Theoretical calculations of the reactions of CH3SSR (R = H or CH3) with fluoride, hydroxide or allyl anion in the gas phase have been performed to determine the mechanism for both elimination and substitution reactions.6 The elimination reactions have [Pg.278]

Theoretical calculations of two-electron ion energy levels have been the topic of much research since the discovery of quantum mechanics. The contribution of relativistic effects via the Dirac equation and QED contributions has been intensely studied in the last three decades [1]. Two-electron systems provide a test-bed for quantum electrodynamics and relativistic effects calculations, and also for many body formalisms [2]. [Pg.699]

New theoretical calculations of mechanisms of isoxazoline syntheses have been reported. [Pg.293]

On the other hand, in the theoretical calculations of statistical mechanics, it is frequently more convenient to use volume as an independent variable, so it is important to preserve the general importance of the chemical potential as something more than a quantity GTwhose usefulness is restricted to conditions of constant temperature and pressure. [Pg.350]

A fully theoretical calculation of a potential energy surface must be a quantum mechanical calculation, and the mathematical difflculties associated with the method require that approximations be made. The first of these is the Bom-Oppenheimer approximation, which states that it is acceptable to uncouple the electronic and nuclear motions. This is a consequence of the great disparity in the masses of the electron and nuclei. Therefore, the calculation can proceed by fixing the location [Pg.193]

Although the collision and transition state theories represent two important methods of attacking the theoretical calculation of reaction rates, they are not the only approaches available. Alternative methods include theories based on nonequilibrium statistical mechanics, stochastic theories, and Monte Carlo simulations of chemical dynamics. Consult the texts by Johnson (62), Laidler (60), and Benson (59) and the review by Wayne (63) for a further introduction to the theoretical aspects of reaction kinetics. [Pg.118]

Experimentally the single relaxation observed was attributed to step 3 in the mechanism because (a) theoretical calculation of k 2 and k2 predicted an estimated relaxation frequency inaccessible to the equipment used and (b) step 2 is excluded since the rate of displacement of water from the primary hydration sphere of an anion is independent of the cation. The relaxation data were analyzed by the equation [Pg.509]

A perfect crystal structure model is very helpful for theoretical calculations, reaction mechanism analysis, and some physical property analysis such as conductivity, magnetic susceptibility, chemical potential, etc. Powder XRD (or neutron diffraction) Rietveld refinement is one of the most popular methods used to characterize crystal structure. [Pg.27]

This mechanism also accounts for the very large 5-deuterium isotope effect observed for the solvolysis of (4-D)bicyclo[2.2.2]oct-l-yl mesylate. This mechanism is also supported by theoretical calculations of 4-substituted bicyclo[2.2.2]oct-l-yl cations74. [Pg.380]

In addition, the time-dependence of these concentrations also contains (albeit in encoded form) the homogeneous parameters of the particular mechanism being considered. These latter techniques are termed convolutions. Convolution (and its reverse, i.e. deconvolution) are ideal for the electroanalyst because the theoretical calculation of current, and direct comparison with experimental data, is often not viable. This alternative of testing experimental currents via convolutions results in expressions for concentrations at the electrode which arise directly from the data rather than requiring iterations(s). The electrode concentrations thus estimated for a particular mechanism then allow for correlations to be drawn between potential and time, thereby assessing the fit between the data and the model. [Pg.301]

So the popular polarization equations of the type (6.5) for electrochemical reactions thus acquire some physical basis. However, according to current concepts the nature of the activated state is different, and quantum-mechanical approaches must be used for a theoretical calculation of the values and These concepts are discussed in more detail in Chapter 34. [Pg.244]

In summary, this discussion illustrates the general importance of transport processes in many (electro)catalytic reactions. These have to be addressed properly for a detailed (and quantitative) understanding of the molecular-scale mechanism. Because of the problems associated with the direct identification of the reaction intermediates (see above), experiments on nanostructured model electrodes with a well-defined distribution of reaction sites of controlled, variable distance and under equally well-defined transport conditions (first attempts in this direction are described in [Lindstrom et al., submitted Schneider et al., 2008]), in combination with detailed simulations of the ongoing transport processes and theoretical calculations of the [Pg.449]

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