The Kinetic Isotope Effect

Statistical thermodynamics can be used to explain the effect of isotopic substitution on equilibrium constants. Similarly the statistical theory of reaction rates provides a basis for understanding isotope effects in rate constants. Consider a prototype atom-molecule reaction 

The partition functions are determined by nuclear motion on the potential-energy surfaces for the BC molecule or the ABC complex, and the activation energy is the potential step required to traverse the lowest energy path on the ABC surface. The phenomenon is a direct manifestation of quantum mechanics. In the classical limit (massive species) the ratio is 1. 

Simplification of (9.22) is based on the fact that the potential-energy surface is the ground state for electronic motion in a charge distribution determined by the nuclear configuration. Since isotopes have the same nuclear charge, the potential-energy surface is unaffected by isotopic substitution. As a consequence the classical barrier height is isotope independent and (9.22) becomes 

Furthermore the shape of the surface in the reactant valley and at the saddle point is not changed. The force constants for nuclear motion in either region are invariants. Knowledge of the moments of inertia and vibrational frequencies of one isotopic species allows computation of the same quantities for any other. For a diatomic molecule like BC the results are particularly simple 

Similar, but more complicated, expressions can be found relating the properties of any molecular species. 

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Consider the kinetic isotope effect that would be observed in the reaction of semicarbazide with benzaldehyde ... 

When one of the ortho hydrogens is replaced by deuterium, the rate drops from 1.53 X 10 " s to 1.38 X lO s. What is the kinetic isotope effect The product from such a reaction contains 60% of the original deuterium. Give a mechanism for this reaction that is consistent with both the kinetic isotope effect and the deuterium retention data. 

Indicate mechanisms that would account for the formation of each product. Show how the isotopic substitution could cause a change in product composition. Does your mechanism predict that the isotopic substitution would give rise to a primary or secondary deuterium kinetic isotope effect Calculate the magnitude of the kinetic isotope effect from the data given. 

B synchronously moving away from and toward H the H atom does not move (if A and B are of equal mass). If H does not move in a vibration, its replacement with D will not alter (he vibrational frequency. Therefore, there will be no zero-point energy difference between the H and D transition states, so the difference in activation energies is equal to the difference in initial state zero-point energies, just as calculated with Eq. (6-88). The kinetic isotope effect will therefore have its maximal value for this location of the proton in the transition state. 

If the proton is not equidistant between A and B, it will undergo some movement in the symmetric stretching vibration. Isotopic substitution will, therefore, result in a change in transition state vibrational frequency, with the result that there will be a zero-point energy difference in the transition state. This will reduce the kinetic isotope effect below its maximal possible value. For this type of reaction, therefore, should be a maximum when the proton is midway between A and B in the transition state and should decrease as H lies closer to A or to B. 

A distinction between these four possibilities can be made on the basis of the kinetic isotope effect. There is no isotope effect in the arylation of deuterated or tritiated benzenoid compounds with dibenzoyl peroxide, thereby ruling out mechanisms in which a C5— bond is broken in the rate-determining step of the substitution. Paths (ii) and (iii,b) are therefore eliminated. In path (i) the first reaction, Eq. (6), is almost certain to be rate-determining, for the union of tw o radicals, Eq. (7), is a process of very low activation energy, while the abstraction in which a C—H bond is broken would require activation. More significant evidence against this path is that dimers, Arz, should result from it, yet they are never isolated. For instance, no 4,4 -dinitrobiphenyl is formed during the phenylation of... 

The mechanism proposed for the production of radicals from the N,N-dimethylaniline/BPO couple179,1 involves reaction of the aniline with BPO by a Sn-2 mechanism to produce an intermediate (44). This thermally decomposes to benzoyloxy radicals and an amine radical cation (46) both of which might, in principle, initiate polymerization (Scheme 3.29). Pryor and Hendrikson181 were able to distinguish this mechanism from a process involving single electron transfer through a study of the kinetic isotope effect. 

Important additional evidence for aryl cations as intermediates comes from primary nitrogen and secondary deuterium isotope effects, investigated by Loudon et al. (1973) and by Swain et al. (1975 b, 1975 c). The kinetic isotope effect kH/ki5 measured in the dediazoniation of C6H515N = N in 1% aqueous H2S04 at 25 °C is 1.038, close to the calculated value (1.040-1.045) expected for complete C-N bond cleavage in the transition state. It should be mentioned, however, that a partial or almost complete cleavage of the C — N bond, and therefore a nitrogen isotope effect, is also to be expected for an ANDN-like mechanism, but not for an AN + DN mechanism. 

The kinetic isotope effect with 2-naphthol-8-sulfonic acid in Table 12-3 was reported only three years later (Ernst et al., 1958) based on a suggestion of P.D. Bartlett. That paper was publication no. 1 of the first-mentioned author. At that time he was an ETH student. He obtained the Nobel Prize 33 years later for his work on NMR spectroscopy ... 

The kinetic isotope effect will thus be observed when k 2lk 1 is small this will be occasioned by low reactivity of the reagents, and steric hindrance to reaction. 

