Metals, band theory Molecular orbital

Band theory molecular orbital theory of metals. (13 J) Barometer a device for measuring the pressure of the atmosphere. (5.1)... 

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 ... 

Band theory proposes that atomic orbitals of many atoms combine to form a continuum, or band, of molecular orbitals. Metals are electrical conductors because electrons move freely from the filled (valence) band to the empty (conduction) band. Insulators have a large energy gap between the two bands, and semiconductors have a small gap, which can be bridged by heating. Superconductors conduct with no loss of energy. 

Recall that molecular orbitals form between two atoms when atomic orbitals on the atoms overlap. In some cases, the atomic orbitals on three or more atoms overlap to form molecular orbitals that encompass all of the atoms. These molecular orbitals are said to be delocalized. The number of molecular orbitals that form by the overlap of atomic orbitals always equals the number of atomic orbitals. In a metal, the outer orbitals of an enormous number of metal atoms overlap to form an enormous number of molecular orbitals that are delocalized over the metal. As a result, a large number of energy levels are crowded together into bands. Because of these euCTgy bands, the molecular orbital theory of metals is often referred to as band theory. 

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... 

Gas-surface interactions and reactions on surfaces play a crucial role in many technologically important areas such as corrosion, adhesion, synthesis of new materials, electrochemistry and heterogeneous catalysis. This chapter aims to describe the interaction of gases with metal surfaces in terms of chemical bonding. Molecular orbital and band structure theory are the basic tools for this. We limit ourselves to metals. 

The theory of band structures belongs to the world of solid state physicists, who like to think in terms of collective properties, band dispersions, Brillouin zones and reciprocal space [9,10]. This is not the favorite language of a chemist, who prefers to think in terms of molecular orbitals and bonds. Hoffmann gives an excellent and highly instructive comparison of the physical and chemical pictures of bonding [6], In this appendix we try to use as much as possible the chemical language of molecular orbitals. Before talking about metals we recall a few concepts from molecular orbital theory. 

Metals conduct electricity through conduction bands. Conduction bands arise from the application of Molecular Orbital theory to multi-atom systems. (See Chapter 10.) The bonding molecular orbitals and, sometimes, other molecular... 

According to band theory, the electrons inside a metal populate the valence band up to the highest occupied molecular orbital, which is called the Fermi level. The potential applied to a metallic electrode governs the energy of its electrons according to Figure 5. 

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. 

Next, we consider the electronic structure of a metal formed from atoms each contributing two electrons. We have seen that overlap of v orbitals in N atoms produces A/ molecular orbitals and that each orbital can accommodate two electrons. The maximum number of electrons that can be placed in N orbitals is 2N, When each atom contributes two electrons, there are 2A/ electrons to be placed in molecular orbitals. Thus, when each atom contributes two electrons, the band is full and the material is an insulator (Fig. 3,12b). The major success of band theory rests on the explanation of the three types of electrical conductors (Fig. 3.12). 

Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the n electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional. Metallic bonding is best described in terms of band theory, which is in essence an extension of molecular orbital (MO) theory (widely used to represent bonding in small molecules) to arrays of atoms of quasi-infinite extent. 

Our results will be based on the one electron energy band theory of solids (13) that forms the basis for the present-day understanding of metal and semiconductor physics. It is the counterpart of the chemist s molecular orbital theory, and we shall try to relate our results back to the underlying atomic structure. 

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