Stepwise HHHH-transfer

In Ref [26] three limiting cases were considered, i.e. a single barrier (Fig. 6.10), a double barrier (Fig. 6.17) and a quadruple-barrier reaction pathway (Fig. 6.18). The first process does not involve any intermediate. The second process consists essentially of consecutive double proton transfer steps, where each step involves a single barrier. There are two possibilities, either protons 1, 2 are transferred first, followed by protons 3, 4, or vice versa, proceeding via the zwitterionic intermediates 1100 or 0011. It is again assumed that the intermediates can be treated as separate species, i.e. that there are no delocalized states involving different potential wells. This assumption will be realized when the barriers are large. Each reaction step is then characterized by an individual rate constant. The process con- 

The expected kinetic isotope effects obtained by neglecting secondary kinetic isotope effects are summarized in Table 6.3. The results are visualized in Fig. 6.19, where again a simple Arrhenius law was assumed for the HHHH reaction with the same arbitrary parameters as for the HH and the HHH reactions in Fig. 6.14 and 6.16. 

In the case of the single-barrier mechanism, all four hydrons are in flight in the transition state. Subsequent replacement of H by D involves similar primary kinetic isotope effects P, leading to equally spaced Arrhenius curves of the isotopic reactions in Fig. 6.19(a), with an overall kinetic isotope effect of k nnn/ki DDD P. This result is analogous to the single-barrier HH and the HHH-transfer cases discussed above. Note that, generally, the transfer of n hydrons is expected to give rise to an overall kinetic isotope effect of P [26]. 

For the two-barrier HHHH case it was assumed that the first and second primary kinetic isotope effects of the double proton transfer in the dissociation steps 

Pjjand 3 ie equal. represents the single H/D fractionation factor of the dissociation step, corresponding to the equilibrium constant of the formal reaction 

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The kinetics of the HHHH-transfer in the cyclic tetramer of 3,5-diphenyl-4-pyr-azole (DPP) has been evaluated recently [27]. The overall kinetic HHHH/DDDD isotope effects were found to be only around 12. This value indicated absence of a single barrier HHHH process where one would expect a larger overall effect. Instead, the Arrhenius pattern depicted in Fig. 6.36 could be explained in terms of a stepwise HH+HH process according to the profile of Fig. 6.17, where two hydrons are transferred in each step, leading to the expected isotope effects depicted in Fig. 6.19(b) and (c). This means that the rate constants of the HHHD and the HDHD reaction are very similar, and also those of the DDHH, DDHD, DDDD reactions. This leads to a very special dependence of the rate constants observed on the deuterium fraction in the mobile proton sites. The mole fractions of all isotopologs according to a statistical distribution are depicted in Fig. 6.37(a), and the sums of mole fractions of the relevant species exhibiting similar rate constants in Fig. 6.37(b). It is clear, that practically only three different species and rate constants are observed in this case. 

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