Localization of electrons

Structural parameters and interatomic distances derived from electron diffraction (7) (77JST(42)l2i) and X-ray diffraction (8) studies (76AX(B)3178) provide unequivocal evidence that pyrazine is planar with >2a symmetry. There is an increased localization of electron density in the carbon-nitrogen bonds, with carbon-carbon bonds being similar in length to those in benzene. ... 

In the spectra of the MA/TBSM mixture, the absorption band of the C = C bond is observed to shift to a shorter wavelength which indicates localization of electron density toward the trialkylstannyl group 2,19). 

Electrons in the core of an atom are fully localized into spherical shells but not into opposite-spin pairs. In an isolated atom the valence shell electrons are similarly localized into a spherical shell. The Laplacian shows that in each of these spherical shells there is a spherical region of charge concentration and a spherical region of charge depletion. But in these regions there is no localization of electrons of opposite spin into pairs. There are no Lewis pairs or electron pair domains in an inner shell. The domain of each electron is spherical and fully delocalized through the shell. 

The second difference caused by photo-excitation is to decrease the bond dissociation energy (see Figure 9.13). We will call the new value of bond dissociation energy A//i ( 1 here because we refer to the first excited state.) This decrease arises from differences in the localization of electrons within the molecular orbitals in the ground and excited states. 

The localization of electron density on heteroatoms is seen during the nitration of anilines which are A-nitrated in aprotic media. " Anilines can give abnormal o p-isomer ratios resulting from a process of A-nitration followed by rearrangement to the ring nitrated product, a process which often occurs in situ in the strongly acidic medium of mixed acid (Section 4.5). 

Transforming Eq. (1.4a), which exhibits a ri —rj dependence, at least partially into a rj I dependence is not obvious and deserves special attention for, a priori, electron Coulomb repulsion cannot be ignored. The energy contribution from the repulsive Coulombic term will be represented by t/. In transition metals and their oxides, electrons experience strong Coulombic repulsion due to spatial confinement in d and / orbitals. Spatial confinement and electronic correlations are closely related and because of the localization of electrons materials may become insulators. 

Anderson localization is the localization of electrons on low-dimensional materials, which is induced by the irregularity of the periodic potential field [43]. Figure 17 gives a schematic representation of Anderson localization of a particle in one-dimensional box. The same is true for an electron on a polymer skeleton. A localized state in a completely periodic... 

In this chapter we are concerned with the magnetic properties of the actinides. How the localization of electrons belonging to an incomplete shell is related to their magnetic properties This is an old question to which it is possible to answer qualitatively if not quantitatively. There are 2 extreme points of view to approach this crucial problem,... 

Solid HjPMo o reduced by H2 at a lower temperature shows a very weak ESR signal intensity of Mo5 +, probably because most of the Mo5+ ions are not detectable due to the rapid hopping of electrons. Heat treatment, which eliminates oxide ions from the heteropoly anion, leads to development of the Mo5 + signal, indicating the localization of electrons (101, 102). Early reports of ESR spectra of reduced PMo C o are likely due to these species. Several different species are observed in highly reduced samples. 

The Laplacian of the electron density plays a dominant role throughout the theory.191 In addition, Bader has shown that the topology of the Laplacian recovers the Lewis model of the electron pair, a model that is not evident in the topology of the electron density itself. The Laplacian of the density thus provides a physical valence-shell electron pair repulsion (VSEPR) basis for the model of molecular geometry and for the prediction of the reaction sites and their relative alignment in acid-base reactions. This work is closely tied to earlier studies by Bader of the electron pair density, demonstrating that the spatial localization of electrons is a result of a corresponding localization of the Fermi correlation hole. 

The ejection of atoms or molecules from the surface of solid in response to primary electronic excitation is referred to as electronically stimulated desorption (ESD) or desorption induced by electronic transitions (DIET). Localization of electronic excitations at the surface of RGS induces DIET of atoms both in excited and in ground states, excimers and ions. Most authors (see e.g. Refs. [8,11,23,30] and references therein) discuss their results on DIET from RGS in terms of three different desorption mechanisms namely (i) M-STE-induced desorption of ground-state atoms (ii) "cavity-ejection" (CE) mechanism of desorption of excited atoms and excimers induced by exciton self-trapping at surface and (iii) "dissociative recombination" (DR) mechanism of desorption of excimers induced by dissociative recombination of trapped holes with electrons. 

If total number of dipoles ft surrounded M nanoparticle is equal to C, the number of dipoles Cat oriented toward particle in a time t, after localization of electron on a particle can be, in the first approximation, presented as Cdt — C[ 1 — exp(—Tt/ti)]. According to the proposed model this rearrangement of molecular dipoles creates in a nearest environment of particle dipole... 

Electron-Hole Pairs. Localization of electrons and holes occurs via the processes of non-radiative charge trapping. These processes are represented phenomenologically in Figure 1. An example of a simple trapping process is the coulombic attraction of an electron and an... 

The size-dependent properties of nanoparticles differ greatly from the corresponding bulk materials. An example is the size quantization phenomenon commonly observed in II-VI and III-V inorganic semiconductor nanocrystals.6 During the intermediate transition towards that of the bulk metal (usually between 2 and 20 nm), localization of electrons and holes in a confined volume causes an increase in its effective optical band gap as the size of the nanoparticle decreases, observed as a blue shift in its optical spectrum. Bms predicted that there should also be a dependence on the redox potential for these same classes of quantum dots.7 Bard and coworkers showed this experimentally and have reported on the direct observation between the... 

There is no quantum-mechanical evidence for the localization of electron pairs between atomic nuclei, and atomic orbitals, in so far as they correspond to spherical surface harmonics, have their nodal curves in the surface of the density sphere. Sets of real hybrid orbitals are physically undefined. To understand intramolecular interactions as a quantum phenomenon it is necessary to approach the problem with the minimum of assumptions and to state all essential assumptions clearly and precisely at the outset. 

In 1958, Anderson [9] showed that localization of electronic wavefunctions occurs if the random component of the disorder potential is large with respect to the bandwidth of the system, as shown in the schematic diagram in Fig. 3.1. The mean free path ( ) in a system with bandwidth B, random potential Vo, and interatomic distance a is given by... 

Here, an is the Bohr orbit radius of the isolated center and nc is the critical carrier density at the M-NM transition. Another way of viewing the transition is that of an electronic instability which ensues when the trapping of an electron into a localized level also removes one electron from the Fermi gas of electrons. This must clearly lead to a further reduction in the screening properties (which are themselves directly related to the conduction electron density) and a catastrophic situation then ensures the localization of electrons from the previously metallic electron gas. 

The M-I transition in doped CPs is mainly governed by the extent of disorder, inter-chain interaction and doping level.88 89 It is well known that disorder potentials can localize the electronic states. If the random component of the disorder potential is large with respect to the bandwidth, then the localization of electronic wave functions can occur. In the presence of strong disorder, the overlap of the wave functions drops off exponentially and the system moves towards the insulating regime. 

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