eqs (7.14), (7.15), (7.17), (7.18), and (7.28). 

A posteriori Brillouin-Wigner correction of limited multireference configuration interaction analysis... 

In this equation the first term alone suffices for high barriers and small values of u, but for large tunnel corrections the later terms are needed. The Wigner correction is the first two terms in the expansion of the first term of equation 1 as a power series in u. 

A posteriori Brillouin-Wigner correction to limited multi-reference configuration interaction... 

WC includes the Wigner correction. Adapted from reference 3b. 

Calculations of the rate constant of reaction (R2) using transition state theory and the ab initio surface discussed above have been reported by Schatz and Walch. The results of these calculations, without and with the Wigner correction, are given in Fig. 8. With the correction for tunneling the calculated rate constants are in excellent agreement with those obtained from experiment over the entire temperature range from 300-2000 K. 

Fig. 8. The calculated (—,—) and experimental (o) rate constants for the OH 4- H2 H2O + H reaction. The rate constant labeled WC includes the Wigner correction. Adapted from reference 4b.

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