Internal isotope effect

The differences in rate for the two positions of naphthalene show clearly that an additional-elimination mechanism may be ruled out. On the other hand, the magnitude of the above isotope effect is smaller than would be expected for a reaction involving rate-determining abstraction of hydrogen, so a mechanism involving significant internal return had been proposed, equilibria (239) and (240), p. 266. In this base-catalysed (B-SE2) reaction both k and k 2 must be fast in view of the reaction path symmetry. If diffusion away of the labelled solvent molecule BH is not rapid compared with the return reaction kLt a considerable fraction of ArLi reacts with BH rather than BH, the former possibility leading to no nett isotope effect. Since the diffusion process is unlikely to have an isotope effect then the overall observed effect will be less than that for the step k. ... 

The lack of a substrate isotope effect suggests very extensive internal return and is readily explained in terms of the fact that conversion of the hydrocarbon to the anion would require very little structural reorganisation. Since koba = k 1k 2/(kLl+k 2) and k 2 is deduced as > k2, then kobs = Kk 2, the product of the equilibrium constant and the rate of diffusion away of a solvent molecule, neither of the steps having an appreciable isotope effect. If the diffusion rates are the same for reactions of each compound then the derived logarithms of partial rate factors (above) become pAT differences between benzene and fluorobenzene hydrogens in methanol. However, since the logarithms of the partial rate factors were similar to those obtained with lithium cyclohexylamide, a Bronsted cor-... 

Collisions at low ion energies (where Equation 1 can be applied) lead to a short-lived complex between the ion and the molecule—i.e., both collision partners move with the same linear velocity in the direction of the incident ion. The decay of the complex may be described by the theory of unimolecular rate processes if its excess energy can fluctuate between the various internal degrees of freedom. For example, the isotope effect in the reaction of Ar+ with HD may be explained by the properties of... 

Trager, W.F. (1988). Isotope effects as mechanistic probes of cytochrome P450-catalysed reactions. In Synthesis and Application of Isotopically Labelled Compounds Proceedings of the Third International Symposium T.A. Baillie and J.R. Jones (Eds.) Amsterdam Elsevier 333-340. 

Any mechanism which involves isoenergetic, radiationless internal conversion from C, P, or T to a high vibrational level of the ground state would be expected to show a large deuterium isotope effect on the rate of internal conversion. In the direct photolysis of perdeuterio and perhydrostilbene, Saltiel<8a) found no isotope effect on the photostationary state or upon the quantum yields of cis-to-trans and trans-to-cis conversion. 

The first factor is responsible for normal isotope effects, which arise because the bonds being affected by deuteriation are weakened in the transition state, but the absolute effect is greater on the bonds to deuterium rather than protium because the former have higher vibrational frequencies (typically by a factor of ca 1.37). This factor essentially reflects zero-point energy effects, so it becomes progressively more important at lower internal energies. 

The Bartell mechanical model has also been used to estimate the isotope effect on molar volume due to the over all motion (i.e. hindered translation) of molecules interacting in a Lennard-Jones potential. For C6H6/C6D6 one finds AV/V 4 x 10-5, about two orders of magnitude smaller than the contribution of the internal modes (and experiment). We conclude that for all but very light molecules this contribution can be neglected. 

If the cell is well supplied with nutrients, then the production of activated enzyme is great and this step is relatively fast. If the transport of sulfate into the cell cannot keep up with the reduction of sulfate, the concentration of sulfate within the cell becomes small, and very little of the isotopically fractionated sulfate inside the cell can leak back out of the cell. Thus, the effect of the internal isotopic fractionation on the outside world is minimal and the overall fractionation of the process is small. In a hypothetical extreme case, every sulfate anion entering the cell would be consumed by reduction. This would require a complete lack of isotopic fractionation, because when all S atoms entering are consumed, there can be no selection of light vs. heavy isotopes. The isotopic fractionation of the overall reduction reaction would be equal to that which occurs during the diffusion step only. 

Fig. 2.17. Calculated fcn(E) and d(E) curves for the a-cleavage of deuterated amine molecular ions. The curves can be regarded as parallel over a small range of internal energies, but they are not in the strict sense. They may even cross to cause inverse isotope effects in the domain of highly excited ions. Reproduced from Ref. [76] with permission. John Wiley Sons, 1991.

Also, a rigorous treatment of isotope effects within the framework of QET reveals that the assumption /muZ/mD = hZZ d represents a simplification. [69] It is only valid for when the species studied populate a small internal energy distribution, e.g., as metastable ions do, whereas wide internal energy distributions, e.g., those of ions fragmenting in the ion source after 70 eV electron ionization, may cause erroneous results. This is because the fc(E) functions of isotopic reactions are not truly parallel, [76] but they fulfill this requirement over a small range of internal energies (Figs. 2.17 and 2.18)... 

Secondary kinetic isotope effects are observed if an isotopic label is located adjacent to or remote from the bond that is being broken or formed during the reaction. Again, these depend on the internal energy of the decomposing ions. Secondary kinetic isotope effects, 4ec, are generally much smaller than their primary analogues. 

Example The ratio [M-CH3]V[M-CD3] from isopropylbenzene molecular ions decomposing by benzylic cleavage (Chap. 6.4) varied from 1.02 for ion source fragmentations (70eVEI) over 1.28 for metastable ions in the FFR to 1.56 in the 2 FFR, thus clearly demonstrating the dependence of the secondary kinetic isotope effect on internal energy. [77]... 

Howe, I. McLafferty, F.W. Unimolecular Decomposition of Toluene and Cyclohep-tatriene Molecular Ions. Variation of the Degree of Scrambling and Isotope Effect with Internal Energy. J. Am. Chem. Soc. 1971,93,99-105. 

Nacson, S. Harrison, A.G. Dependence of Secondary Hydrogen/Deuterium Isotope Effects on Internal Energy. Org. Mass Spectrom. 1985,20,429-430. 

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