Hydrogen tunneling Bell model

Fig. 3 Hydrogen tunneling according to the Bell model can generate anomalous isotopic Arrhenius parameters. A semiclassical model with = 0 (thus Ah = A ) and...

In electrochemical proton transfer, such as may occur as a primary step in the hydrogen evolution reaction (h.e.r.) or as a secondary, followup step in organic electrode reactions or O2 reduction, the possibility exists that nonclassical transfer of the H particle may occur by quantum-mechanical tunneling. In homogeneous proton transfer reactions, the consequences of this possibility were investigated quantitatively by Bernal and Fowler and Bell, while Bawn and Ogden examined the H/D kinetic isotope effect that would arise, albeit on the basis of a primitive model, in electrochemical proton discharge and transfer in the h.e.r. 

The scope of this chapter is, therefore, (i) to review the Bell-Limbach tunneling model in comparison with other models and its use for describing single steps of multiple hydrogen transfer networks and (ii) to review applications of this approach in a number of cases which have been studied mainly by NMR. A description of the techniques used for the determination of rate constants of Id-transfer will not be included in this chapter readers interested in this problem are referred to a recent review [4]. 

Eor a better comparison, the Arrhenius curves of all hydrogen transfers discussed in this section have been recalculated for this review using the Bell-Lim-bach tunneling model described in the theoretical section. Some systems have already been presented recently in a mini-review [54]. The parameters used are assembled in Table 6.4. Finally, note that in all cases where hydrogen isotopes are transferred from and to nitrogen the compounds had to be enriched for NMR measurements with the isotope. 

Figure 11.3. Temperature dependence of the primary hydrogen isotope effect calculated using a 9-atom vibrational model for hydrogen transfer (model HHIE3 [37] with simple stretch-stretch coupling to generate a reaction-coordinate frequency). Triangles mark calculated results for models with a reaction-coordinate frequency for H transfer of 9841 cm including the truncated Bell tunnel correction [6, 22]. The circles show results for models with a sufficiently low reaction-coordinate frequency (901 cm ) to make the...

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