Grovenstein and Kilby218 showed that the kinetic isotope effect kH/kD is 3.97 for the iodination 2,4,6-trideuterophenol by iodine in aqueous buffer at 25 °C, and this is in accord with the base catalysis described above. However, this large isotope effect means that the intermediate is in fairly rapid equilibrium with the reactants, so that it is difficult to determine from kinetic studies which iodinating species is involved. Thus it might be positive iodine, equilibria (112), (113), (115)... 

The kinetic isotope effect kD kT for hydrogen exchange of ferrocene in both trifluoroacetic acid-acetic acid and trifluoroacetic acid-dichloromethane has been measured558. In the former medium (1 1 molar ratio at 25 °C) kD kT was 1.2—1.3, which was less than that obtained for the 2 position of thiophene (D) = 1,200 xlO-7, ki(T) = 660xl0-7, kD kT = 1.9. It is also lower than that obtained for pentamethylbenzene fcx(D) = 3,300 x 10-7, Art(T) =... 

A recent paper by Leffek and Matheson (1971) nicely complements this work, as it describes the results of a careful investigation of the temperature dependence of the kinetic isotope effect in the reaction studied by Kaplan and Thornton (1967). It is found that AAH = 134 + 30 cal mol and dd/S = 0-15 + 0-09 cal mol deg , demonstrating that the isotope effect is primarily due to an enthalpy difference, and providing support for the steric interpretation suggested by Kaplan and Thornton (1967). 

The kinetic isotope effect of the protonation h/ d = 3.9 suggests that an in-nitrogen atom is protonated directly rather than conformational changes exposing the lone pair of a nitrogen atom to the outside prior to protonation. It is assumed that a protonated nitrogen does not invert. Inversion is only possible by a deprotonation-inversion-reprotonation sequence (Kjaer etal., 1979). 

Transition state theory has been useful in providing a rationale for the so-called kinetic isotope effect. The kinetic isotope effect is used by enzy-mologists to probe various aspects of mechanism. Importantly, measured kinetic isotope effects have also been used to monitor if non-classical behaviour is a feature of enzyme-catalysed hydrogen transfer reactions. The kinetic isotope effect arises because of the differential reactivity of, for example, a C-H (protium), a C-D (deuterium) and a C-T (tritium) bond. 

The electronic, rotational and translational properties of the H, D and T atoms are identical. However, by virtue of the larger mass of T compared with D and H, the vibrational energy of C-H> C-D > C-T. In the transition state, one vibrational degree of freedom is lost, which leads to differences between isotopes in activation energy. This leads in turn to an isotope-dependent difference in rate - the lower the mass of the isotope, the lower the activation energy and thus the faster the rate. The kinetic isotope effects therefore have different values depending on the isotopes being compared - (rate of H-transfer) (rate of D-transfer) = 7 1 (rate of H-transfer) (rate of T-transfer) 15 1 at 25 °C. 

One-step hydroxylation of aromatic nucleus with nitrous oxide (N2O) is among recently discovered organic reactions. A high eflSciency of FeZSM-5 zeolites in this reaction relates to a pronounced biomimetic-type activity of iron complexes stabilized in ZSM-5 matrix. N2O decomposition on these complexes produces particular atomic oj gen form (a-oxygen), whose chemistry is similar to that performed by the active oxygen of enzyme monooxygenases. Room temperature oxidation reactions of a-oxygen as well as the data on the kinetic isotope effect and Moessbauer spectroscopy show FeZSM-5 zeolite to be a successfiil biomimetic model. 

Interestingly, in a comparison of the CD3 and CHj carbenes, an unusual temperature dependence of the kinetic isotope effect was observed. In contrast to typical reactions, the ratio of rates of H versus D shift, k /ko, actually increased as temperature was raised. In fact, k was measured to be larger than k at 248 K. It was suggested that these results required a normal temperature dependence of the isotope effect for the classical component of the reaction, but an unusual diminished isotope effect for the QMT reaction. 

Specifically, following the rate expression of QTST in Eq. (4-1) and assuming the quantum transmission coefficients the dynamic frequency factors are the same, the kinetic isotope effect between two isopotic reactions L and H is rewritten in terms of the ratio of the partial partition functions at the centroid reactant and transition state... 

Transfer hydrogenolysis of benzyl acetate was studied on Pd/C at room temperature using different formate salts.244 Hydrogen-donating abilities were found to depend on the counterion K+ > NH4 + > Na+ > Li+ > H+. Formate ion is the active species in this reaction. Adsorption of the formate ion on the Pd metal surface leads to dissociative chemisorption resulting in the formation of PdH- and C02. The kinetic isotope effect proves that the dissociative chemisorption of formate is the rate-limiting step. The adsorption and the surface reaction of benzyl acetate occurs very rapidly. 

German ED, Kuznetsov AM, Dogonadze RR (1980) Theory of the kinetic isotope effect in proton transfer reactions in a polar medium. J Chem Soc, Faraday Trans 2 76 1128-1146... 

Corey et al. investigated the kinetic isotopic effect (KIE) in asymmetric dihydroxylation. 12C/13C KIE was measured for the dihydroxylation of styrene, p-nitrostyrene, and 4-methoxy-benzoate (Figure 7).197 The observed similar 12C/13C isotopic effect of two olefinic carbons... 

The kinetic isotope effect proves the attack of ozone on the C—H bond and consequently the C—D bond of the oxidized compound. The values of the kinetic isotope effect (kH/kD) are collected in Table 3.6. 

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