Anomalous Kinetic Isotope Effects

Anomalous Kinetic Isotope Effects Because of the (mass) de-... 

Most of the work reported is covered in Section 4.12.5 on oscillating reactions. Anomalous kinetic isotope effects, which lead to values of the... 

Fig. 1 Lewis and Funderburk found that the H/D primary kinetic isotope effects (25 °C in aqueous t-butyl alcohol) for proton abstraction from 2-nitropropane by pyridine derivatives all exceed the maximum isotope effect that could have been derived from the isotopic difference in reactant-state zero-point energies alone (a value around 7). The magnitude of the isotope effect increases with the degree of steric hindrance to reaction presented by the pyridine derivative, the identical results for 2,6-lutidine and 2,4,6-collidine ruling out any role for electronic effects of the substituents. The temperature dependence shown for 2,4,6-collidine is exceedingly anomalous the pre-exponential factor Ahis expected to be near unity but is instead about 1/7, while the value of AH — AH = 3030 cal/mol would have generated an isotope effect at 25 °C of 165 if the pre-exponential factor had indeed been unity.

A number of other proton transfer reactions from carbon which have been studied using this approach are shown in Table 8. The results should be treated with reserve as it has not yet been established fully that the derived Bronsted exponents correspond exactly with those determined in the conventional way. One problem concerns the assumption that the activity coefficient ratios cancel, but doubts have also been raised by one of the originators of the method that, unless solvent effects on the transition state are intermediate between those on the reactants and products, anomalous Bronsted exponents will be obtained [172(c)]. The Bronsted exponents determined for menthone and the other ketones in Table 8 are roughly those expected by comparison with the values obtained for ketones using the conventional procedure (Table 2). For nitroethane the two values j3 = 0.72 and 0.65 which are shown in Table 8 result from the use of different H functions determined with amine and carbon acid indicators, respectively. Both values are roughly similar to the values (0.50 [103], 0.65 [104]), obtained by varying the base catalyst in aqueous solution. The result for 2-methyl-3-phenylpropionitrile fits in well with the exponents determined for malononitriles by general base catalysis but differs from the value j3 0.71 shown for l,4-dicyano-2-butene in Table 8. This latter result is also different from the values j3 = 0.94 and 0.98 determined for l,4-dicyano-2-butene in aqueous solution with phenolate ions and amines, respectively. However, the different results for l,4-dicyano-2-butene are to be expected, since hydroxide ion is the base catalyst used in the acidity function procedure and this does not fit the Bronsted plot observed for phenolate ions and amines. The primary kinetic isotope effects [114] also show that there are differences between the hydroxide ion catalysed reaction (feH/feD = 3.5) and the reaction catalysed by phenolate ions (kH /kP = 1.4). The result for chloroform, (3 = 0.98 shown in Table 8, fits in satisfactorily with the most recent results for amine catalysed detritiation [171(a)] from which a value 3 = 1.15 0.07 was obtained. 

In the previous sections, it has heen demonstrated that both equilibrium and kinetic isotope effects can be well understood in terms of mass differences between different isotopes. However, there are some isotope effects that either do not depend on mass or exhibit an anomalous mass-dependence. 

In calculating the isotope effect, Bigeleisen considers all partition functions of translation and rotation, vibrational excitation, and vibrational zero-point energies. Complete analysis of a kinetic isotope effect may be carried out if the frequencies of all (3N-6) modes of the reagents and (3N-7) modes of the transition state are known (in the transition state, the stretching of the bond being broken is not a true vibration, but an anomalous one, with an imaginary frequency v ). 

Kurz, L.C. and Erieden, C. (1980). Anomalous equilibrium and kinetic alpha-deuterium secondary isotope effects accompanying hydride transfer from reduced nicotinamide adenine dinucleotide. J. Am. Chem. Soc. 102, 4198-4203... 

Competitive KIEs can reduce the uncertainty in prefactor isotope effects, and have been used to demonstrate tunneling in several enzymes [24, 36, 65]. As discussed above, the competitive, double-label, technique for measuring KIEs is inherently more precise than noncompetitive techniques, and can reduce the experimental uncertainty in the KIE on the Arrhenius prefactor and energy of activation. The use of tritium also provides multiple ratios Ah/At and Ad/At, which are helpful in resolving kinetic complexity [61]. It has been noted that a change in the rate-limiting step over the temperature range can lead to anomalous Arrhenius... 

The steady-state rate equation for the random mechanism will also simplify to the form of Eq. (1) if the relative values of the velocity constants are such that net reaction is largely confined to one of the alternative pathways from reactants to products, of course. It is important, however, that dissociation of the coenzymes from the reactant ternary complexes need not be excluded. Thus, considering the reaction from left to right in Eq. (13), if k-2 k-i, then product dissociation will be effectively confined to the upper pathway this condition can be demonstrated by isotope exchange experiments (Section II,C). Further, if kakiB kik-3 -f- kikiA, then the rate of net reaction through EB will be small compared with that through EA 39). The rate equation is then the same as that for the simple ordered mechanism, except that a is now a function of the dissociation constant for A from the ternary complex, k-i/ki, as well as fci (Table I). Thus, Eqs. (5), (6), and (7) do not hold instead, l/4> < fci and ab/ a b < fc-i, and this mechanism can account for anomalous maximum rate relations. In contrast to the ordered mechanism with isomeric complexes, however, the same values for these two functions of kinetic coefficients would not be expected if an alterna-... 

---