Limiting isotope effect

ADDITIVITY PRINCIPLE LIMIT DEXTRAN LIMITING ISOTOPE EFFECT Limits,... 

One obtains then for the limiting isotope effect at very low pressure for an activated complex with 3 —7 real vibrations ... 

Consider an Ordered Bi Bi reaction depicted in Fig. 3. For deuterium effects, and if the exchangeable position is completely or nearly completely substituted by deuterium, one simply mns reciprocal plots with deuterated and hydrogen-containing molecules and takes the ratio of slopes as the V/K effect, and the ratio of the intercepts as the V effect. The computation of limiting isotope effects from apparent values requires extrapolation as a function of the cosubstrate concentration (Fig. 4). 

At low substrate concentrations, the observed isotope effect approaches iV/K), as the limiting isotope effect at zero substrate concentration. However, one can see from Eq. (17.19) that, if the reverse commitment to eatalysis becomes large, the reaction step containing the bond-breaking reaction nears a chemical equilibrium, and the isotope effect expressed on V/K approaches the value of the equihbrium isotope effect. Obviously, the lower the commitments to catalysis, the more fully the kinetic isotope effect wUl be expressed on V/K. 

Hence, Eq. (17.41), describing the limiting isotope effect on V/K, is independent of the concentration of A. In practice, what we do is to vary [B] at different levels of labeled or unlabeled [A] and determine (V/JCb) from the slope ratio this minimizes any external commitment factors. 

At high substrate concentrations, measured isotope effects approach governed by Eq. (17.23). For the Ordered Bi Bi mechanism in Fig. 3, a quotient of Rp (Eq. (17.24)) and Ep (Eq. (17.28)) becomes a complex expression (Eq. (17.29)) which can be substituted into Eq. (17.23) the resulting equation then becomes far too complex for a practical use (Northrop, 1982). For practical purposes, the extrapolation of apparent values of obtained at saturating concentrations of A, to saturating concentrations of B, will afford the limiting isotope effect on V. 

Similarly, for the limiting isotope effect on V, at low pH, approaches the limit ... 

To obtain the upper Mmit, ( kR)cALc can be calculated from data in the forward direction by first multiplying the limiting isotope effect by the equilibrium isotope effect, because... 

Similarly, comparing diminished internal to diminished limiting isotope effects provides a measure of the "stickiness" of substrates (Eqs. (17.36) and (17.37)). 

Alkenes lacking phenyl substituents appear to react by a similar mechanism. Both the observation of general acid catalysis and the kinetic evidence of a solvent isotope effect are consistent with rate-limiting protonation with simple alkenes such as 2-metlQ lpropene and 2,3-dimethyl-2-butene. 

This variation from the ester hydrolysis mechanism also reflects the poorer leaving ability of amide ions as compared to alkoxide ions. The evidence for the involvement of the dianion comes from kinetic studies and from solvent isotope effects, which suggest that a rate-limiting proton transfer is involved. The reaction is also higher than first-order in hydroxide ion under these circumstances, which is consistent with the dianion mechanism. 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

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 direct irreversible proton transfer in limiting stage of 1-ethoxybut- l-en-3-yne hydration is confirmed by the value of kinetic isotopic effect k ilk = 2.9. For fast reversible proton transitions this value is less than 1. 

Much evidence has been obtained in support of the El mechanism. For example, El reactions show first-order kinetics, consistent with a rate-limiting spontaneous dissociation process, l- urthermore, El reactions show- no deuterium isotope effect because rupture of the C—H (or C—D) bond occurs after the rate-limiting step rather than during it. Thus, we can t measure a rate difference between a deuterated and nondeuterated substrate. 

In the El reaction, C-X bond-breaking occurs first. The substrate dissociates to yield a carbocation in the slow rate-limiting step before losing H+ from an adjacent carbon in a second step. The reaction shows first-order kinetics and no deuterium isotope effect and occurs when a tertiary substrate reacts in polar, nonbasic solution. 

Deuterium isotope effect (Section 11.8) A tool used in mechanistic investigations to establish whether a C-H bond is broken in tbe rate-limiting step of a reaction. 

Dediazoniation does not show a significant solvent isotope effect ( h2o/ d2o = 0.98 0.01 Crossley et al., 1940 Swain et al., 1975 a). This result is definitely not consistent with a mechanism in which charge is built up on oxygen in the rate-limiting transition state, as expected for an ANDN-like process. 

If one limits the consideration to only that limited number of reactions which clearly belong to the category of nucleophilic aromatic substitutions presently under discussion, only a few experimental observations are pertinent. Bunnett and Bernasconi30 and Hart and Bourns40 have studied the deuterium solvent isotope effect and its dependence on hydroxide ion concentration for the reaction of 2,4-dinitrophenyl phenyl ether with piperidine in dioxan-water. In both studies it was found that the solvent isotope effect decreased with increasing concentration of hydroxide ion, and Hart and Bourns were able to estimate that fc 1/ for conversion of intermediate to product was approximately 1.8. Also, Pietra and Vitali41 have reported that in the reaction of piperidine with cyclohexyl 2,4-dinitrophenyl ether in benzene, the reaction becomes 1.5 times slower on substitution of the N-deuteriated amine at the highest amine concentration studied. 

It is claimed that the limiting value of k bs, 2.81 x 10" sec-1, represents the rate coefficient for the rearrangement reaction above (k,). The ring deuterium isotope effect kH kD was re-determined for this individual rate coefficient for rearrangement by finding the limiting value in the presence of added N-methylaniline and was found to be 2.4 at two different acidities, as compared with 1.7 for the ratio of the observed composite rate coefficients, as expected, since no isotope effect would be predicted for the de-nitrosation step. 

Apart from a few studies (ref. 7), the use of deuterium kinetic isotope effects (kie s) appears to have had limited use in mechanistic studies of electrophilic bromination of olefins. Secondary alpha D-kie s have been reported for two cases, trans-stilbene fi and p-substituted a-d-styrenes 2, these giving relatively small inverse kie s of... 

The experiments of Bott (17) and Noyce (19-21) show that a vinyl cation best represents the intermediate in the hydration of phenylacetylenes. In particular, the large solvent Isotope effects observed indicate a rate-limiting protonation and formation of a vinyl cation, for these values are not in agreement with solvent isotope effects observed for compounds which react by other possible mechanisms, such as one involving equilibrium formation of the vinyl cation followed by the slow attack by water. 

The evidence presented includes the observed solvent isotope effect of kHjSO./ DjSO =2.2-3.9, the high negative rho of -4.21, and the high negative entropies of activation (-27 e.u. to -35 e.u.). The negative entropy of activation is in line with values observed for other rate-limiting transfers to unsaturated carbons (29). 

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