Isotope effects linear transition states

Isotope effects in linear transition states Let us now analyze the kinetic isotope effect in a simple system, a transfer of hydrogen from AH to B through a linear transition state (Equation 2.74).53 We assume that A and B are polyatomic fragments. In the reactants we have to consider the A—H stretching... 

Primary isotope effects in non-linear transition states If the transition state is nonlinear, the vibration corresponding to the symmetric stretch looks like 33. Now even for the symmetrical case, the H (D) moves with relatively high... 

Persky and Klein have measured the temperature dependence of the isotope effect over the range — 30 °C—h 70 °C for the photochlorination of isotopic hydrogen molecules by comparing the rate of H2 chlorination with the rate for HD, D2, HT, DT and T2. Assuming a linear transition state, four force constants characterize the potential energy surface contours at the transition state configuration. Four independent isotope effect measurements are necessary to determine the four force constants for comparison with theoretical surface models hence, Persky and Klein have one isotope effect measurement which serves as a test of their method. 

Attempts to calculate theoretical values for the isotope effects and their temperature dependence were made using a linear activated complex model and a Sato potential energy surface. Various tunneling corrections were applied but only the Bell model ° predicts the curvature observed in log (fcio/ ii) versus l/T. Similar theoretical isotope effect predictions were found using a non-linear transition state model. 

The activation parameters (TMP A// +7kcalmoH A5 —39 cal. K-. mor TXP A// +17kcalmor A5 -25cal.K .mor, the rate law (rate = fc[(por)Rh ] [CH4]) and large kinetic isotope effects (fcn/fe >8) derived from kinetic studies of the reactions in Fig. 58 (166, 167), are consistent with the proposed concerted four-centered pathway with a near linear transition state in Fig. 59(a). Similar kinetic smdies suggest that toluene and methane C—H bond cleavage reactions (and also H—H bond reactions of H2) proceed via related mechanisms (166, 168, 169). 

If secondary isotope effects are neglected, the ratio ky k can be estimated as 8.9 from the zero-point energies of the N-H and N-D bonds if we assume a linear transition state for proton transfer [28, 51 ]. and kjk y can then be used to estimate F = 0.63 [46]. At 263 K, a temperature at which both A j. and were measured, this gives k = 2.7 x 10 M s and p = 2.8 x 10" M s [46]. On this basis hydride protonation is ten times faster than metal protonation, thus the kinetic site of protonation of 3 is the hydride ligand [46]. 

An insight into the nature of the transition state was provided by deuterium kinetic isotope effect studies in which 1 /1 for conversion of 5-methyl-CPD to 1-methyl-CPD using the perdeuterio compound was used to determine A . Here, log /l = -1.0 - 2450/2.3RT, which indicates hydrogen, and not deuterium, tunneling although the large temperature dependence was also attributed to a non-linear transition state with nearly complete loss of one C-H bending mode (Scheme 6.2). ... 

Attack of an atom or free radical upon alkanes generally involves attack on hydrogen atoms via a more or less linear transition state (1). Attack at carbon in acyclic alkanes is excluded by a number of experimental observations including the absence of rupture of carbon-carbon bonds. Reactions proceeding via transition state 2 are excluded by the observed primary deuterium isotope effects which vary considerably with the nature of the attacking radical or atom. Moreover, when X = D , no hydrogen-deuterium exchange is observed by EPR spectroscopy for the radicals formed by attack of D upon... 

Primary Kinetic Isotope Effects for Linear Transition States as a Function ofExothermicity and Endothermicity... 

Isotope Effects for Linear vs. Non-Linear Transition States... 

More O Ferrall, R. A. "Model Calculations of Hydrogen Isotope Effects for Non-linear Transition States." J. Chem. Soc. B, 785 (1970). 

Non-linear transition states. The operation of the Westheimer effect depends on the transition state being linear. If it is not, the balance of forces that leads to isotopic insensitivity for the real stretching vibration in a symmetrical transition state cannot occur. An obvious... 

The proposal that low isotope effects may be associated with bent transition states was made before Westheimer s treatment of linear transition states became available [93]. Nonetheless experimental confirmation would clearly provide evidence in its support. In fact there are a number of reactions, most notably 1,2-hyride rearrangements and carbene and nitrene insertions, for which the consistent observation of small isotope effects can reasonably be ascribed to non-linear transition states [90]. On the other hand the mechanisms of the reactions have not always been entirely clear and it may perhaps be questioned whether a definite and general conclusion can yet be drawn. 

White et al.1A have obtained similar kinetic results for the acid-catalysed rearrangement of N-nitro-N-methylaniline, i.e. a first-order dependence on the nitroamine with a linear H0 plot of slope 1.19 for phosphoric acid, and a deuterium solvent isotope effect of about three, although the results have only been presented in preliminary form. Further, an excellent Hammett a+ correlation was claimed for thirteen para substituted nitroamines which gave a p value of —3.9. Since it is expected that the rate coefficients would correlate with a (rather than different basicities of the amines, the a+ correlation implies that the amino nitrogen is electron-deficient in the transition state,... 

