Proton transfer Bell model

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. 

This means that at low temperature where P is large the HD reaction is ca. twice as fast as the DD reaction. Equation (6.31) has been used in connection with the Bell-Limbach tunneling model to describe the stepwise double proton transfer in porphyrins, azophenine, and oxalamidines, as will be discussed in Section 6.3. Smedarchina et al. [16] used the same equations for their quantum-mechanical treatment of the porphyrin tautomerism. 

Figure 6.41 Visualization of a modified Bell tunneling model for degenerate, stepwise double proton transfers involving an intermediate. A minimum energy , is required for proton tunneling, which can take place only in the hatched regions. Ej barrier energy, (a) and (d) E , is given by the energy of the...

Looking back on the past twenty years which marked the development of enzyme-mechanistic studies, one cannot help but notice that the progress in the understanding of enzymatic reactions was always critically dependent upon the existence of appropriate model studies. From this point of view, the pioneering work of Professor R. P. Bell on proton transfer reactions is an invaluable asset without which enzyme mechanistic studies would probably still be in the exploratory stage. 

Solid state proton transfer (SSPT) occurs between tautomers and, even if the initial and the final are the same (degenerate tautomerism, K = 1), it constitutes one ofthe best known kinetic processes. The loss of freedom due to the crystal structure allows for accurate kinetic models to be used, including the Car-Parrinello [51] and Bell-Limbach tunneling model [52]. This field owes much to the works of Limbach et /. [53, 54] and of Claramunt ef /. [55, 56]. 

Figure 6.34 Arrhenius diagram for the double proton and deuteron transfer in the cyclic trimers of solid DMP. Adapted from Ref [25aj. The solid curves were calculated using the Bell-Limbach tunneling model as described in the text.

Using dynamic solid-state CP MAS NMR spectroscopy, the kinetics of the degenerate intermolecular double and quadruple proton and deuteron transfers in the cyclic dimer of N labelled polycrystalline 3,5-diphenyl-4-bromopyrazole (DPBrP) and in the cyclic tetramer of N labelled polycrystalline 3,5-diphenylpyrazole (DPP) have been studied in a wide temperature range at different deuterium fractions in the mobile proton sites. Rate constants were measured on a millisecond time scale by line shape analysis of the doubly N labelled eompounds and by magnetisation transfer experiments on a second timescale of the singly N labelled compounds in order to minimise the effeets of proton-driven N spin diffusion. The Arhenius curves of all processes were found to be nonlinear and indicated tunneling processes at low temperatures. In a preliminary analysis, they were modelled in terms of the Bell-Limbach tuimeling model. 

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