Deuterium isotope effects hydrogen tunneling

A very large deuterium isotope effect has been observed240 by ESR at 77 K on hydrogen-deuterium elimination reaction from 2,3-dimethylbutane (H-DMB)-SFg and 2,3-dimethylbutane-2,3-D2 (D-DMB)-SFg (0.6 mol% mixtures), /-irradiated at 70 K and then stored at 77 K. The significant isotope effect, h2 Ad2 = 1-69 x 104 at 77 K, has been explained by tunnelling elimination of hydrogen (H2) molecules from a DMB+ ion240. 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

The two chief experimental criteria for tunneling in chemical reactions are an abnormal isotope effect (the tunnel effect is much more pronounced for hydrogen than for deuterium), which does not concern us here, and a curved Arrhenius plot. The reason for this is that the effect becomes most marked at low temperatures, when the fraction of systems which are able to cross the barrier becomes considerably higher than that calculated from classical considerations. As a result, the rate decreases with decreasing temperature less than expected, and the Arrhenius plot becomes concave upward. We cannot go into the quantum-mechanical details, and refer the reader to the literature on the subject. (See, e.g., Refs. 2b, 23, 77, 99, 105.)... 

Qualitatively the results are explained in the following way. Although the transferring deuterium atom does not introduce a primary isotope effect due to zero-point energy differences into ko/ko, there is less tunnelling when deuterium is transferred than when hydrogen is transferred. Therefore, the tunnel correction to the secondary /c°//cd is small relative to that for k /k. Thus, the experimental results are in agreement with the results of the model calculations. 

Complications that arise with this simple reaction are twofold. First, because of the low mass of the hydrogen atom its movement frequently exhibits non-classical behavior, in particular quantum-mechanical tunneling, which contributes significantly to the observed kinetic isotope effect, and in fact dominates at low temperature (Section 6.3). Secondly, in reaction 10.2 protium rather than deuterium transfer may occur ... 

Just as in the preceding examples, early indications of tunneling in enzyme-catalyzed reactions depended on the failure of experiments to conform to the traditional expectations for kinetic isotope effects (Chart 3). Table 1 describes experimental determinations of -secondary isotope effects for redox reactions of the cofactors NADH and NAD. The two hydrogenic positions at C4 of NADH are stereochemically distinct and can be labeled individually by synthetic use of enzyme-catalyzed reactions. In reactions where the deuterium label is not transferred (see below), an... 

The overall conclusion drawn by Huskey and Schowen was that a combination of coupled motion and tunneling through a relatively sharp barrier was required to explain the exaltation of secondary isotope effects. They also noted that this combination predicts that a reduction of exaltation in the secondary effect will occur if the transferring hydrogen is changed from protium to deuterium for point A in Fig. 4, the secondary effect is reduced by a factor of 1.09. Experimentally, reduction factors of 1.03 to 1.14 had been reported. For points B, C, and D on the diagram, all of which lack a combination of coupled motion and tunneling, no such reductions in the secondary isotope effect were calculated. 

The temperature dependence of this rate constant was measured by Al-Soufi et al. [1991], and is shown in Figure 6.17. It exhibits a low-temperature limit of rate constant kc = 8x 105 s 1 and a crossover temperature 7 C = 80K. In accordance with the discussion in Section 2.5, the crossover temperature is approximately the same for hydrogen and deuterium transfer, showing that the low-temperature limit appears when the low-frequency vibrations, whose masses are independent of tunneling mass, become quantal at Tisotope effect increases with decreasing temperature in the Arrhenius region by about two orders of magnitude and approaches a constant value kH/kD = 1.5 x 103 at T[Pg.174]

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