Equilibrium state parameters, electron models

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

Because of its simplicity the impulsive model is very appealing and frequently employed to model measured rotational state distributions (Dugan and Anthony 1987 Levene and Valentini 1987 Butenhoff, Car-leton, and Moore 1990). In most applications, however, it is necessary to incorporate at least one fit parameter or some dynamical constraints in order to obtain agreement with experimental results, for example, the equilibrium angle in the excited electronic state or the point at which the repulsive force vector intersects the BC-axis. The impulsive model is not an a priori theory. 

Electron transfer (ET) reactions are analyzed by Newton in terms of continuum solvation models. Their role in the determination of the ET critical parameters (i.e. the solvent reorganization energy and the electronic coupling between the initial and final states) is analyzed using both an equilibrium and nonequilibrium solvation framework. 

Fig. 16.2 A model for the energetics of electron transfer reactions. The two potential surfaces are associated with two electronic states that transform to each other when the electron is transferred. The coordinate X stands for the nuclear configuration. The model may be characterized by the curvature of these surfaces, by the energy gap AE between the two electronic origins and by the reorganization energy Ex. Other important parameters that can be expressed in terms of these are the equilibrium configuration shift Ay, — Xa and the activation energy E. ...

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