Arrhenius prefactor

Four distinct hopping events were considered in the calculations, which correspond to the movement of the benzene molecules between the cation and window sites of minimum energy in NaY, i.e., cation to window (C-W), C-C, W-C, and W-W. The associated rate constants of these processes were used to calculate the activation barrier to each hopping process and the Arrhenius prefactor. The MEP of benzene molecules was followed by a constrained optimization method that drags benzene from its initial site of minimum energy, through the transition state, to the final state. 

Moreover, the small trend in exponents with temperature can be shown to lead to H/T KIE s on the Arrhenius prefactors smaller than the intrinsic values for the lighter glycoforms and larger than the intrinsic value for the heavy one. This is a trend that further emphasizes the differences between them (Kohen et al., 1996). However, as the D/T KIE measurements are likely to be virtually free of kinetic complexity, the Ap/Ax values reported in table I reflect the chemical step of the GO reaction. 

Competitive KIEs can reduce the uncertainty in prefactor isotope effects, and have been used to demonstrate tunneling in several enzymes [24, 36, 65]. As discussed above, the competitive, double-label, technique for measuring KIEs is inherently more precise than noncompetitive techniques, and can reduce the experimental uncertainty in the KIE on the Arrhenius prefactor and energy of activation. The use of tritium also provides multiple ratios Ah/At and Ad/At, which are helpful in resolving kinetic complexity [61]. It has been noted that a change in the rate-limiting step over the temperature range can lead to anomalous Arrhenius... 

The primary KIEs on kcat also indicated a transition at 30 °C, below which the primary kn/ko ratio is very temperature dependent, extrapolating to Ah/Ad 1 [24]. This inverse Arrhenius prefactor ratio is predicted within the Bell tunnel correction for a moderate extent of tunneling, and is consistent with an elevated a-secondary RS exponent. Above 30 °C, the primary kn/ko ratio is nearly independent of temperature, resulting in an isotope effect on the prefactor of Ah /Ad = 2 [24]. A tunnel correction would also predict such an elevated Arrhenius prefactors ratio when both H and D react almost exclusively by turmeling however this condition requires a very small activation energy for k at, while a value of = 14 kcal mol is observed [24]. 

Termination reactions such as (1.5) decrease the number of radicals and produce nonradical products such as alcohols and ketones. Mutual termination reactions of primary and secondary peroxyl radicals have near-zero activation energies but unusually low Arrhenius prefactors, suggesting a strained transition state. The exothermicity of this termination is sufficient to produce electronically excited states of either the carbonyl compound or oxygen. Besides the termination reaction (1.5), peroxyl radicals can also undergo a self-reaction without termination (2ROO 2RO -I- O2) that is often ignored but is equally important as the termination channel itself [9,10]. 

Detailed treatment of ET between Ru and Co coordination complexes tethered by a tetrapro-line B has led to estimates of entropy as well as enthalpy of activation, a distinction shown to be crucial when it comes to extracting the magnitude from the Arrhenius prefactor. ... 

In these equations E is the potential difference between the two electrodes, F is the Faraday constant Cr+ etc. are Arrhenius prefactors R+, Ai are concentrations (0) is the Gibbs free energy of activation of the electrode... 

Figure 5.8 demonstrates the temperature dependence of exact and JSA rate constants for the D+H2(t = l,j) reaction. The temperature range is 200 - 1000/if, plotted in inverse Kelvin. The exact rate constants were obtained from Eq. (5.4) and the cross sections in Fig. 5.7, and the JSA rate constants were obtained from Eqs. (5.41)-(5.43) and the J = 0 reaction probabilities in Fig. 5.4. Very good agreement is obtained for all j values. In all cases, the JSA predicts the correct Arrhenius activation energy (i.e. negative of the slope of log k(T) vs. 1/ksT) and is qualitatively correct in predicting the Arrhenius prefactor (i.e. y-intercept). The overall agreement is truly excellent for = 1 and 2. However, the JSA systematically underestimates the rate constant by roughly 40% for j = 0 and 3.

Figure 5.8 Exact and approximate (JSA) rate constants for the D+H2(u = l,j) reaction. The JSA predicts the correct Arrhenius activation energy (i.e. slope) in all cases, and is qualitatively correct in predicting the Arrhenius prefactor (i.e. y-intercept). Agreement is excellent for i = 1 and 2. However, the JSA systematically underestimates the rate constant by roughly 40% for j = 0 and 3.

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