Isotope effects tunnelling

For heavy atom isotope effects tunneling is relatively unimportant and the TST model suffices. As an example the dehalogenation of 1,2-dichloroethane (DCE) to 2-chloroethanol catalyzed by haloalkane dehalogenase DhlA is discussed below. This example has been chosen because the chlorine kinetic isotope effect for this reaction has been computed using three different schemes, and this system is among the most thoroughly studied examples of heavy atom isotope effects in enzymatic reactions. 

In the H/D isotope effect case, m2/wi = 2, the interval of temperatures between re(H) and re(D) is wider than AT as predicted by (2.19), and in this interval the H atom tunnels while the D atom classically overcomes the barrier. For this reason the isotope effect becomes several orders larger than that described by (2.70). At 7" < 7 c(m2) the tunneling isotope effect becomes independent of the temperature. 

The measured dependence of kn(T) and T) consists of an Arrhenius region ( = 9.6 kcal/mol) going over to the low-temperature plateau below IlOK, where k 10 s . The isotope effect grows as the temperature drops, kn/ko — 20 at T = 100 K (fig. 15). Tunneling is promoted by the torsional vibrations of the OH and CH groups, as well as the oxy-group bending vibration. 

Lifnbach et al. [92JA9657 97BBPG889] made an exhaustive study of proton transfer in solid pyrazoles. For instance, the activation barriers, isotope and tunneling effects of the dimer 67, the trimer 68, and the tetramer 69 were determined. Catemers, like pyrazole itself, do not show dynamic behavior. 

Isotope effect between the HH, HD, DH, and DD isotopomers was used as an important tool to determine the mechanism of the double-proton transfer. For concerted degenerate double-proton transfers in the absence of tunneling, the rule of the geometrical mean (RGM) should hold in good approximation, which states that /chh/ hd = /cdh/ dd-Tunneling may lead to a breakdown of this rule but the relation /chh > hd = dh > dd should remain valid. In the absence of secondary isotope effects the relation /chh HD = DH = 2 /cdd sliould liold for a stepwise pathway, even if tunneling is involved. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

The only (to the best of our knowledge) theoretical treatment of hydrogen transfer by tunnelling to explicitly recognise the role of protein dynamics, and relate this in turn to the observed kinetic isotope effect, was described by Bruno and Bialek. This approach has been termed vibration-ally enhanced ground state tunnelling theory. A key feature of this theory... 

Based on C-H versus C-D zero point vibrational differences, the authors estimated maximum classical kinetic isotope effects of 17, 53, and 260 for h/ d at -30, -100, and -150°C, respectively. In contrast, ratios of 80,1400, and 13,000 were measured experimentally at those temperatures. Based on the temperature dependence of the atom transfers, the difference in activation energies for H- versus D-abstraction was found to be significantly greater than the theoretical difference of 1.3kcal/mol. These results clearly reflected the smaller tunneling probability of the heavier deuterium atom. 

More recent theoretical work has raised questions about these conclusions, how-ever. Particularly extensive calculational treatment of the rearrangement of 54 to vinyl chloride by several research groups failed to duplicate the predictions of an atypical kinetic isotope effect. These later studies indicate that tunneling effects should indeed be greater for H-shift than for the heavier D rearrangement. Consequently, the k /ko ratio should actually decrease at higher temperatures. The discrepancy in predicted results was eventually traced to an error in the earlier calculations. Nevertheless, it... 

Product analysis by NMR indicated an isotope effect at 118°C of = 2.14, corrected for numbers of H versus D. On lowering the temperature to -12°C, however, it was found that the isotope effect increased to 3.25. Referring to earlier experimental results on the C-H shift in methylchlorocarbene, " the authors cited the normal temperature dependence of the isotope effect as evidence against tunneling in 64. In retrospect, however, as noted above, theoretical support for an atypical inverse temperature dependence in methylchlorocarbene has been refuted. Hence, the involvement of tunneling in 62/64 at ambient temperatures is still an open question. 

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