Mechanisms of Electronic Transitions

We have seen that the MNM transition and state-dependent interactions are central features of the phase behavior of fluid metals and semiconductors. The existence of a critical point forces us to deal not only with the discontinuous electronic transition coinciding with the liquid-vapor transition, but also with the continuous transition fl om metal to nonmetal implied by the trajectory shown in Fig. 2.2(a). Let us now consider some microscopic electronic mechanisms that could underlie such continuous transitions. We begin with a description of the metallic limit and the model of nearly-ffee-electrons. 

The characteristic properties of the metallic state of matter follow from two overwhelmingly important physical effects the overlap of valence electron wave functions on neighboring atoms and the Pauli exclusion principle. These effects are embodied in the nearly-free-electron (NFE) model of metals. 

Consider an assembly of N atoms. For simplicity let us suppose that these are alkali metal atoms each with a single valence electron out- 

The same spectrum of electronic states can be generated conceptually by increasing the density of a fixed number N of atoms. In either case, the overlap of the wave functions is very large in the condensed state and the individual bands superimpose to give a single broad continuum of states as shown in Fig. 2.8(d). Near the band edges, the density of states per unit energy, N(E), resembles that of a free electron gas (see, e.g., Ashcroft and Mermin, 1976) but with the electron mass ntg replaced by an effective mass m ff, namely. 

The development of energy bands can also be conceived by a gedanken experiment in which one starts with a free electron gas of 

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Lucidity. The authors have found students who understand advanced courses in quantum mechanics but find difficulty in comprehending a field at whose center lies the quantum mechanics of electron transitions across interfaces. The difficulty is associated, perhaps, with the interdisciplinary character of the material a background knowledge of physical chemistiy is not enough. Material has therefore sometimes been presented in several ways and occasionally the same explanations are repeated in different parts of the book. The language has been made informal and highly explanatory. It retains, sometimes, the lecture style. In this respect, the authors have been influenced by The Feynman Lectures on Physics. 

Although radiation can travel in a vacuum, it originates from matter. All forms of matter emit radiation through the mechanisms of electronic transitions and lattice vibrations. In most solids and liquids, radiation emitted from the interior is strongly absorbed by adjoining molecules. Therefore, radiation from these materials can be treated as a surface phenomenon. Radiation in gases and some semitransparent sohds and liquids, however, must be treated as a volumetric phenomenon. 

H. Nakamura, What are the basic mechanisms of electronic transitions in molecular dynamic processes , Int. Rev. Phys. Chem. 10 123 (1991). 

The first term of Eq. 8.46 is the FC term, while the remaining terms arise from the Herzberg-Teller (HT) borrowing mechanism of electronic transitions. By inspection of Eq. 8.33, one may notice that the antisymmetric anisotropy vanishes for pure EC transitions but is in general different from zero when the HT effect is... 

Frequently, electrochemical information can be interpreted better in the presence of additional nonelectrochemical information. Typically, however, there is one significant restriction electrochemical and spectroscopic techniques often do not detect exactly the same mechanisms. With spectroscopic measurements (e.g., infrared spectroscopy), products that are formed by electrochemical processes may be detected. In other cases (luminescence techniques) mechanisms may be found by which charge carriers are trapped and recombine. Other techniques (electroreflection studies) allow the nature of electronic transitions to be determined and provide information on the presence or absence of an electric field in the surface of an electrode. With no traditional technique, however, is it... 

Kuzmin MG, Soboleva IV, Dolotova EV (2007) The behavior of exciplex decay processes and interplay of radiationless transition and preliminary reorganization mechanisms of electron transfer in loose and tight pairs of reactants. J Phys Chem A 111 206... 

The accurate quantum mechanical first-principles description of all interactions within a transition-metal cluster represented as a collection of electrons and atomic nuclei is a prerequisite for understanding and predicting such properties. The standard semi-classical theory of the quantum mechanics of electrons and atomic nuclei interacting via electromagnetic waves, i.e., described by Maxwell electrodynamics, turns out to be the theory sufficient to describe all such interactions (21). In semi-classical theory, the motion of the elementary particles of chemistry, i.e., of electrons and nuclei, is described quantum mechanically, while their electromagnetic interactions are described by classical electric and magnetic fields, E and B, often represented in terms of the non-redundant four components of the 4-potential, namely the scalar potential and the vector potential A. 

Electron transfer from the excited states of Fe(II) to the H30 f cation in aqueous solutions of H2S04 which results in the formation of Fe(III) and of H atoms has been studied by Korolev and Bazhin [36, 37]. The quantum yield of the formation of Fe(III) in 5.5 M H2S04 at 77 K has been found to be only two times smaller than at room temperature. Photo-oxidation of Fe(II) is also observed at 4.2 K. The actual very weak dependence of the efficiency of Fe(II) photo-oxidation on temperature points to the tunneling mechanism of this process [36, 37]. Bazhin and Korolev [38], have made a detailed theoretical analysis in terms of the theory of radiationless transitions of the mechanism of electron transfer from the excited ions Fe(II) to H30 1 in solutions. In this work a simple way is suggested for an a priori estimation of the maximum possible distance, RmSiX, of tunneling between a donor and an acceptor in solid matrices. This method is based on taking into account the dependence... 

Baer, M. (1983). Quantum mechanical treatment of electronic transitions in atom-molecule collisions, in Molecular Collision Dynamics, ed. J.M. Bowman (Springer, Berlin Heidelberg). 

In this contribution we have presented some specific aspects of the quantum mechanical modelling of electronic transitions in solvated systems. In particular, attention has been focused on the ASC continuum models as in the last years they have become the most popular approach to include solvent effects in QM studies of absorption and emission phenomena. The main issues concerning these kinds of calculations, namely nonequilibrium effects and state-specific versus linear response formulations, have been presented and discussed within the most recent developments of modern continuum models. 

During the past four decades the dynamics and mechanisms of electron-transfer processes have been studied via the application of transition-state theory to the kinetics for electrochemical processes. As a result, both the kinetics of the electron-transfer processes (from solid electrode to the solution species) as well as of pre- and post-electron-transfer homogeneous processes can be characterized quantitatively. 

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