Localizing electrons

Hamers R J and Kohler U K 1989 Determination of the local electronic structure of atomic-sized defects on Si(OOI) by tunnelling spectroscopy J. Vac. Sc/. Technol. A 7 2854... 

There are otlier, more exotic, possibilities. For example, if a defect has an empty level near the CB, an electron may become trapped in it. This localized electron may in turn bind a hole in a loose orbit, fonning a boundexciton. 

Eig. 3. Absorption spectra of dyes (12) showing local electron transition (28). See Eig. 2 for curve descriptions. 

The methods described above are used widely in the synthesis of dyes with new heterocycHc residues such as tropjlium (25) [76430-96-1] (102), 2,4-diphen5lpyryHum and its heteroanalogues (26) with a high effective length (103,104), or exotic systems (27) with long-wavelength local electron transitions (105) (Fig. 7). 

The first step for any structure elucidation is the assignment of the frequencies (chemical shifts) of the protons and other NMR-active nuclei ( C, N). Although the frequencies of the nuclei in the magnetic field depend on the local electronic environment produced by the three-dimensional structure, a direct correlation to structure is very complicated. The application of chemical shift in structure calculation has been limited to final structure refinements, using empirical relations [14,15] for proton and chemical shifts and ab initio calculation for chemical shifts of certain residues [16]. 

Parameters measured Surface topography (SFM and STM) local electronic structure (STM)... 

Other artifacts that have been mentioned arise from the sensitivity of STM to local electronic structure, and the sensitivity of SFM to the rigidity of the sample s surface. Regions of variable conductivity will be convolved with topographic features in STM, and soft surfaces can deform under the pressure of the SFM tip. The latter can be addressed by operating SFM in the attractive mode, at some sacrifice in the lateral resolution. A limitation of both techniques is their inability to distinguish among atomic species, except in a limited number of circumstances with STM microscopy. 

The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. 

Langer et al. [10] measured also electrical resistance of individual MWCNTs at very low temperatures and in the presence of a transverse magnetic field. As for the case of the microbundle, the CNTs were synthesised using the standard carbon arc-discharge technique. Electrical gold contacts have been attached to the CNTs via local electron beam lithography with an STM. The measured individual MWCNT had a diameter of about 20 nm and a total length of the order of 1 im. 

Natural population analysis is carried out in terms of localized electron-pair bonding units. Here are the charges computed by natural population analysis (the essential output is extracted) ... 

Implementation of the Kohn-Sham-LCAO procedure is quite simple we replace the standard exchange term in the HF-LCAO expression by an appropriate Vxc that will depend on the local electron density and perhaps also its gradient. The new integrals involved contain fractional powers of the electron density and cannot be evaluated analytically. There are various ways forward, all of which... 

Another aspect of wave function instability concerns symmetry breaking, i.e. the wave function has a lower symmetry than the nuclear framework. It occurs for example for the allyl radical with an ROHF type wave function. The nuclear geometry has C21, symmetry, but the Cay symmetric wave function corresponds to a (first-order) saddle point. The lowest energy ROHF solution has only Cj symmetry, and corresponds to a localized double bond and a localized electron (radical). Relaxing the double occupancy constraint, and allowing the wave function to become UHF, re-establish the correct Cay symmetry. Such symmetry breaking phenomena usually indicate that the type of wave function used is not flexible enough for even a qualitatively correct description. 

According to its IR spectrum, phospharinane 141 exists in the solid state exclusively as the tautomer 141b possessing the localized electronic structure (Scheme 43) (83UK1761). However, by means of NMR and IR spectroscopy, it was shown that in CDCI3 solution the delocalized structure 141a is also present, although at a low relative concentration. 

Figure. 3 (a) Partial pair correlation function.s gij(B.) in liquid K-Sb alloys, (b) Total, partial, and local electronic densities of states in liquid Ko.soSbo.so- Cf. text. 

In this contribution, we review our recent work on disordered quasi-one-dimen-sional Peierls systems. In Section 3-2, we introduce the basic models and concepts. In Section 3-3, we discuss the localized electron stales in the FGM, while, in Section 3-4, we allow for lattice relaxation, leading to disorder-induced solitons. Finally, Section 3-5 contains the concluding remarks. 

In the 1,4-dihelerocine scries 1 with different heteroatoms only the 1,4-oxazocines 2 are known. As in the case of the 1,4-diazocines, depending upon the substituent on the nitrogen, these systems exhibit either nonplanarity with a localized -electron system for acceptor substituents or planar delocalized structures for donor-substituted or the unsubstituted systems.10... 

The Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... 

Homogeneous alloys of metals with atoms of similar radius are substitutional alloys. For example, in brass, zinc atoms readily replace copper atoms in the crystalline lattice, because they are nearly the same size (Fig. 16.41). However, the presence of the substituted atoms changes the lattice parameters and distorts the local electronic structure. This distortion lowers the electrical and thermal conductivity of the host metal, but it also increases hardness and strength. Coinage alloys are usually substitutional alloys. They are selected for durability—a coin must last for at least 3 years—and electrical resistance so that genuine coins can be identified by vending machines. 

Values for c in each method are obtained by solving the equation for various values of each c and choosing the solution of lowest energy. In practice, both methods give similar solutions for molecules that contain only localized electrons, and these are in agreement with the Lewis structures long familiar to the organic chemist. Delocalized systems are considered in Chapter 2. 

For each molecule, ion, or free radical that has only localized electrons, it is possible to draw an electronic formula, called a Lewis structure, that shows the location of these electrons. Only the valence electrons are shown. Valence electrons may be found in covalent bonds connecting two atoms or they may be unshared. The student must be able to draw these structures correctly, since the position of electrons changes in the course of a reaction, and it is necessary to know where the electrons are initially before one can follow where they are going. To this end, the following rules operate ... 

Mezey PG (1999) Local Electron Densities and Functional Groups in Quantum Chemistry. 203 167-186... 

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