Isotope-effect exponent

The compound Ceo is not itself a superconductor, but when alkali metals are added it becomes superconducting. The doped compound forms a face-centered cubic lattice with a lattice constant of 10.04 A, and this structure has two tetrahedral holes and one octahedral hole per Ceo molecule. If all of these holes are occupied by alkali metals A, the resulting compound is A Ceo- An example of such a compound is K2RbC6o with potassium in the smaller tetrahedral holes and rubidium in the larger octahedral holes. The transition temperatures of these doped fullerenes range from 19 to 47 K. The compound RbsCeo was found to have an isotope effect exponent a = 0.37, somewhat less than the BCS value 0.5. 

Limits proposed by Kohen and Jensen [39] should not be considered with the single-site Swain-Schaad values discussed in this section. Kohen and Jensen [39] proposed that a value of 4.8 be treated as an upper limit in a non-tunneling system for a secondary isotope effect exponent defined as in Section 11.5 describing mixed-label experiments. As shown in Section 11.5, it useful to separate these mixed-label exponents into two factors one that arises from H/D/T substitutions, and one that arises from isotopic substitution that amounts to an isotope effect on an isotope effect. Also note that it is not straightforward to convert a mixed-label exponent based on D/T isotope effects into one based on H/D isotope effects as Eq. (11.9) shows for single-site exponents. 

It was concluded that while kinetic isotope effects are much more sensitive than Bronsted exponents to variations in pKa, the use of either quantity as an index of transition state symmetry may be doubtful. 

Fig. 10.5 Distribution of exponents, Equation 10.21, for exact harmonic calculated equilibrium and TST kinetic isotope effects (Hirschi, J. and Singleton, D. A., J. Am. Chem. Soc. 127, 3294 (2005))...

Ah/At = 7.4 and A /Ax = 1.8 and isotopic activation energy differences that are within the experimental error of zero. The values of the two A-ratios correspond to a Swain-Schaad exponent of 3.4, not much different from the semiclassical expectation of 3.3. The a-secondary isotope effects are 1.19 (H/T), 1.13 (H/D), and 1.05 (D/T), which are exactly at the limiting semiclassical value of the equilibrium isotope effect. The secondary isotope effects generate a Swain-Schaad exponent of 3.5, again close to the semiclassical expectation. At the same time that the isotope effects are temperature-independent, the kinetic parameter shows... 

Bahnson et al. extended the series of mutations to include ones in which reductions occurred in the second-order rate constant / cat/ M by as much as a factor of 100. No substantial changes were observed in the primary isotope effects or their Swain-Schaad exponent. However, the precisely measured secondary isotope effects changed systematically as the rate constant decreased, such that the Swain-Schaad exponent decreased monotonically with decreasing fecat/ M from exponent of 8.5 for the L57F mutant (reactivity equivalent to the wild-type enzyme) to an exponent of 3.3 for the V203G mutant, slower by 100-fold. 

Fig. 6 Illustration from Chin and Klinman. Increased catalytic activity of horse-liver alcohol dehydrogenase in the oxidation of benzyl alcohol to benzaldehyde by NAD, measured by cat/ M (ordinate), correlates with the Swain-Schaad exponent for the -secondary isotope effect (abscissa), for which values above about four are indicators of tunneling. This is a direct test of the hypothesis that tunneling in the action of this enzyme contributes to catalysis. As the rate increases by over two orders of magnitude and then levels off, the anomalous Swain-Schaad exponents also increase and then level off. Reproduced from Ref. 28 with the permission of the American Chemical Society.

Rp is an exponent that describes the relationship of a primary isotope effect with H in the secondary position to a primary isotope effect with D in the secondary position. Rs is an exponent that describes the relationship of a secondary isotope effect with H in the primary position to a secondary isotope effect with D in the primary position. According to the Rule of the... 

The observation of a primary tritium isotope effect (H/T) that is substantially larger than the value predicted on the basis of the semiclassical Swain-Schaad relation (Chart 3) from a heavy-hydrogen (DAT) isotope effect. The same information can be expressed in terms of a Swain-Schaad exponent required to relate the two isotope effects that is substantially larger than the semiclassical value of 3.26. 

In order to understand these extreme changes in physical and chemical properties of hydrogen-bonded systems, first attempts to model their dynamics were related to rather simple structures, as exhibited by the KDP family or squaric acid and its analogues. The isotope effects on their ferro- or anti-ferroelectric transition temperatures are listed in Table 1 together with the corresponding isotope exponent. 

Table 1 Isotope effects and exponent a various hydrogen-bonded systems on the ferroelectric transition temperatiu es for...

Kinetic isotope effects and Bronsted exponents / A i Ha, for the third-order rate constants for a set of carboxylic acid-carboxylate ion buffers seem to be... 

The Bruno and Bialik, (1992) theory which takes into account nuclear tunneling (Section 4.2.1), was applied to an analysis of anomalous Schaad-Swain exponents in a reaction catalyzed by bovine serum amine oxidase, BSAO (Grant and Klinman, 1989). The isotope effect in this reaction is found to be markedly larger than one, expected classically. Theoretical values of H/T and D/T KIFs and its temperature dependence match Grant and Klinman s experimental data. 

Experimental data on primary and secondary kinetic isotope effects in the hydride-transfer step in liver alcohol dehydrogenase, LADH, were analyzed using canonical variational transition theory (CVT) for overbarrier dynamics and the optimized multidimentional path (OMT) for the nuclear tunneling (Alhambra et al., 2000 and references therein). This work demonstrates somewhat better agreement of theoretical values of primary and secondary Schaad- Swein exponents calculated by combining CVT/OMT methods with the experimental values instead of CVT and classical transition states (TST). 

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