Activation energy kinetic isotope effects

More elaborate and ambitious studies on the dissolution reactions of silica were conducted by Xiao and Lasaga (1994, 1996). Their objective was to provide full descriptions of the reaction pathway of quartz dissolution in acidic and basic solutions, from the adsorption of H2O or OH on a site, the formation of possible reaction intermediates and transition states, to the hydrolysis of the Si-O-Si bonds. Also, their aim was to extract kinetic properties such as changes in activation energy, kinetic isotope effects, catalytic and temperature effects, and the overall rate law form. The reaction mechanisms investigated were... 

Zero point energy kinetic isotope effects lie exclusively in the energy of activation, so that rate-ratios have the form of equation 1.13, where AA(ZPE) is... 

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. 

Calculate the difference in activation energies corresponding to a primary kinetic isotope effect of kyi/ko = 7 at 25°C. 

A distinction between these four possibilities can be made on the basis of the kinetic isotope effect. There is no isotope effect in the arylation of deuterated or tritiated benzenoid compounds with dibenzoyl peroxide, thereby ruling out mechanisms in which a C5— bond is broken in the rate-determining step of the substitution. Paths (ii) and (iii,b) are therefore eliminated. In path (i) the first reaction, Eq. (6), is almost certain to be rate-determining, for the union of tw o radicals, Eq. (7), is a process of very low activation energy, while the abstraction in which a C—H bond is broken would require activation. More significant evidence against this path is that dimers, Arz, should result from it, yet they are never isolated. For instance, no 4,4 -dinitrobiphenyl is formed during the phenylation of... 

However, measurements of substituent effects supported the hypothesis that the aryl cation is a key intermediate in dediazoniations, provided that they were interpreted in an appropriate way (Zollinger, 1973a Ehrenson et al., 1973 Swain et al., 1975 a). We will first consider the activation energy and then discuss the influence of substituents, as well as additional data concerning the aryl cation as a metastable intermediate (kinetic isotope effects, influence of water acitivity in hydroxy-de-di-azoniations). Finally, the cases of dediazoniation in which the rate of reaction is first-order with regard to the concentration of the nucleophile will be critically evaluated. 

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. 

Based on C-H versus C-D zero point vibrational differences, the authors estimated maximum classical kinetic isotope effects of 17, 53, and 260 for h/ d at -30, -100, and -150°C, respectively. In contrast, ratios of 80,1400, and 13,000 were measured experimentally at those temperatures. Based on the temperature dependence of the atom transfers, the difference in activation energies for H- versus D-abstraction was found to be significantly greater than the theoretical difference of 1.3kcal/mol. These results clearly reflected the smaller tunneling probability of the heavier deuterium atom. 

Experimental studies of the oxidative cleavage of cinnamic acid by acidic permanganate [35] resulted in secondary kinetic isotope effects, kn/kp, of 0.77 (a) and 0.75 (P), while another paper from the same group on the same reaction with quaternary ammonium permanganates [36] reported very different isotope effects of 1.0 (a) and 0.91 - 0.94 (P) depending on the counterion. Different mechanisms were discussed in the literature [37, 38] to explain the variety of experimental results available, but the mechanistic issues were unresolved. The reported activation energy for the oxidation of... 

It can be concluded that the [3+2] pathway seems to be the only feasible reaction pathway for the dihydroxylation by permanganate. The study on the free activation energies for the oxidation of a. P unsaturated carboxylic acids by permanganate shows that the [3+2] mechanism is in better agreement with experimental data than the [2+2] pathway. Experimentally determined kinetic isotope effects for cinnamic acid are in good agreement with calculated isotope effects for the [3+2] pathway, therefore it can be concluded that a pathway via an oxetane intermediate is not feasible. 

Kinetic isotope effect studies have contributed greatly to our understanding of the details of C-H activation by these types of metal complexes. The simplest energy scheme for kinetic isotope effects is presented schematically in Figure 19.7. 

Fig. 2.16. Origin of kinetic isotope effects. [4,5,66] The change in vibrational frequencies, and thus in density of states causes somewhat higher activation energy and consequently smaller excess energy for the reaction of the deuterated bond, and thus reduces kxj.

Hydrogen abstraction from propan-2-ol and propan-2-ol- /7 by hydrogen and deuterium atoms has been studied by pulsed radiolysis FT-ESR. A secondary kinetic isotope effect was observed for H (D ) abstraction from the C—H (C—D) bonds. The results were compared with ab initio data. In similar work, the kinetic isotope effects in H and D abstraction from a variety of other alcohols in aqueous solvents have been measured. It was found that, compared with the gas phase, the reactions exhibit higher activation energies in agreement with the ability of solvation to decrease the dipole moment from the reactant alcohol to the transition state. 

The kinetic isotope effect (KIE) produced in the photorearrangement of 4-me-thoxyphenyl acetate to 2-hydroxy-5-methoxyacetophenone has been measured by determining the isotope ratios before and after irradiation (k, and ka, respectively) in the starting material and the rearranged products. A value of KIE = kjk, different from unity would indicate that the rearrangement proceeds along an activation energy barrier. This is neither the case for the [48,49] nor for the case of isotope, both included in the carbonyl moiety [49]. In fact, the obtained values are KIE ( C) = 0.9988 0.0051 and KIE ( 0) = 1.0000 0.0023. 

Arnett and coworkers later examined the reaction of lithium pinacolone enoiate with substituted benzaldehydes in THE at 25 °C. The determination of the heat of reaction indicated that the Hammett p value for the process is 331. Although the aldol reaction was instantaneous in THF at 25 °C, the reaction with o- or p-methylbenzaldehyde could be followed using a rapid injection NMR method in methylcyclohexane solvent at —80 °C. Application of Eberson s criterion based on the Marcus equation, which relates the free energy of ET determined electrochemically and the free energy of activation determined by kinetics, revealed that the barriers for the ET mechanism should be unacceptably high. They concluded that the reaction proceeds via the polar mechanism . Consistent with the polar mechanism, cyclizable probe experiments were negative . The mechanistic discrepancy between the reactions of benzaldehyde and benzophenone was later solved by carbon kinetic isotope effect study vide infraf. ... 

Quantum chemical calculations need not be limited to the description of the structures and properties of stable molecules, that is, molecules which can actually be observed and characterized experimentally. They may as easily be applied to molecules which are highly reactive ( reactive intermediates ) and, even more interesting, to molecules which are not minima on the overall potential energy surface, but rather correspond to species which connect energy minima ( transition states or transition structures ). In the latter case, there are (and there can be) no experimental structure data. Transition states do not exist in the sense that they can be observed let alone characterized. However, the energies of transition states, relative to energies of reactants, may be inferred from experimental reaction rates, and qualitative information about transition-state geometries may be inferred from such quantities as activation entropies and activation volumes as well as kinetic isotope effects. 

Experiments cannot tell us what transition states look like. The fact is that transition states cannot even be detected experimentally let alone characterized, at least not directly. While measured activation energies relate to the energies of transition states above reactants, and while activation entropies and activation volumes, as well as kinetic isotope effects, may be invoked to imply some aspects of transition-state structure, no experiment can actually provide direct information about the detailed geometries and/or other physical properties of transition states. Quite simply, transition states do not exist in terms of a stable population of molecules on which experimental measurements may be made. Experimental activation parameters provide some guide, but tell us little detail about what actually transpires in going from reactants to products. 

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