Electronic structure of metals

The free-clectron approximation described in Chapter 15 is so successful that it is natural to expect that any effects of the pseudopotential can be treated as small perturbations, and this turns out to be true for the simple metals. This is only possible, however, if it is the pscudopotential, not the true potential, which is treated as the perturbation. If we were to start with a frcc-electron gas and slowly introduce the true potential, states of negative energy would occur, becoming finally the tightly bound core states these arc drastic modifications of the electron gas. If, however, we start with the valence-electron gas and introduce the pscudopotential, the core states arc already there, and full, and the effects of the pseudopotential arc small, as would be suggested by the small magnitude of the empty-core pseudopotential shown in Fig. 15-3. 

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In this section the electronic structure of metal/polymcr/metal devices is considered. This is the essential starting point to describe the operating characteristics of LEDs. The first section describes internal photoemission measurements of metal/ polymer Schottky energy barriers in device structures. The second section presents measurements of built-in potentials which occur in device structures employing metals with different Schottky energy barriers. The Schottky energy barriers and the diode built-in potential largely determine the electrical characteristics of polymer LEDs. 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

The resonating-valence-bond theory of the electronic structure of metals is based upon the idea that pairs of electrons, occupying bond positions between adjacent pairs of atoms, are able to carry out unsynchronized or partially unsynchronized resonance through the crystal.4 In the course of the development of the theory a wave function was formulated describing the crystal in terms of two-electron functions in the various bond positions, with use of Bloch factors corresponding to different values of the electron-pair momentum.5 The part of the wave function corresponding to the electron pair was given as... 

In this contribution it is shown that local density functional (LDF) theory accurately predicts structural and electronic properties of metallic systems (such as W and its (001) surface) and covalently bonded systems (such as graphite and the ethylene and fluorine molecules). Furthermore, electron density related quantities such as the spin density compare excellently with experiment as illustrated for the di-phenyl-picryl-hydrazyl (DPPH) radical. Finally, the capabilities of this approach are demonstrated for the bonding of Cu and Ag on a Si(lll) surface as related to their catalytic activities. Thus, LDF theory provides a unified approach to the electronic structures of metals, covalendy bonded molecules, as well as semiconductor surfaces. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

Electrochemical reactions at semiconductor electrodes have a number of special features relative to reactions at metal electrodes these arise from the electronic structure found in the bulk and at the surface of semiconductors. The electronic structure of metals is mainly a function only of their chemical nature. That of semiconductors is also a function of other factors acceptor- or donor-type impurities present in bulk, the character of surface states (which in turn is determined largely by surface pretreatment), the action of light, and so on. Therefore, the electronic structure of semiconductors having a particular chemical composition can vary widely. This is part of the explanation for the appreciable scatter of experimental data obtained by different workers. For reproducible results one must clearly define all factors that may influence the state of the semiconductor. 

Photoemission has been proved to be a tool for measurement of the electronic structure of metal nanoparticles. The information is gained for DOS in the valence-band region, ionization threshold, core-level positions, and adsorbate structure. In a very simplified picture photoemission transforms the energy distribution of the bounded electrons into the kinetic energy distribution of free electrons leaving the sample, which can easily be measured ... 

In this section we outline briefly the spectral and magnetic properties of complexes of the metals of Table 5. These are the properties that enable the stereo-chemical and electronic structures of metal complexes to be determined in solution and, hence in a biological environment. A study of these properties will be necessary to understand the nature of the interaction of the anti-tumour compounds with biological systems. 

We begin with a presentation of the ideas of the electronic structure of metals. A liquid or solid metal of course consists of positively charged nuclei and electrons. However, since most of the electrons are tightly bound to individual nuclei, one can treat a system of positive ions or ion cores (nuclei plus core electrons) and free electrons, bound to the metal as a whole. In a simple metal, the electrons of the latter type, which are treated explicitly, are the conduction electrons, whose parentage is the valence electrons of the metal atoms all others are considered as part of the cores. In some metals, such as the transition elements, the distinction between core and conduction electrons is not as sharp. 

It is well-established that the molecular and electronic structures of metal complexes of azamacrocycles are greatly affected upon N-alkylation (197). This is mainly due to two factors (a) the decrease of the ligand field strength and (b) the increase in the steric requirements upon going from a secondary to a tertiary amine donor function (251). To examine whether the properties of the dinuclear amine-thiophenolate complexes are affected by the N-alkyl substituents, analogous complexes of the... 

In this section we treat the bulk and surface properties of metals relevant to the problems of electrochemical deposition. First, we discuss briefly the bulk and electronic structure of metals and then analyze the surface properties. Surface properties of the greatest interest in electrodeposition are atomic and electronic structure, surface diffusion, and interaction with the metal surface (adsorption) of atoms and molecules in solution. 

Electronic structures of metal vinylidene and allenylidene complexes... 

Electronic Structures of Metal Vinylidene and Allenylidene Complexes... 

Electronic Structures of Metal VinYlidene and Allenylidene Complexes 131... 

In this chapter, we first analyzed the electronic structures of metal vinylidene and allenylidene complexes. The electronic structures allow us to understand the reactivities of these complexes. For metal vinylidene complexes of the Fischer-type, nucleophilic attack usually occurs at the a-carbon and electrophilic attack at the P-carbon. For the corresponding metal allenylidenes, electrophilic attack occurs at the P-carbon and/or the metal center. Then we briefly reviewed the theoretical study of the barriers ofrotation ofvinylidene ligands in various flve-coordinate complexes M (X) C1(=C=CHR)L2 (M = Os, Ru L = phosphine). The study showed that 7t-acceptor ligands (X), electron-withdrawing substituents and lighter metals gave smaller barriers. 

Lang, N. D. (1973). The density-functional formalism and the electronic structure of metal surfaces. In Solid State Physics, edited by H. Ehrenreich, F. Seitz, and D. Turnbull, Vol. 28, Academic, New York. 

Research on alloy catalysts started in the 1950s with attempts to investigate the role in catalysis of the electronic structure of metals. This research was initiated by several papers of Dowden which, measured by their response in the literature, rank among the most important papers ever written on catalysis. However, it appeared later (for reviews, see 1-5) that two basic ideas, on which the so-called electronic theory of catalysis was built up, were not correct. These ideas were as follows ... 

From the various methods to be used to investigate the electronic structure of metals, probably the ultraviolet photoelectron spectroscopy (UPS) and X-ray photoelectron spectroscopy (XPS) methods brought forth the information most relevant for catalysis and surface science. These methods are best suited to monitor the changes in characteristics parameters of the d-bands by alloying, and since the most catalytically active metals are transition metals where d-orbitals are the frontier orbitals (Fermi level is cutting the d-band), the interest in these methods is not incidental. 

Considerable progress has been made in accumulating information on the electronic structure of metals and alloys, on some aspects of the structure of hydrocarbon adsorption complexes, etc. Also, information on the relative importance of the electronic structure effects of alloying—as contrasted to the geometric, ensemble size effects—has grown appreciably. 

The electron transfer series of [Fe(NO)(cyclam-ac)F (x = +2, +1, and 0) (102) (Fig. 14) that composes the FeNO " (re = 6, 7, and 8) complex series in the convenient notation suggested by Enemark and Feltham (103) is a good example that clearly shows the value of DFT calculations applied together with experimental Moss-bauer and IR spectroscopy to gain insight into the electronic structure of metal—radical complexes. 

Percentage d-character Considering the electronic structure of metals thus derived, Pauling then calculates the percentage d-character of the metallic bonds, the percentage d-character being an indication of bond strength. As examples, we have chosen cobalt, nickel and copper (Table I). 

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