Tunneling isotope effect

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 thermodynamic and kinetic isotope effects are mainly due to the differences in frequencies of isotope vibrations in the initial, transition, and final states (Chapter 8). The tunneling isotope effects become considerable, for example, when vibrational frequencies of bonds near the activation barrier exceed 1000 cm at the barrier value E > 20RT. Under these ctmditions, a proton tunnelates approximately twofold more rapidly than doiterium. The tunneling isotope effect increases substantially with die temperature decrease. 

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. 

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. 

Hydrogen motion, H+, H or H, is often involved in the rate-limiting step of many enzyme catalysed reactions. Here, QM tunnelling can be important and is reflected in the values of the measured kinetic isotope effects (KIEs) [75], Enzyme motion... 

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