Bonding molecular orbital band theory

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. 

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... 

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. 

Molecular orbital (MO) theory has been used to explain the bonding in metallic crystals, such as pure sodium or pure aluminum. Each MO, instead of dealing with a few atoms in a typical molecule, must cover the entire crystal (might be 1020 or more atoms ). Following the rule that the number of MOs must equal the number of atomic orbitals (AOs) combined, this many MOs must be so close on an energy level diagram that they form a continuous band of energies. Because of this factor, the theory is known as band theory. 

The essential feature of the interpretation of a PE spectrum and an important reason for the success of the technique is the role of molecular orbital (MO) theory in both its qualitative and quantitative aspects. The qualitative description of ionization bands as associated with particular atoms or groups of atoms, or with particular bonds in a molecule relates closely to the chemist s picture of the molecule. The quantitative description, where the data from MO calculations are related to the experimental observations, commences with the Koopmans approximation, that the IEs of a molecule are in 1 1 correspondence with its orbital eigenvalues (e) according to the relation illustrated in Figure 2. 

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. 

Molecular orbital (MO) theory offers another explanation of bonding in solids. It is a more quantitative, and therefore more useful, model called band theory. We ll focus on bonding in metals and the conductivity of metals, metalloids, and nonmetals. 

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... 

With the absorption of a quantum with an energy of more than 3.05 eV resp. 3.29 eV, an electron is lifted out of the valence band and into the conduction band, thereby forming an exciton (Fig. 5). This interpretation is also supported by the molecular orbital theory and the crystal field theory regarding the bonding conditions in the TiC lattice. 

Chemical bonds are defined by their frontier orbitals. That is, by the highest molecular orbital that is occupied by electrons (HOMO), and the lowest unoccupied molecular orbital (LUMO). These are analogous with the top of the valence band and the bottom of the conduction band in electron band theory. However, since kinks are localized and non-periodic, band theory is not appropriate for this discussion. 

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. 

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). 

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. 

This success of density functional theory allows the whole question of bonding and structure to be formulated within an effective one-electron framework that is so beloved by chemists in their molecular orbital description of molecules and by physicists in their band theory description of solids. In this book I have tried to follow Einstein s dictum by simplifying the one-electron problem to the barest... 

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