Isotope effects activation energy

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. 

These data led to the model already described several times above. The enzyme executes a search for a tunneling sub-state, apparently 13 kcaFmol in energy above the principal state from this state the hydrogen atom tunnels with no further vibrational excitation. Probably motion of the secondary center is coupled into the tunneling coordinate. The result is large, temperature-independent primary and secondary isotope effects in the context of an isotope-independent activation energy. 

Various mechanisms for the aerobic oxidation of alcohols catalysed by (NHC)Pd (carboxylate)2(H20) complexes [NHC = l,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene] were investigated using DFT combined with a solvent model. Of these, reductive j3-hydride elimination, in which the -hydrogen of a palladium-bound alkoxide is transferred directly to the free oxygen of the bound carboxylate, provided the lowest-energy route and explained the published kinetic isotope effect, activation enthalpy, reaction orders, and dependence of rate on carboxylate pKa.26S... 

Tunneling of atomic nuclei in the course of an elementary act of chemical reaction was first considered theoretically in Refs. [5-8] soon after quantum mechanics had been created. It has been shown that nuclear tunneling may lead to unusually large isotope effects for reactions in which light atoms (hydrogen, deuterium, tritium) are transferred and to a decrease in the effective activation energy of chemical processes as the temperature decreases. 

The correlation with cr parameters gives the value = -1.5. The same sequence of rates and value have been obtained for the y-induced process. The isotope effect for the photoreaction was kn/kry = 2. The effective activation energy of the photo-induced reaction is ca. 5 kca moU. ... 

The isotopic substitution affects, in general, not only the rate constant, but also the effective activation energy and the effective collision (frequency) factor. 

Differential scanning calorimetry experiments revealed the presence of at least four types of lactose besides the known a- and 3-modifications, some of which are dehydrated forms. Attempts have been made to identify the rate-determining step in the dehydration of fructose to S-(hydroxymethyl)furfural by measuring kinetic isotope effects." A spin-probe EPR study at elevated temperatures of some sugars in connection with the desiccation tolerance of biologiGal materials indicated that trehalose and sucrose-raffinose mixtures are distinguished by stability of thdr phase state and their low effective activation energy for rotational molecular motions. ... 

At this point, attention can be given to specific electrophilic substitution reactions. The kinds of data that have been especially useful for determining mechanistic details include linear ffee-energy relationships, kinetic studies, isotope effects, and selectivity patterns. In general, the basic questions that need to be asked about each mechanism are (1) What is the active electrophile (2) Which step in the general mechanism for electrophilic aromatic substitution is rate-determining (3) What are the orientation and selectivity patterns ... 

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. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

The extent or nature of solvent-solute interactions may be different in the deuterated and nondeuterated solvents this may change the energies of the transition state, and hence the activation energy of the reaction. These are secondary isotope effects. Two physical models for this third factor have been constructed. ... 

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