Kinetic isotope effects apparent

Despite its apparent simplicity, the PK pyrrole synthesis has retained its mystique since being discovered. Several investigations into the PK mechanism have been reported, including a gas phase study. Current evidence (intermediate isolation, kinetics, isotope effects) suggests the following (abbreviated) mechanism for the formation of pyrrole 13. However, the specific PK mechanism is often dependent on pH, solvent, and amine and dicarbonyl structure, especially with regard to the ringclosing step. 

It is apparent from equation (16) that if k x becomes much larger than k 2, the rate will depend upon k 2 and so a kinetic isotope effect will be observed. Now kL j will become large if there is steric hindrance to formation of the intermediate, and a number of examples are now known where an electrophile which normally gives no isotope effect, does so if formation of the intermediate is hindered. 

For the exchanges carried out in liquid ammonia, kinetic isotope effects kD kT of 2.3-2.5 have been obtained for reaction of benzene, toluene, and naphthalene and for the reactions of the 2 positions of furan and thiophene with -butoxide in dimethyl sulphoxide somewhat lower values, 1.5 and 1.3, respectively, were obtained591, but whether this was a solvent or a substituent effect is not apparent from the data. 

Using the various simplifications above, we have arrived at a model for reaction 11.9 in which only one step, the chemical conversion occurring at the active site of the enzyme characterized by the rate constant k3, exhibits the kinetic isotope effect Hk3. From Equations 11.29 and 11.30, however, it is apparent that the observed isotope effects, HV and H(V/K), are not directly equal to this kinetic isotope effect, Hk3, which is called the intrinsic kinetic isotope effect. The complexity of the reaction may cause part or all of Hk3 to be masked by an amount depending on the ratios k3/ks and k3/k2. The first ratio, k3/k3, compares the intrinsic rate to the rate of product dissociation, and is called the ratio of catalysis, r(=k3/ks). The second, k3/k2, compares the intrinsic rate to the rate of the substrate dissociation and is called forward commitment to catalysis, Cf(=k3/k2), or in short, commitment. The term partitioning factor is sometimes used in the literature for this ratio of rate constants. 

The third equation in Equation 11.47 represents a kinetic isotope effect of the first isotopomer pair measured in the presence of the second (which IE has perturbed the commitment). In order to make the changes in apparent commitment (cf/H2k3) sufficiently pronounced, deuterium is usually selected as the second isotope (H2). The first, (HI), on the other hand, is usually a heavy-atom (e.g. 13C, lsO, etc.). Most frequently this approach has been used for carbon kinetic isotope effects in which case Equation 11.47 becomes ... 

If the isotope sensitive step is reversible the equations get more complicated and cannot be solved explicitly for the intrinsic isotope effects (unless Cf = 0, or the equilibrium isotope effect is unity). The last two equations in Equation 11.48 demonstrate that a normal deuterium kinetic isotope effect diminishes the apparent commitment if both isotopes are present. Thus 13(V/K) is smaller than 13(V/K)d when both isotope effects are related to the same step. 

In the earliest work, Krouse and Thode (1962) found the Se isotope fractionation factor Sse(iv)-se(o) to bc 10%o ( l%o) with hydroxylamine (NH2OH) as the reductant. Rees and Thode (1966) obtained a larger value, 12.8%o, for reduction by ascorbic acid. Webster (1972) later obtained 10%o for NHjOH reduction. Rashid and Krouse (1985) completed a more detailed study, and found that the fractionation factor varied with time over the course of the experiments. They explained the variations observed among the experiments in all four studies using a model in which reduction consists of two steps. With the rate constant of the second step two orders of magnitude smaller than the first, and kinetic isotope effects of 4.8%o and 13.2%o for the hrst and second steps, respectively, all the data (Table 3) were fit. Thus, kinetic isotope effects of apparently simple abiotic reactions can depend on reaction conditions. 

C kinetic isotope effects (A ( C)/ ( C)) are more difficult to measure accurately. The values for a variety of metal ion-catalyzed decarboxylations of oxaloacetate (2.113) are similar (1.04-1.05). This suggests that the transition state for decarboxylation (a) involves a marked breakage of the C — C bond and (b) is similar for the various metal ions, even though enhancement rates vary widely. This apparent paradox is ascribed to an alteration of the distribution of oxaloacetate between the keto and enol forms. ... 

Participation of the hydride-formyl equilibrium in (16) is also plausible in light of an apparent inverse kinetic deuterium isotope effect for the catalytic process. Use of deuterium gas instead of hydrogen (cf. Expts. 6 and 4 in Table II) causes an increased rate, with kH/k = 0.73 (37). The existence of an isotope effect implies that hydrogen atom transfer occurs before or during the rate-determining step, and an inverse kinetic isotope effect may be possible in the case of a highly endothermic, product-like transition state (73). On the other hand, Bell has concluded that inverse kinetic isotope... 

Apparent activation energies and kinetic isotope effects using the reaction order approach... 

In eqn. (54),feapp was considered to be a constant. In the determination of apparent activation energies and kinetic isotope effects, it is the variations in feapp as reflected in variations in vc with temperature or isotopic substitution while the concentrations are held constant that must be determined. The appropriate relationship becomes... 

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