Localization-Delocalization

In the band model, the electron wave functions are mathematically written as delocalized wave functions. Most metals conform to this picture as far as metallic conductivity, optical properties, and magnetic properties are concerned. 

The question of delocalization has nothing to do with the mathematical model used in the calculations of metals, but it is a physical problem. The test, as usual, is to remove or drop an electron and check whether it localizes or delocalizes over the whole system. If there is localization, the site geometry will deform. On the other hand, if it delocalizes, the geometry is exactly the same for all the sites. 

An increase of the temperature may cause geometric changes and this may be enough to cause localization, as proposed in P. W. Anderson s model. However, metal-insulator (MI) transitions are not always caused by thermal disorder. 

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Ndi g5Ceo.i5Cu04 Localization-delocalization of copper pairs on Zn impurity centers in the copper sublattice of the HTc superconductor Ndj g5Ceo.i5Cu04 was observed by Zn Mossbauer emission spectroscopy... 

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

For the elements highlighted by the diagonal strip there is an indication that the / and d electrons may be balanced between being localized and itinerant. According to Smith and Kmetko (1983), materials close to this localization-delocalization transition can have their properties modified appreciably by small... 

This has been developed since 1986. The title letters stand for Localized Delocalized Response. The localized effect is Charton s preferred name for the inductive effect and delocalized effect is his preferred name for the resonance effect. Indeed, he would like to change the usual symbols from <7/ to 0/, and or to op for the purposes of the Extended Hammett (EH or LD) equation109. The response referred to is that of the substituent to the electronic demand of the site (i.e. reaction site in the correlation analysis of reactivity). Thus this equation, like the PSP equation, is concerned with the parametrization of substituent polarizability. 

The formation and transport properties of a large polaron in DNA are discussed in detail by Conwell in a separate chapter of this volume. Further information about the competition of quantum charge delocalization and their localization due to solvation forces can be found in Sect. 10.1. In Sect. 10.1 we also compare a theoretical description of localization/delocalization processes with an approach used to study large polaron formation. Here we focus on the theoretical framework appropriate for analysis of the influence of solvent polarization on charge transport. A convenient method to treat this effect is based on the combination of a tight-binding model for electronic motion and linear response theory for polarization of the water surroundings. To be more specific, let us consider a sequence... 

The conclusions reached by Costentin and SavOant are in fact quite consistent with our own. The main difference is that, according to these authors, the notion of an imbalanced transition state should be placed within the context of charge localization-delocalization heavy-atom intramolecular reorganization rather than of synchronization (or lack thereof) between charge delocalization and proton transfer. ... 

This has been developed since 1986. The title letters stand for Localized Delocalized Response. The localized effect is Charton s preferred name for the inductive effect and... 

The electrostatic interaction is apparently insufficient to bind both 0 to the cation vacancy While one 0 remains with the vacancy, though locally delocalized (22.), the other becomes unbound (22). An unbound 0 is a mobile charge carrier moving through the host matrix by a succession of electron jumps from 02 to 02". Because the 0 states are positively charged with respect to 02 they have been called "positive holes" (22). 0 states repel each other in the bulk and tend to diffuse towards the surface causing the surface to become positively charged. 

Three types of solvent or solute delocalization have now been examined, as summarized in Table III for three different adsorbent types (four, if we distinguish Cig-deactivated silica from silica). The theoretical requirements on the configuration and density of adsorption sites were discussed earlier (Section II,B) for a given type of localization/delocalization to be possible. In each case the nature of adsorption sites is fairly well understood for the four adsorbents of Table III, as disucssed in Ref. / and 17 and shown in Fig. 14. Thus, in the case of alumina, surface hydroxyls do not function as adsorption sites. Although surface oxide atoms are capable of interacting with acidic adsorbate molecules (see below), in most cases the adsorbate will interact with a cationic center (either aluminum atom or lattice defect) in the next layer. As a result, we can say that in most cases adsorption sites on alumina are buried within the surface, rather than being exposed for covalent site-adsorbate interaction. These sites are also rigidly positioned within the surface. Finally, the... 

Localization-Delocalization Effects for Different Adsorbents. The Nature of Adsorption Sites... 

In this paper, we studied the glass transition and the localization-delocalization transition in a disparate-size hard-sphere mixture from a dynamical viewpoint. For Cl = 0.5, the existence of the delocalized phase of the small particles is confirmed by investigating the frequency-dependent diffusion constant. Near the glass transition, we found an additional quasi-elastic structure in " q,uj) and Di(u>) at small o), which suggests that the diffusion mechanism of the small particles would change from the liquid-like diffusion to a slow diffusion in a random potential. 

If the Fermi level is at an energy such that the electronic states are extended, then finite conductivity at zero temperature is expected. This model assumes that the substantial disorder is homogeneous through the isotropic three-dimensional sample. Other external parameters such as magnetic field or pressure can affect the localization/delocalization transition and the localization lengths. This model has received much experimental attention for doped and ion implanted polymers [2,49], although more recent studies of ion-implanted rigid rod and ladder polymers reveals a three-dimensional semimetallic conductor with weak localization effects [50]. 

Robin and Day Classification in Generalized Vibronic Model Localization-Delocalization, Hyperfine Constants... 

The results obtained shows that only one kind of minima can exist in each particular case these can be either the minima in which the system is partially or fully localized (delocalized states are unstable) or the minima in which the system is delocalized (localized states are unstable). The coexistence of the localized and delocalized minima proves to be impossible. This is similar to the well-known situation in the classical Jahn-Teller T2 (g) (e -b t2) problem, for which either tetragonal or trigonal minima can exist but never both of them simultaneously [46,47]. 

Multimode Jahn-Teller Problem in Mixed-Valence Trimers Vibronic Localization-Delocalization... 

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