Secondary deuterium KIEs and tunnelling

Quantum-mechanical tunnelling has been recognized as a possible contributor to the rate of a chemical reaction for many years. For instance, the theory of tunnelling for proton transfer reactions was developed by Bell (1959) in his famous book The Proton in Chemistry. Later, Bell (1980a) published a more thorough treatment of tunnelling in his book The Tunnel Effect in Chemistry. 

Thnnelling has sometimes been regarded as a mysterious phenomenon by chemists. It is worth stressing, therefore, that tunnelling has the same firm foundation in quantum mechanics as zero-point energy, which is the most important component of a KIE both these phenomena are a consequence of Heisenberg s uncertainty principle. 

Because of their dependence on mass, KIEs have been used in two ways to detect tunnelling. One is that primary deuterium KIEs are larger than predicted on the basis of zero-point energy alone when tunnelling makes a significant contribution to the KIE. For example, primary deuterium KIEs larger than 25 have been reported (Lewis and Funderburk, 1967 Wilson et al., 1973) for proton transfer reactions where tunnelling is important. 

The second method of detecting tunnelling relies on the fact that the primary hydrogen KIE shows an anomalous temperature dependence when significant tunnelling takes place. In the absence of tunnelling, the temperature dependence of the rate constant should follow the Arrhenius equation (42) 

Because unexpectedly large primary deuterium KIEs are observed in reactions where tunnelling is important, and unexpectedly large secondary deuterium KIEs have been observed in some hydron transfers in elimination and enzyme-catalysed hydride transfer reactions, Saunders (vide infra) wondered whether very large secondary deuterium KIEs were also indicative of tunnelling. 

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Saunders (1985) extended his investigation of the effect of tunnelling on the magnitude of secondary deuterium KIEs in a theoretical study of the E2 reaction between hydroxide ion and a model substrate (reaction (54)). 

Since the reaction is not reversible, the EIE could not be measured. However, the secondary deuterium EIE could be estimated using the fractionation factors published by Hartshorn and Shiner (1972). This approach predicted that the secondary EIE, (KH/KD)sec, would be equal to 1.115 at 45°C. This corresponds to a (Kh/Kt)kc = 1.170 in the absence of tunnelling. Because the secondary tritium KIE is much larger than the EIE, it seems likely that tunnelling is important in this reaction. 

Saunders also used calculations on his model reaction (54) to determine the relationship between the secondary hydrogen-deuterium (secondary hydrogen-tritium) KIEs and secondary deuterium-tritium KIEs for doubly labelled substrates and to investigate how tunnelling affects this relationship. To obtain secondary KIEs that could be checked experimentally, Saunders calculated the secondary k lk% and k lk KIEs for the hypothetical E2 reaction of a pair of doubly labelled substrates [17] and [18]. 

The secondary Hke/T H KIE in the eliminations of 373, 374 and 375 presented above which are higher than this maximum possible secondary IE value, are taken as strongly implicating tunnelling. This conclusion has been supported also by intercomparison of secondary H/T and D/T isotope effects in E2 reactions of RNM3 1 Br at 50 °C. The secondary IE is depressed markedly when deuterium rather than proton is transferred, which also implicates tunnelling ... 

It is important to note that these equations are based on the Swain-Schaad relationship, which assumes that there is no tunnelling in any of the isotopic reactions (the KIEs are semiclassical) and that the relationship between the KIEs is determined only by the masses of the hydrogen, deuterium and tritium atoms. The secondary and kfyko KIEs calculated both with and... 

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