Bonding in metals

In a cubic-primitive structure (a-polonium, Fig. 2.4, p. 7) the situation is similar. By stacking square nets and considering how the orbitals interact at different points of the Brillouin zone, a qualitative picture of the band structure can be obtained. 

Schematic sketch of the density of states and the crystal orbital overlap population for metals 

10 MOLECULAR ORBITAL THEORY AND CHEMICAL BONDING IN SOLIDS 

The outlined sketch is rather rough, but it correctly shows the tendencies, as can be exemplified by the melting points of the metals (values in °C)  

In reality there are subtle deviations from this simple picture. The energy levels shift somewhat from element to element, and different structure types have different band structures that become more or less favorable depending on the valence electron concentration. Furthermore, in the COOP diagram of Fig. 10.13 the s-p, s-d and p-d interactions were not taken into account, although they cannot be neglected. A more exact calculation shows that only antibonding contributions are to be expected from the eleventh valence electron onwards. 

We now introduce some simple models for bonding in metals and semiconductors such as jellium and hydridization and at the same time assess our theoretical tool of choice, DFT, at predicting some of the central cohesive properties of solids. 

A useful quantity for interpreting the characteristics of chemical bonding, that we use throughout to examine metals, is the density of states (DOS). It is defined 

Another useful quantity, which is not readily accessible in any simple manner from experiment, is the state-resolved DOS, also called the projected DOS (PDOS) 

The special properties of a metal result from its delocalized bonding, in which bonding electrons are spread over a number of atoms. In this section, we will look first at the electron-sea model of a metal and then at the molecular orbital theory of bonding in metals. 

A very simple picture of a metal depicts an array of positive ions surrounded by a sea of valence electrons free to move ovct the entire metal crystal. When the metal is connected to a source of electric current, the electrons easily move away from the negative side of the electric source and toward the positive side, forming an electric current in the metal. In other words, the metal is a conductor of electric current because of the mobility of the valence electrons. A metal is also a good heat conductor because the mobile electrons can carry additional kinetic energy across the metal.  

The electron-sea model of metals is a simplified view that accounts in only a qualitative way for properties of a metal such as electrical conductivity. Molecular orbital theory gives a more detailed picture of the bonding in a metal and other solids as well.  

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. 

We can now explain the electrical conductivity of sodium metal. Electrons become free to move throughout a crystal when they are excited to unoccupied orbitals of a 

Pj orbitals that are oriented perpendicular to the square lattice interact in the same way as the s orbitals, but the r-type interactions are inferior and correspondingly the band width is smaller. For and orbitals the situation is somewhat more complicated, because T and 71 interactions have to be considered between adjacent atoms (Fig. 10.12). For example, at F the p. orbitals are cr-antibonding, but /r-bonding. At X p and Py differ most, one being cr and rr-bonding, and the other cr and rr-antibonding. 

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Ceramics and metals are entirely held together by primary bonds - the ionic and covalent bond in ceramics, and the metallic and covalent bond in metals. These strong, stiff bonds give high moduli. 

The metallic bond, as the name says, is the dominant (though not the only) bond in metals and their alloys. In a solid (or, for that matter, a liquid) metal, the highest energy electrons tend to leave the parent atoms (which become ions) and combine to form a sea of freely wandering electrons, not attached to any ion in particular (Fig. 4.8). This gives an energy curve that is very similar to that for covalent bonding it is well described by eqn. (4.4) and has a shape like that of Fig. 4.6. 

Figure 19.26 Orbitals u.sed in descnbing the bonding in metal-ij - cyclobutadiene complexe.s. The sign convention and axes arc as in Fig. 19.23...

Figure 9.1 Id illustrates a simple model of bonding in metals known as the electron-sea model. The metallic crystal is pictured as an array of positive ions, for example, Na+, Mg2+. These are anchored in position, like buoys in a mobile sea of electrons. These electrons are not attached to any particular positive ion but rather can wander through the crystal. The electron-sea model explains many of the characteristic properties of metals ...

