Rate constants isotope effects

It has been previously noted that the first quantum correction to the classical high temperature limit for an isotope effect on an equilibrium constant is interesting. Each vibrational frequency makes a contribution c[>(u) to RPFR and this contribution can be expanded in powers of u with the first non-vanishing term proportional to u2/24, the so called first quantum correction. Similarly, for rates one introduces the first quantum correction for the reduced partition function ratios, includes the Wigner correction for k /k2 and makes use of relations like Equation 4.103 for small x and small y, to find a value for the rate constant isotope effect (omitting the noninteresting symmetry number term)... 

The origin of the isotope effect is the dependence of coq and co on the reacting particle mass. Classically, this dependence comes about only via the prefactor coq [see (2.14)], and the ratio of the rate constants of transfer of isotopes with masses mj and m2 m2 > mj) is temperature-independent and equal to... 

The second-order rate constants for hydration and the kinetic solvent isotope effect for hydration of several 2-substituted 1,3-butadienes ate given below. Discuss the information these data provide about the hydration mechanism. 

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-... 

Realizing that the last four reactions of the ion-atom interchange mechanism listed each have only one-half the statistical probability of occurring as do the first four and assuming no isotope effect on the rate constants, we can write the following set of rate equations ... 

At this point several assumptions must be made. The first requires the absence of isotope effects on the rate of Reaction O—i.e., the rate constants of Reactions O, U + V, and W are identical this is termed k, and the plausibility of the assumption is indicated by the absence of isotope effects on the rate constant of Reaction I. The second assumption requires that in proton transfer reactions like Reaction O, a deuteron... 

The lack of steric effects in oxidations of hydrocarbons by Cr(VI) renders D and E unacceptable. The activated complex of scheme C is non-linear and hence does not comply with the magnitude of the observed isotope effect. Two pieces of evidence are quoted which indicate A to be the more probable of the remaining two. Firstly, the p constant of —1.17 is more in agreement with that obtained for bromine atom abstraction from toluenes (—1.369 to —1.806) than those found for solvolyses involving electron-deficient carbon ( — 2.57 to —4.67) . Secondly, the correlation between the relative rates of oxidation of the series... 

Kinetic data exist for all these oxidants and some are given in Table 12. The important features are (i) Ce(IV) perchlorate forms 1 1 complexes with ketones with spectroscopically determined formation constants in good agreement with kinetic values (ii) only Co(III) fails to give an appreciable primary kinetic isotope effect (Ir(IV) has yet to be examined in this respect) (/ ) the acidity dependence for Co(III) oxidation is characteristic of the oxidant and iv) in some cases [Co(III) Ce(IV) perchlorate , Mn(III) sulphate ] the rate of disappearance of ketone considerably exceeds the corresponding rate of enolisation however, with Mn(ril) pyrophosphate and Ir(IV) the rates of the two processes are identical and with Ce(IV) sulphate and V(V) the rate of enolisation of ketone exceeds its rate of oxidation. (The opposite has been stated for Ce(IV) sulphate , but this was based on an erroneous value for k(enolisation) for cyclohexanone The oxidation of acetophenone by Mn(III) acetate in acetic acid is a crucial step in the Mn(II)-catalysed autoxidation of this substrate. The rate of autoxidation equals that of enolisation, determined by isotopic exchange , under these conditions, and evidently Mn(III) attacks the enolic form. 

Investigation of water motion in AOT reverse micelles determining the solvent correlation function, C i), was first reported by Sarkar et al. [29]. They obtained time-resolved fluorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles. Das et al. [37] reported that the solvation dynamics of D2O is 1.5 times slower than H2O motion. 

The deuterium kinetic isotope effect between BH3-THF and BD3-THF was obtained by measuring the reaction rate constants of the two reactions with the unsaturated sulfoxide (Sj-40 independently via React-IR. The k(BH3)/k(BD3) is 1.4, consistent with hydrogen transfer not being the rate-limiting step [15, 16]. 

The reactions of the bare sodium ion with all neutrals were determined to proceed via a three-body association mechanism and the rate constants measured cover a large range from a slow association reaction with NH3 to a near-collision rate with CH3OC2H4OCH3 (DMOE). The lifetimes of the intermediate complexes obtained using parameterized trajectory results and the experimental rates compare fairly well with predictions based on RRKM theory. The calculations also accounted for the large isotope effect observed for the more rapid clustering of ND3 than NH3 to Na+. 

Needless to say, an analysis which will finally allow one to nail down all rates, activation parameters, and equilibrium constants requires a large amount of precise and reliable kinetic data from appropriate experiments, including the determination of isotope effects and the like, as well as a rather sophisticated treatment and solution of the complete kinetic scheme. Then a comparison is necessary between various organosilanes with different types of C-H and C-Si bonds as well as the comparison between the dtbpm and the dcpm ligand systems, not to speak of model calculations in order to understand the molecular origin of the kinetic and thermodynamic numbers. We are presently in the process of solving these problems. 

As an example, consider an early calculation of isotope effects on enzyme kinetics by Hwang and Warshel [31]. This study examines isotope effects on the catalytic reaction of carbonic anhydrase. The expected rate-limiting step is a proton transfer reaction from a zinc-bound water molecule to a neighboring water. The TST expression for the rate constant k is... 

Reactions of eh with H and OH were once considered diffusion-controlled see, however, Elliot et al. (1990). The rate constants, 2.5—3.0 x 1010 M-1s 1 (see Table 6.6), are high. In both cases, a vacancy exists in the partially filled orbitals of the reactants into which the electron can jump. Thus, hydrogen formation by the reaction eh + H may be visualized in two steps (Hart and Anbar, 1970) eh + H—H, followed by H + H20— OH" This reaction has no isotope effect, which is consistent with the proposed mechanism. The rate of reaction with OH is obtained from the eh decay curve at pH 10.5 in the absence of dissolved hydrogen or oxygen, where computer analysis is required to take into account some residual reactions. At higher pH (>13), OH exists as O- and the rate of eh + O—"02 has been measured as 2.2 x 1010 M-1s-1. 

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