Band theory of metallic bonding

Let us now summarize some of the physical properties of metals in terms of the band theory of metallic bonding. 

Phase Diagrams (P versus T) 13-14 Amorphous Solids and Crystalline Solids 13-15 Structures of Crystals 13-16 Bonding in Solids 13-17 Band Theory of Metals... 

Bonding in metals is called metallic bonding. It results from the electrical attractions among positively charged metal ions and mobile, delocalized electrons belonging to the crystal as a whole. The properties associated with metals—metallic luster, high thermal and electrical conductivity, and so on—can be explained by the band theory of metals, which we now describe. 

Band theory of metals A theory that accounts for the bonding and properties of metallic solids. 

A Use an internet search engine (such as http //www. google.com) to locate information on the comparison of other bonding theories (such as valence bond theory, crystal field theory, band theory, and metallic bonding) to molecular orbital theory How are they related ... 

In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

The free-electron model is a simplified representation of metallic bonding. While it is helpful for visualizing metals at the atomic level, this model cannot sufficiently explain the properties of all metals. Quantum mechanics offers a more comprehensive model for metallic bonding. Go to the web site above, and click on Web Links. This will launch you into the world of molecular orbitals and band theory. Use a graphic organizer or write a brief report that compares the free-electron and band-theory models of metallic bonding. 

The distances found between platinum centers in these molecules have been correlated with the resonating valence bond theory of metals introduced by Pauling. The experimentally characterized partially oxidized one-dimensional platinum complexes fit a correlation of bond number vs. metal-metal distances, and evidence is presented that Pt—Pt bond formation in the one-dimensional chains is resonance stabilized to produce equivalent Pt—Pt distances.297 The band structure of the Pt(CN)2- chain has also been studied by the extended Huckel method. From the band structure and the density of states it is possible to derive an expression for the total energy per unit cell as a function of partial oxidation of the polymer. The equilibrium Pt-Pt separation estimated from this calculation decreases to less than 3 A for a loss of 0.3 electrons per platinum.298... 

The band picture of metals developed by physicists accounts very well for conduction and other electric and magnetic properties. The valence bond description of the bonds in metals related to the concepts of chemistry explains much better than the former theory such properties as lattice energies and bond distances. Today, however, the V.B. picture does not lend itself well to a priori quantitative calculations of these properties and it seems doubtful to what extent a bond in solid lithium with a bond order of o. 11 (with respect to the bond order one in a gas molecule) has any fundamental meaning. There is no doubt, however, that in less typical metals and compounds Pauling s theory is valuable as a counterpart to the band picture, just as the V.B. and the M.O. methods are both of great importance for the description of the constitution of organic molecules. 

Besides the electron occupation of the d bands, another description can be used for obtaining correlations, namely, the valence bond theory of metals. The bonding in a transition metal is partially due to impaired electrons in bonding d orbitals. The contribution of these d electrons to the valence bonding was termed percentage d... 

In the previous chapters, we discussed various models of bonding for covalent and polar covalent molecules (the VSEPR and LCP models, valence bond theory, and molecular orbital theory). We shall now turn our focus to a discussion of models describing metallic bonding. We begin with the free electron model, which assumes that the ionized electrons in a metallic solid have been completely removed from the influence of the atoms in the crystal and exist essentially as an electron gas. Freshman chemistry books typically describe this simplified version of metallic bonding as a sea of electrons that is delocalized over all the metal atoms in the crystalline solid. We shall then progress to the band theory of solids, which results from introducing the periodic potential of the crystalline lattice. 

Bonding in Solids Metals, Insulators, and Semiconductors Models of Metallic Bonding Band Theory and Conductivity Semiconductors... 

In Section 6.3, we saw that the ability of metals to conduct heat and electricity can be explained by considering the metal to be an array of positive ions immersed in a sea of highly mobile delocalized valence electrons. In this section, we will use our knowledge of quantum mechanics and molecular orbital theory to develop a more detailed model for the conductivity of metals. The model we will use to study metallic bonding is the band theory of conductivity, so called because it states that delocalized electrons move freely through "bands formed by overlapping molecular orbitals. We will also apply band theory to understand the properties of semiconductors and insulators. 

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