Band structure electron transfer

In outer sphere electron transfer, the reactant is not adsorbed therefore, the interaction with the metal is not as strong as with the catal5d ic reactions discussed below. Hence, the details of the metal band structure are not important, and the couphng A(s) can be taken as constant. This is the so-called wide band approximation, because it corresponds to the interaction with a wide, structureless band on the metal. In this approximation, the function A(s) vanishes, and the reactant s density of states takes the form of a Lorentzian. The simation is illustrated in Fig. 2.3. 

In the electron transfer theories discussed so far, the metal has been treated as a structureless donor or acceptor of electrons—its electronic structure has not been considered. Mathematically, this view is expressed in the wide band approximation, in which A is considered as independent of the electronic energy e. For the. sp-metals, which near the Fermi level have just a wide, stmctureless band composed of. s- and p-states, this approximation is justified. However, these metals are generally bad catalysts for example, the hydrogen oxidation reaction proceeds very slowly on all. sp-metals, but rapidly on transition metals such as platinum and palladium [Trasatti, 1977]. Therefore, a theory of electrocatalysis must abandon the wide band approximation, and take account of the details of the electronic structure of the metal near the Fermi level [Santos and Schmickler, 2007a, b, c Santos and Schmickler, 2006]. 

Proton-coupled intramolecular electron transfer has been investigated for the quinonoid compounds linked to the ferrocene moiety by a 7r-conjugated spacer, 72 (171) and 75 (172). The complex 72 undergoes 2e oxidation in methanol to afford 74, which consists of an unusual allene and a quinonoid structure, with the loss of two hydrogen atoms from 72 (Scheme 2). The addition of CF3SO3H to an acetonitrile solution of 74 results in two intense bands around 450 nm, characteristic of a semi-quinone radical, and a weak broad band at lOOOnm in the electronic... 

Conductivity means that an electron moves under the influence of an applied field, which implies that field energy transferred to the electron promotes it to a higher level. Should the valence level be completely filled there are no extra higher-energy levels available in that band. Promotion to a higher level would then require sufficient energy to jump across the gap into a conduction level in the next band. The width of the band gap determines whether the solid is a conductor, a semi-conductor or an insulator. It is emphasized that in three-dimensional solids the band structure can be much more complicated than for the illustrative one-dimensional model considered above and could be further complicated by impurity levels. 

A quantitative description must account for the band structure of the electrode, and can be formulated within the theory of electron-transfer reactions presented in Chapter 6. We start from Eq. (6.12) for the rate of electron transfer from a reduced state in the solution to a state of energy e on the electrode, and rewrite it in the form ... 

It is well known that the flotation of sulphides is an electrochemical process, and the adsorption of collectors on the surface of mineral results from the electrons transfer between the mineral surface and the oxidation-reduction composition in the pulp. According to the electrochemical principles and the semiconductor energy band theories, we know that this kind of electron transfer process is decided by electronic structure of the mineral surface and oxidation-reduction activity of the reagent. In this chapter, the flotation mechanism and electron transferring mechanism between a mineral and a reagent will be discussed in the light of the quantum chemistry calculation and the density fimction theory (DFT) as tools. 

The electronic properties of CNTs, and especially their band structure, in terms of DOS, is very important for the interfacial electron transfer between a redox system in solution and the carbon electrode. There should be a correlation between the density of electronic states and electron-transfer reactivity. As expected, the electron-transfer kinetics is faster when there is a high density of electronic states with energy values in the range of donor and acceptor levels in the redox system [2]. Conventional metals (Pt, Au, etc.) have a large DOS in the electrochemical potential... 

All materials in the Lai- r ,Coi- Fe/)3-(5 (LSCF) family of materials have electronic transference numbers approaching unity. The electronic structure LSC and LSF has often been described in terms of partially delocalized O p—Co band states based on the tg and e levels of crystal-field theory. In... 

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