Band local model

The long-wavelength absorption bands exhibited by solutions of methiodides of aza analogues of benzenoid hydrocarbons have been attributed to the presence of charge-transfer complexes.01 There is a correlation between the excitation energies of the bands and the calculated electron affinity of the cations, in agreement with the delocalized rather than the localized model of the excited state in the charge-transfer complex.91... 

The resonance Raman spectrum of rans-[ (bpy)2Ru(CN) 2(/ -CN)]2+ under near-resonance conditions with the MMCT band showed enhancement of the bridging cyanide stretching as expected for this type of electronic transition (109). Analysis of the IR spectrum supports the valence-localized model in contrast to a previous study (110). 

Fig. 7.15. Illustration of the Anderson localization model showing atomic potentials and the shape of the band, with and without the disorder.

Fig. 6.16 The local band-structure model [53]. The band energy parameter AE = Ef — Es, the width of the d-band W and the distance Rj between the hydrogen atom and the next neighboring atoms.

Two models exist vdiich are in a sense complementary and allow valence transitions to be discussed. The Anderson localization model is mostly applied in a parametric scheme, and allows many phenomena to be considered together as resulting fi om hybridisation effects in the conduction band. However, atomic effects are not so well accounted for in this picture essentially, they are added in by hand. Another proach is the quasi-atomic double-well model. This scheme is not parametric, since it is based on ab initio Hartree-Fock calculations. It accounts for atomic aspects, such as the general region of the Periodic Table vriiere such phenomena are encountered. Also, it provides a mechanism for localization (orbital collapse). Finally, it allows one to understand and explain the properties of rather special states (the extended 4f states) which are delocalized, but retain certain atomic features. However, this model is unable to incorporate solid state efifects in a simple way. 

The (i-band center model has been used extensively to describe experimentally measured catalytic activities, as a descriptor of catalyst behavior. Most computations have been performed on flat surfaces or surfaces with steps and kinks [7, 24,46 9]. The electronic stmcture of nanoparticles is expected to be deeply affected by the characteristic particle size and morphology. Particle size is therefore a critical parameter. The surface science studies that involve the reactions on a uniform single crystal surfaces and introduce the complexity characteristic to real nanoparticles by involving the defects, kinks, and steps in the models may not be sufficient to model the catalytic behavior at nanoscale. Such model does not take into account an inherent particle property sensitively dependent on structural parameters such as the particle size, strain, and local surface morphology. 

In the mixed-valent compound SmB6 the exchange interactions between the impurity and the host 4f electrons contribute the main part to the g-shift. The ESR linewidths show a remarkable temperature dependence. As the temperature increases the linewidth of the Gd " -absorption line remains nearly constant below 4K, increases rapidly between 4 and 10 K, followed by a more gradual increase above lOK. This broadening is less developed in the case of Eu. This temperature behavior of the linewidths can be explained by a band-structure model of Kasuya (1976), assuming that the localized 4f electrons and the delocalized 5d orbitals are strongly mixed and form a hybridization gap. 

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