Electronic properties of solids

This conclnsion is not corrrpatible with the Pauli exelrrsion prineiple, which states that two electrons cannot have the same energy level irrtless their spin values 

Historically, it is Drade who, in around 1900, first speculated that valence electrons could form a gas, and a classical theory based on the kinetic theory of gases made it possible to explain the high electrical conductivity of metals. 

However, since this theory was not in agreement with many experimental results, the calculations had to be redone using the principles of quantum mechanics.  

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D.G. Barton, M. Shtein, R.D. Wilson, S.L. Soled, and E. Iglesia, Structure and Electronic Properties of Solid Acids Based on Tungsten Oxide Nanostmctures, J. Phys. Chem. 103(4), 630-640 (1999). 

The reciprocal lattice is useful in defining some of the electronic properties of solids. That is, when we have a semi-conductor (or even a conductor like a metal), we find that the electrons are confined in a band, defined by the reciprocal lattice. This has important effects upon the conductivity of any solid and is known as the "band theory" of solids. It turns out that the reciprocal lattice is also the site of the Brillouin zones, i.e.- the "allowed" electron energy bands in the solid. How this originates is explciined as follows. 

The electronic properties of solids can be described by various theories which complement each other. For example band theory is suited for the analysis of the effect of a crystal lattice on the energy of the electrons. When the isolated atoms, which are characterized by filled or vacant orbitals, are assembled into a lattice containing ca. 5 x 1022 atoms cm 3, new molecular orbitals form (Bard, 1980). These orbitals are so closely spaced that they form essentially continuous bands the filled bonding orbitals form the valence band (vb) and the vacant antibonding orbitals form the conduction band (cb) (Fig. 10.5). These bands are separated by a forbidden region or band gap of energy Eg (eV). 

ELECTRONIC PROPERTIES OF SOLIDS USING CLUSTER METHODS Edited by T. A. Kaplan and S. D. Mahanti... 

Since the electronic properties of solids depend on the crystal structure, the transition from the crystalline to the amorphous state is expected to result in some modification of electronic (and surface) properties. Amorphous materials have first been used in catalysis [558-560] where some evidence for higher activity has been obtained [561]. In particular, hydrogenation reactions are catalyzed by this class of materials [562]. Studies on the H recombination reaction are also available [563]. However, the evidence that the amorphous state is really the origin of enhanced catalytic activity is not completely clear [562, 564]. These materials have the peculiarity that their surface is relatively homogeneous for a solid and in particular it is free from grain boundaries [565, 566]. Therefore, they have been suggested [562] as ideal model surfaces for studying elementary catalytic reactions, since they can be prepared with controlled electronic properties and controlled dispersion. Nevertheless, many prob-... 

T. Yildirim et al., First-principles investigation of structural and electronic properties of solid cubane and its doped derivatives. Phys. Rev. B 62, 7625 (2000)... 

The electronic properties of solid materials are normally described in terms of the band gap. In this description, the valence band is the ground state and the... 

Electronic Properties of Solids in Different Environments. When discussing the effect of wetting upon the structures of surface films, the author (39) paid particular attention to the electronic properties of solids, partly because they are directly visible (color, fluorescence), partly because they are easily measured (electrical conductivity) with great accuracy, and partly because they are of considerable technical interest. 

Within the last 30 years there has developed a lively interest in the electronic properties of solids, many of which depend upon the existence of lattice defects and departures from stoichiometry. 

OK, fine you say. So far we are treating the extended chain like a giant molecule and we are still stuck with drawing in 1023 levels for a mole of H atoms. In the manner of Hoffmann, we would like to have a detailed and informative model that we can use in discussions of the electronic properties of solids without dealing explicitly with all these levels. In addition, we want to emphasize connections between clusters (molecules) and extended systems (solid state). So let s dig around in this band a little bit more and see if we can eliminate the necessity of talking about 1023 orbitals in order to discuss and rationalize properties of extended systems. 

Bagus, P. S. lUas, F. Sousa, C. Pacchioni, G. The ground and excited state ofoxides in Electronic properties of solids using cluster models, p. 93, Edited by Kaplan T. A. and Mahanti S D., Plenum, New York, 1995. 

In circumstances where the electron energy bands arc neither completely full nor completely empty, the behavior of individual electrons in the bands will be of interest. This is not the principal area of concern in this text, but it is important to understand electron dynamics because this provides the link between the band properties and electronic properties of solids. 

The electronic properties of solids can be described by various theories that complement each other. For example, band theory is suited for the analysis of the effect of a crystal lattice on the energy of the electrons. When the isolated atoms, which are characterized by filled or vacant orbitals, are assembled into... 

Models that attempt to predict the behavior of materials using first principles quantum theory fall within this regime. These methods are applied to the development of traditional materials such as steels, refractory materials, ceramics, etc. as well as new materials such as those for microelectronics industries, catalysts of various kinds, materials for fuel cell applications, to name a few. Some examples of such properties are electronic properties of solids such as conductivity, absorption spectra, etc., reactivity of molecules, " selective binding of molecules to specific sites on surfaces, catalytic reaction pathways, and active sites on molecules. 

This leads to the appearance of local energy levels within the bandgap, which themselves lead to changes in the optical and electronic properties of solids. 

L. M. Tolhert, Acc. Chem. Res., 1992, 25, 561 R. Hoffmann, C. Janiak and C. Kollmar, Macromolecules, 1991, 24, 3725 J. Singleton, Band Theory and Electronic Properties of Solids, Oxford University Press, Oxford, 2001. 

An accurate representation of the electronic structure of atoms and molecules requires the incorporation of the effects of electron correlation, and this process imposes severe computational difficulties. It is, therefore, only natural to investigate the use of new and alternative formulations of the problem. Many-body theory methods offer a wide variety of attractive approaches to the treatment of electron correlation, in part because of their great successes in treating problems in quantum field theory, the statistical mechanics of many-body systems, and the electronic properties of solids. 

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