Localized vs. delocalized

Charge Localized vs. Delocalized Wavefunctions. In the spirit of the Condon approximation discussed above, we do not include the full dependence of the purely electronic matrix elements on q n, but rather evaluate them where the diabatic curves... 

High-Nuclearity Mixed-Valence Clusters Localization vs. Delocalization of the Electronic Pair in the Double Reduced Polyoxometallates with Keggin Structure... 

It should be noted that such a local view is entirely inappropriate for covalent semiconductors such as silicon, in which the electrons are completely delocalized over the material. This local vs. delocalized view is a key feature that distinguishes metal oxide semiconductors from their covalently bonded counterparts. The local character of the energy bands in metal oxides sometimes leads to ambiguous interpretatiOTis. For example, free electrons in Ti02 are sometimes distinguished from Ti species. While such a distinction may be realistic at the surface of a material, where the electronic structure is distorted due to a disruption of the lattice symmetry, it is not obvious in the bulk in which the conduction band is mainly composed of Ti 3d orbitals. 

One of the consequences of universality, well known from the study of phase transitions, is that systems with different microscopic Hamiltonians can have similar behaviors. This may be an important contributing factor to the observation that despite the basic difference between lanthanides and actinides (localized vs. delocalized electrons) the heavy-fermion behavior is similar. To the extent that this is so, pressure studies will not distinguish the two cases. Conversely, it is only to the extent that universality is violated, or is not expected, that we can expect to observe differences between itinerant and localized systems. Apart from deviations from scaling in measurements where universal behavior is expected, we will show from measurements of magnetic phase boundaries and of X-ray absorption spectra that differences between lanthanide and actinide behaviors are observable. 

Localized vs. Delocalized Electrons Oxygen Desorption and Perovskite Stability Equations for Oxygen Transport Electronic Conductivity... 

The theoretical treatment of a solid-state transition involving covalent (localized) vs. conduction (delocalized) electronic transformation was first enunciated by Mott [44], By considering the Pauli Exclusion Principle and the electron-electron interaction during the transformation, it was shown that such transition will be critically dependent upon the inter-atomic distances. The number of electrons already existing in the conduction state will in turn influence the critical inter-atomic distances and the transition therefore, it is necessarily a cooperative phenomenon. Later, in a theoretical treatment of the same subject, but based on a different context, Goodenough [45] has shown that the transition is likely to be second-order if the number of electrons per like atom is non-integral. Further, a crystallographic distortion is a prominent manifestation of such a transition. 

The organometallic compound shown below is represented with a Cr=Cr triple bond in the literature. Describe it as a cluster compound. The measured Cr-Cr distance is 2.34 A consistent with a triple bond. Comment on factors that favor localized Cr-Cr multiple bonding vs. delocalized cluster bonding as a mechanism for accommodating the electronic unsaturation. 

In summary, the anions of group 14 metalloles (C4E rings) have either localized nonaromatic or delocalized aromatic structures, depending of the metal E, Si vs Ge and Sn, and on the substituents, methyl vs phenyl group. As pointed out by West and coworkers198, structural studies of metallole anions and dianions of this kind with different substituents will be of value. Additionally, it should be noted that experimentally observed structures in the solid state for silole and germole dianions are greatly influenced by the nature of the alkali metal counterion. 

Figs. 7 and 8 illustrate the HEP analysis for the XT-CT model in more detail. Fig. 7 shows the decomposition of the first three modes of the hierarchy (Xi, X2, X3) into the primitive phonon modes [93], As mentioned above, these modes constituting Heg, are all of high-frequency type. Two of these effective modes can be seen to be localized on the TFB vs. F8BT moieties, whereas the third mode is delocalized over both chains. 

Eg 3.5 eV, of the (C2S) helix polymer and indicated that the electron localization occurs already for n < 7 [64]. These results are in contrast to electron delocalization in [n]heliphenes, [njhelicenes and [njthiahelicenes, which possess much lower Eg values of 2.1-2.5 eV. These results are consistent with cyclic voltam-metric data. [nJHelicenes 40, 44 and 45 showed reversible cyclic voltammetric waves (1.2-1.3 V vs. SCE) the second oxidation wave for 40 was found at 1.8 V, i.e. at a significantly more positive potential [64, 85]. 

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