Core electrons properties

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

The fractal-like organization led, therefore, to conductivity measurements at three different scales (1) the macroscopic, mm-size core of nanotube containing material, (2) a large (60 nm) bundle of nanotubes and, (3) a single microbundle, 50 nm in diameter. These measurements, though they do not allow direct insights on the electronic properties of an individual tube give, nevertheless, at a different scale and within certain limits fairly useful information on these properties. 

Although CNTs showed similar EELS pattern in plasmon-loss and core-loss regions to graphite, SWCNT and fine MWCNT with a diameter less than 5 nm had different features. Furthermore, it has been found out that the angular-dependent EELS along the direction normal to the longitudinal axis of CNT shows stronger contribution from Jt electrons than [Pg.38]

The chemical similarities of periodic elements arise because the valence electrons determine most of the chemical properties of molecules. The core electrons are only slightly affected by their chemical environment and act primarily to shield the nuclei. They also provide an effective field for the valence electrons. 

The effect of core-electron correlation is small, as shown in Table 11.16. It should be noted that the valence and core correlation energy per electron pair is of the same magnitude, however, the core correlation is almost constant over the whole energy surface and consequently contributes very little to properties depending on relative energies, like vibrational frequencies. It should be noted that relativistic corrections for the frequencies are expected to be of the order of 1 cm" or less. ... 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

The basic idea of the pseudopotential theory is to replace the strong electron-ion potential by a much weaker potential - a pseudopotential that can describe the salient features of the valence electrons which determine most physical properties of molecules to a much greater extent than the core electrons do. Within the pseudopotential approximation, the core electrons are totally ignored and only the behaviour of the valence electrons outside the core region is considered as important and is described as accurately as possible [54]. Thus the core electrons and the strong ionic potential are replaced by a much weaker pseudopotential which acts on the associated valence pseudo wave functions rather than the real valence wave functions (p ). As... 

By flourescence techniques, it was observed that the fluorescence yield and lifetime of 1,8-anilinonaphthalenesulfonate decrease with an increase in the aqueous core of AOT-reversed micelles, while the position of the emission maximum shifts to longer wavelengths [64], These changes in the electronic properties were attributed to the peculiar effective polarity and viscosity of the micellar core and to their evolution with R. 

The metal size clearly increases when the decomposition takes place on the substrate. Nevertheless, the overall shift after complete decomposition is the same both on crystalline and amorphous substrates. This can be explained by the assumption that the increase of the number of the metal atoms in the cluster takes place also on an amorphous substrate, on a scale high enough to shift the core levels but low enough to maintain a constant emitted intensity ratio between the substrate and the metal core levels. The authors concluded therefore that the core-level position is highly size-sensitive in the range of very small particles, e.g. < 100 atoms where the associated electronic properties are primarily atomic. However, on approaching the metallic state for >100 atoms, the corelevel shift is a much poorer criterion of the cluster size. 

As was mentioned previously, photoemission has proved to be a valuable tool for measurement of the electronic structure of metal cluster particles. The information measured includes mapping the cluster DOS, ionization threshold, core-level positions, and adsorbate structure. These studies have been directed mainly toward elucidation of the convergence of these electronic properties towards their bulk analogues. Although we will explore several studies in detail, we can say that studies from different laboratories support the view that particles of 150 atoms or more are required to attain nearly bulk-like photoemission properties of transition and noble metal clusters. This result is probably one of the most firmly established findings in the area of small particles. 

Interpretation of this observed correlation between a lowered affinity of the metal surface to oxygen and a higher rate of ORR measured at a Pt shell over a Pt-alloy core has also been at the center of recent theoretical work, based primarily on DFT calculations of electronic properties and surface bond strengths for a variety of expected ORR intermediates at metal and metal alloy catalysts. The second part of this chapter contains a discussion of these valuable contributions and of outstanding issues in tying together this recent theoretical work and ORR experimental data. 

Most of the other metal-related deep levels in Si are also passivated by reaction with hydrogen (Pearton, 1985). Silver, for example, gives rise in general to a donor level at Ee + 0.54 eV and an acceptor level at Ec - 0.54 e V (Chen and Milnes, 1980 Milnes, 1973). These levels are very similar to those shown by Au, Co and Rh and raise the question of whether Au might actually be introduced into all of the reported samples or a contaminant, or whether as discussed by several authors there is a similar core to these impurity centers giving rise to similar electronic properties (Mesli et al., 1987 Lang et al., 1980). This problem has not been adequately decided at this time. It has been... 

A further simplication often used in density-functional calculations is the use of pseudopotentials. Most properties of molecules and solids are indeed determined by the valence electrons, i.e., those electrons in outer shells that take part in the bonding between atoms. The core electrons can be removed from the problem by representing the ionic core (i.e., nucleus plus inner shells of electrons) by a pseudopotential. State-of-the-art calculations employ nonlocal, norm-conserving pseudopotentials that are generated from atomic calculations and do not contain any fitting to experiment (Hamann et al., 1979). Such calculations can therefore be called ab initio, or first-principles. ... 

The fundamental physical properties of nanowire materials can be improved even more to surpass their bulk counterpart using precisely engineered NW heterostructures. It has been recently demonstrated that Si/Ge/Si core/shell nanowires exhibit electron mobility surpassing that of state-of-the-art technology.46 Group III-V nitride core/shell NWs of multiple layers of epitaxial structures with atomically sharp interfaces have also been demonstrated with well-controlled and tunable optical and electronic properties.47,48 Together, the studies demonstrate that semiconductor nanowires represent one of the best-defined nanoscale building block classes, with well-controlled chemical composition, physical size, and superior electronic/optical properties, and therefore, that they are ideally suited for assembly of more complex functional systems. 

The timescale of a microwave observation is ca 10 12s so that an average of the properties of the species in equilibrium (35) is obtained if the equilibrium occurs in a time shorter than this. The X-ray photoelectron spectra of intramolecularly hydrogen-bonded species in the gas phase have been studied in an attempt to obtain an instantaneous picture of the structure of these molecules. In this technique the ionisation of core electrons which occurs within 10 16s is observed. For malondialdehyde, 6-hydroxy-2-formyl-fulvene, 2-hydroxy-1,1,1,5,5,5-hexafluoropent-2-ene-4-one, 9-hydroxyphen-alenone [19], and tropolone [20], two peaks are observed in the Ou region of the photoelectron spectrum (Brown et al., 1979). If these molecules existed in the C2v form with a symmetrical hydrogen bond and equivalent oxygen... 

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