Tunneling correction factor

This tunneling correction factor appeared as a natural consequence of the fundamental formulation of transition-state theory. This clarifies the situation, since the precise definition of this factor is occasionally discussed in the literature [8]. We will return to a discussion of tunneling and the tunneling correction factor in Section 6.4. 

In Section 6.2, we derived a tunneling correction factor for transition-state theory, see Eq. (6.24). The derivation showed that k sriT) of Eq. (6.8) is replaced by Ktunnei(T) x fc rs r(7 ) when tunneling is included. 

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. 

This expression is identical to the tunneling correction factor for a parabolic barrier. 

To arrive at K and k, our task is to express the following terms appearing in eqns. (5.15) and 5.16) the partition functions (Q) of reactants, products and of the activated complex, the heat of reaction at absolute zero, AHq, the enthalpy of activation at absolute zero, Hq, and the tunnelling correction factor, P. For an ideal gas the total partition function can be expressed within the rigid-rotor and harmonic oscillator (RRHO) approximation as a product... 

A reaction involving hydrogen atom transfer is usually characterized by a significant tunneling effect, which is represented in the rate constant calculation by the tunneling correction factor kw as... 

For this reaction, both LCG3 and SCT methods were applied to calculate tunneling correction factors [24]. The SCT method gave larger tunneling probabilities. 

A number of modern and quite sophisticated treatments of H-transfer in the condensed phase are not that dissimilar from the approach taken by Bell, in that they formulate the rate constant for H-transfer as a semi-classical term multiplied by a tunneling correction factor, e.g. Eqs. (10.16a) and (10.16b). 

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