Transition states kinetic isotope effects

The essential features of the results and the mechanistic model can be summarized as follows (1) proton transfer occurs for n = 3 and 4 clusters in the state and is suggested to occur in the S0 state for n > 5, (2) no transfer is found for n < 3 clusters, (3) substitution of deuterium for hydrogen in these clusters [i.e., l-naphthol-d1(ND3)3] has dramatic effects on the observed transfer rates, (4) at the origin of the St - S0 transition the kinetic isotope effect is at least a factor of 20 (D+ transfer is slower than H+ transfer) but at an energy of 1400 cm -1 the kinetic isotope effect is about a factor of 6, (5) the proposed model for proton transfer in these clusters equates proton transfer with a simple barrier penetration... 

Deuterium substitution may give rise to important effects on the reaction kinetics. The maximum kinetic isotope effect is obtained when the bond is broken in the transition state (primary isotope effect). In reactions involving several stages, isotope effects can naturally be observed only if the bond to the isotope is broken in the rate-determining step . In this case, deuterium substitution would be expected to depress the reaction rate. We give below two examples relative to acetylenes, showing how the effect, kulkn, may specify the reaction process or, on the contrary, allow the rejection of a possible mechanism. 

Differences in the rate of mutarotation of sugars in water and in deuterium oxide provide a valuable means for studying mutarotation reactions.135,224,233 237,238 The difference in rates arises from a combination of kinetic and solvent isotope-effects, and is usually expressed as a ratio,knlkD, called the isotope effect. Kinetic isotope-effects are caused by differences in the energy required for alteration of the normal and the isotopic bonds in the corresponding transition states solvent isotope-effects can exist when the isotopic compound is used both as a reactant and as a solvent. 

Most isotope effects are attenuated from this value because reactions typically do not involve bonds that are completely broken in the transition state. An example of a reaction with a relatively large isotope effect is the hydroxylation reaction given in the Connections highlight on page 425. To understand any kinetic phenomenon, one always compares reactant with transition state. For isotope effects we compare the ZPEs of the various vibrations of the reactant and the activated complex. Usually the bond is only partially broken at the transition state, or another bond is starting to form at the transition state. Both of these will attenuate the isotope effect from that of total homolysis. To visualize this attenuation, we need to examine reaction coordinate diagrams and the associated vibrational modes. 

Melander first sought for a kinetic isotope effect in aromatic nitration he nitrated tritiobenzene, and several other compounds, in mixed acid and found the tritium to be replaced at the same rate as protium (table 6.1). Whilst the result shows only that the hydrogen is not appreciably loosened in the transition state of the rate-determining step, it is most easily understood in terms of the S 2 mechanism with... 

We now carry the argument over to transition state theory. Suppose that in the transition state the bond has been completely broken then the foregoing argument applies. No real transition state will exist with the bond completely broken—this does not occur until the product state—so we are considering a limiting case. With this realization of the very approximate nature of the argument, we make estimates of the maximum kinetic isotope effect. We write the Arrhenius equation for the R-H and R-D reactions... 

A more rigorous theory of kinetic isotope effects begins with the transition state equation k = (kTlh)K. Writing this for and ito leads to... 

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. 

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. 

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. 

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. 

A. Alkaline Hydrolysis. -The low kinetic isotope effect observed in the protonation of carbanions formed in phosphonium salt hydrolysis leads to the idea that there is little breaking of the phosphorus-carbon bond and correspondingly little transfer of a proton to the incipient carbanion in the transition state (87) of the rate-determining step. ... 

Beno, B. R., Houk, K. N., Singleton, D. A., 1996, Synchronous or Asynchronous An Experimental Transition State from a Direct Comparison of Experimental and Theoretical Kinetic Isotope Effects for a Diels-Alder Reaction , J. Am. Chem. Soc., 118, 9984. 

Today a good understanding of transition state structure can be obtained through a combination of experimental measurements of kinetic isotope effects (KIE) and computational chemistry methods (Schramm, 1998). The basis for the KIE approach is that incorporation of a heavy isotope, at a specific atom in a substrate molecule, will affect the enzymatic reaction rate to an extent that is correlated with the change in bond vibrational environment for that atom, in going from the ground state to the... 

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... 

A kinetic isotope effect 160/180 of 2% in the spontaneous hydrolysis of the 2,4-dinitrophenyl phosphate dianion, whose ester oxygen is labeled, suggests a P/O bond cleavage in the transition state of the reaction, and thus also constitutes compelling evidence for formation of the metaphosphate 66,67). The hydrolysis behavior of some phosphoro-thioates (110) is entirely analogous 68). 

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