Spectra and bonding in metal carbonyls part A, bonding. P. S. Braterman, Struct. Bonding (Berlin), 1972,10, 57-86 (110). 

Anomalous temperature variation of n.q.r. frequencies and bonding in metal complexes. D. Nakamura, R. Ikeda and M. Kubo, Coord. Chem. Rev., 1975,17, 281-316 (136). 

L. Pauling, J. Am. Chem. Soc. 69, 542 (1947) see also L. Pauling, The nature of the bonds in metals and intermetallic compounds, a talk given before Section I, Xlth Intematl. Congress of Pure and Applied Chem., London, July 1947. 

In the course of the further investigation of resonating valence bonds in metals the nature and significance of this previously puzzling unstable orbital have been discovered, and it has become possible to formulate a rational theory of metallic valence and of the structure of metals and intermetallic compounds. 

A Simple Theory of Resonating Covalent Bonds in Metals... 

ABSTRACT The statistical treatment of resonating covalent bonds in metals, previously applied to hypoelectronic metals, is extended to hyperelectronic metals and to metals with two kinds of bonds. The theory leads to half-integral values of the valence for hyperelectronic metallic elements. 

A theory of resonating covalent bonds in metals, developed over the period 1938-1953 (1-3), was recently refined by the formulation of a statistical treatment for hypoelectronic metals (4). We have now extended the statistical treatment to include hyperelectronic metals. This extension has resulted not only in the evaluation of the number of resonance structures for these metals but also in the determination for them of the values of the metallic valence, which have been somewhat uncertain. 

Bradshaw AM, Cederbaum LS, Domcke W (1975) Ultraviolet Photoelectron Spectroscopy of Gases Adsorbed on Metal Surfaces. 24 133-170 Braterman PS (1972) Spectra and Bonding in Metal Carbonyls. Part A Bonding. 10 57-86 Braterman PS (1976) Spectra and Bonding in Metal Carbonyls. Part B Spectra and Their Interpretation. 26 1-42... 

Ernst RD (1984) Structure and Bonding in Metal-Pentadienyl and Related Compounds. 57 1-53... 

The subjects of structure and bonding in metal isocyanide complexes have been discussed before 90, 156) and will not be treated extensively here. A brief discussion of this subject is presented in Section II of course, special emphasis is given to the more recent information which has appeared. Several areas of current study in the field of transition metal-isocyanide complexes have become particularly important and are discussed in this review in Section III. These include the additions of protonic compounds to coordinated isocyanides, probably the subject most actively being studied at this time insertion reactions into metal-carbon bonded species nucleophilic reactions with metal isocyanide complexes and the metal-catalyzed a-addition reactions. Concurrent with these new developments, there has been a general expansion of descriptive chemistry of isocyanide-metal complexes, and further study of the physical properties of selected species. These developments are summarized in Section IV. 

Hydrogen Bonding in Metal Halides Lattice Effects and Electronic Distortions... 

Patrone, L., Paladn, S., CharHer, J., Armand, F., Bourgoin, J.P., Tang, H. and Gauthier, S. (2003) Evidence of ffie Key Role of Metal-Molecule Bonding in Metal-Molecule-Metal Transport Experiments. Physical Review Letters, 91, 096802. 

Braterman, P. S. Spectra and Bonding in Metal Carbonyls. Part B Spectra and Their Interpretation. Vol. 26, pp. 1 2. 

Wade also extended the application of his rules to transition metal clusters the further extension by D. M. P. Mingos mainly concerns the bonding in metal carbonyl and metal phosphane clusters, i.e. organometallic compounds (Wade-Mingos rules) these are beyond the scope of this book. 

A dislocation can move no faster than its core (the region within one to two atoms of position c in Figure 5.7) so the mobility is determined by whatever barrier is presented to the core. Since the core is very localized, so must be the barrier if it is to have a substantial effect. This is why local covalent bonding leads to low mobility while the non-local bonding in metals gives high mobility. 

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