Electron localization indicator

Kohout [10] used this function as an electron localization indicator (ELI). In the electron localization function (ELF), this function is scaled ... 

The issue was investigated in detail by the whole cornucopia of contemporary theoretical methods, among them are the density functional theory (DFT), the electron localization function (ELF), the electron localization indicator (ELI), the quantum theory of atoms in molecules (QTAIM, vide infra Chap. 2) and the valence electron equivalent (/). DFT calculations and QTAIM topological analyses... 

Electrophilic substitution reactions of unsubstituted quinoxaline or phenazine are unusual however, in view of the increased resonance possibilities in the transition states leading to the products one would predict that electrophilic substitution should be more facile than with pyrazine itself (c/. the relationship between pyridine and quinoline). In the case of quinoxaline, electron localization calculations (57JCS2521) indicate the highest electron density at positions 5 and 8 and substitution would be expected to occur at these positions. Nitration is only effected under forcing conditions, e.g. with concentrated nitric acid and oleum at 90 °C for 24 hours a 1.5% yield of 5-nitroquinoxaline (19) is obtained. The major product is 5,6-dinitroquinoxaline (20), formed in 24% yield. 

A quantitative study on local aromaticity based on n-center electron delocalization indices, wheren is the number of atoms in the ring, was performed on benzo[c]furan and benzo[b]furan. 

Fig. 2. We show the electron localization function (ELF) of (from left to right and from above to below) the Cl-, the AlCLj-, the 12 1 , the A12C17-, and the AI4CI13- species. The purple colored space indicates high values of ELF or electron pairs. Therefore, electron deficiency can be recognized from the half open spheres.

Fig. 3. Two STM images of the nickelfl 1 1) surface with 2% (right) and 7% (left) gold coverage, respectively. Au is imaged as dark depressions in the surface. The nickel atoms surrounding the gold appear brighter owing to a local modification of the electronic structure, indicating a changed chemical reactivity of these. Adapted from Reference (79).

Energy levels corresponding to electrons localized near the surface may also be present. These are termed surface states. For example, adsorbed ions are one type of surface state they may be of the form of donors, such as hydrogen, which yield electrons to the material, or in the form of acceptors, such as oxygen, which accept, or trap electrons from the material. In Fig. 1, surface traps of the acceptor type are shown, and it is indicated that there are two possible levels present. Other possibilities are impurity atoms at the surface, which are introduced in the preparation of the sample or diffuse from the interior during heat treatment, or nonstoichiometry of the surface layers of the compound. Surface... 

Neither of the above species is a ground-state quintet (four unpaired electrons). The pairing indicated by the valence bond structures shown above apparently occurs, leaving the unpaired electrons localized in a orbitals that are approximately orthogonal to the n system. The very small zero-field splitting is perhaps a measure of the validity of the o—7r separation which constitutes the basic assumption of 7r-electron theory. 

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]. 

Finally, just as we were able to define in Sect. 5 the nuclear softness, a local nuclear reactivity index in analogy with the electronic local softness, we can now introduce nonlocal nuclear reactivity indices in analogy to the electronic softness kernels [3], We define the nuclear softness kernels as follows... 

The electron diffraction results support the occurrence of soft-segment crystallinity and a more disordered hard-segment phase in the solvent-cast samples. Moreover, electron diffraction indicates isolated crystalline soft-segment regions persist even in samples of up to 43% hard segment. Electron diffraction is very sensitive to small local fluctuations in the overall structure because the diffraction patterns can be obtained from regions less than 1 /un in diameter and less than. l-/un thick, whereas DSC and WAXS, of course, measure bulk polymer which yields averages over the whole sample. 

Similar comparisons between the anion yield functions from basic DNA constituents and those of CE and OH from DNA films [47] indicate that O production arises from temporary electron localization on the phosphate group. The yield function for OH desorption resembles that of CE, but has a lower... 

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