A theoretical study of the hydrolysis of arenediazonium ions, combining Marcus theory with density functional theory (DPT) calculations, indicates the possibility of reaction by an 5 2 pathway, with the transition state (1), rather than an 5 1 pathway There has been a survey of the use of arenediazonium ions in synthetic reactions including their use as aryl radical precursors, aryl cation precursors, and super-electrophiles in transition-metal-catalysed reactions [Pg.218]

Let us now consider the results of theoretical calculation of the reorganization energy. Marcus formulas (3.14) and (3.16) represent the simplest version of the theory. For a reaction involving two ions of the same radius a, which are in direct contact (R = 2a), as well as for the electrode reaction of an ion which approaches the electrode until they are in direct contact (R = a), these formulas can be simplified and lead to the following relations [Pg.257]

Aj may be evaluated from x-ray and infrared (IR) data or from theoretical calculations. However, for organic outer sphere electron transfers, this contribution is usually much smaller than Ao. In our opinion one of the greatest merits of the Marcus [43] and Levich-Dogonadze [44] theories is that they allow rather correct predictions of Aq through simple equations. Thus for most outer sphere electron transfers, reasonably accurate values of the rate constants can be predicted. [Pg.27]

The agreement between the two sets of data is reasonably satisfactory. The ability of the Marcus theory to predict values of k and k has also been tested, and Table 3.2 presents a comparison made by Hale [25] of the experimental and theoretical values of the free energy of activation for electrode processes (the experimental values of have been calculated from k using Equations [Pg.103]

This chapter is organized as follows. Section 18.2 describes the theoretical foundation of Marcus theory, formulated in a molecular rather than dielectric continuum solvent framework. Its non-Gaussian extension is presented in section 18.3 and its implications for rate calculations are discussed in section 18.4. The theory is then confronted to various molecular simulation results in section 18.5 and a conclusion is proposed in section 18.6. [Pg.468]

This confusion initiated a lot of experimental inspections and theoretical revisions of the FEG law. There is no need to review all of them here because the most reliable explanation of the effect was given by Marcus and Siders [108]. In view of the fact that all transient effects are ignored in the Markovian theory, where k(t) = k, it follows from Eq. (3.13) that the Markovian Ko coincides with k but not with ko. Therefore, Marcus and Siders calculated k by means of DET and concluded that the fastest transfer (at the top of the FEG [Pg.143]

Finally, theoretical studies, particularly by Wolfe et al. (26) and more recently by Evleth and co-workers (27), provided some additional justification for our analysis. Quantum calculations of barriers for cross-reactions are in agreement with values that would have been derived from a Marcus theory analysis of other calculated barriers. Jorgensen and co-workers (28, 29) carried this analysis further using statistical mechanics simulations that show that the gas phase potential surface indeed translates into the solution surface in the way that we predicted. (For a dicussion of an alternative way to apply Marcus theory to double-minimum surfaces, as well as a note on Cl + CH3C1, see reference 29a.) [Pg.33]

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