The large isotope effect suggested that carbon-hydrogen bond cleavage occurs via a linear and symmetrical transition state, while the loss of stereochemical integrity via epimerization suggested the involvement of an intermediate. A mechanism that is consistent... 

Saunders10 and by Sims and coworkers11 have shown that the magnitude of the leaving-group heavy-atom isotope effect varies linearly with the extent of C—X bond rupture in the transition state for concerted elimination reactions and for nucleophilic substitution reactions, respectively. Since the magnitude of the isotope effect is directly related to the amount of C—X bond rupture in the transition state, these isotope effects provide detailed information about the structure of the transition state. 

Matsson and coworkers have measured the carbon-1 l/carbon-14 kinetic isotope effects for several Menshutkin reactions (equation 35) in an attempt to model the S/v2 transition state for this important class of organic reaction. These isotope effects are unusual because they are based on the artificially-made radioactive carbon-11 isotope. The radioactive carbon-11 isotope is produced in a cyclotron or linear accelerator by bombarding nitrogen-14 atoms with between 18- and 30-MeV protons (equation 36). 

The general phenomenon of a primary kinetic isotope effect is caused by the higher zero-point vibration energy of a C-H bond compared to a C-D bond. If in the transition state where this bond is being broken the intermediate is linear (C-H-X), the energies of the deuterio and protio species are equal and... 

From his first paper (Mulliken 1925a), Mulliken understood that the band heads did not represent a transition from a non-rotating initial state to non-rotating final state. Yet, he used the band heads to study the vibrational isotope effect since he could measure the band heads more easily and since the rotational energy differences are very small compared to the vibrational energy difference. From the theory, the terms linear in n and n" (ain and bin") arise from the harmonic approximation with the coefficients ai and bi corresponding to the harmonic vibrational frequencies in the... 

Ru" (0)(N40)]"+ oxidizes a variety of organic substrates such as alcohols, alkenes, THE, and saturated hydrocarbons. " In all cases [Ru (0)(N40)] " is reduced to [Ru (N40)(0H2)] ". The C— H deuterium isotope effects for the oxidation of cyclohexane, tetrahydrofuran, 2-propanol, and benzyl alcohol are 5.3, 6.0, 5.3, and 5.9 respectively, indicating the importance of C— H cleavage in the transitions state. For the oxidation of alcohols, a linear correlation is observed between log(rate constant) and the ionization potential of the alcohols. [Ru (0)(N40)] is also able to function as an electrocatalyst for the oxidation of alcohols. Using rotating disk voltammetry, the rate constant for the oxidation of benzyl alcohol by [Ru (0)(N40)] is found to be The Ru electrocatalyst remains active when immobilized inside Nafion films. 

The rate of reaction of Mel with [Rh(CO)2l2] was measured and compared with the rate of reaction of Mel and the kinetic isotope effect (KIE) was shown, through ab initio molecular orbital calculations, to be consistent with an 5 2 mechanism proceeding through a linear (Rh-C-I ) transition state [33]. 

Kinetic Acidities in the Condensed Phase. For very weak acids, it is not always possible to establish proton-transfer equilibria in solution because the carbanions are too basic to be stable in the solvent system or the rate of establishing the equilibrium is too slow. In these cases, workers have turned to kinetic methods that rely on the assumption of a Brpnsted correlation between the rate of proton transfer and the acidity of the hydrocarbon. In other words, log k for isotope exchange is linearly related to the pK of the hydrocarbon (Eq. 13). The a value takes into account the fact that factors that stabilize a carbanion generally are only partially realized at the transition state for proton transfer (there is only partial charge development at that point) so the rate is less sensitive to structural effects than the pAT. As a result, a values are expected to be between zero and one. Once the correlation in Eq. 13 is established for species of known pK, the relationship can be used with kinetic data to extrapolate to values for species of unknown pAT. 

The a-secondary IE of two deuteriums on the rate of base-catalyzed CD exchange of toluene, 3A ( PhC112D)/k(PhCD is 1.31, and the [3-secondary D IE on the rate of base-catalyzed a-C-D exchange of ethylbenzene, k(PhCHDCH3)//t(PhCHDCD3), is 1.11 0.03.58 Similarly, from the rates of base-catalyzed a-C-D exchange of tolucne-a,4-r/2, -a,2,4,6-c/4, and -a,2,3,4,5,6-d6 and with an assumption of linearity of IEs, the contributions of ortho, meta, and para deuteration lead to rate retardations of 2.4, 0.4, and 1.8%, respectively.59 These are all kinetic IEs, but to the extent that the transition state resembles closely the carbanion, or to the extent that the reverse reprotonation is encounter-controlled and independent of isotopic substitution, these kinetic IEs represent equilibrium IEs on acidity. The IEs were interpreted in terms of an electron-donating inductive effect of D relative to H. 

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