The Metallic Bond

The characteristic properties of the metals are the high conductivity for electricity and heat and the metallic lustre. This latter property is a direct consequence of the very strong absorption for light of all wave lengths, as follows from the theory of the propagation of light. In the finely divided state the metals are in fact black. 

Formerly these metallic properties were attributed to the presence of free electrons. The classical theory of this electron gas (Lorentz) leads, however, to absurdities for instance, a specific heat of 3/2 R had to be expected for this monatomic gas, contrary to the experience that Dulong and Petit s rule (atomic specific heat 6/2 R) holds for both conductors and non-conductors. The calculated ratio of heat conductivity to electrical conductivity (Wiedemann-Franz constant) also did not agree with observation. 

However, since the electrons possess a spin 1/2 - this electron 

In Fermi-Dirac statistics each state can accommodate at most only two particles with opposed spins. In Bose-Einstein statistics, just as in the classical Maxwell-Boltzmann statistics, there is no limitation to the number of particles in a given state. In classical statistics the particles in the same state were assumed to be distinguishable one from the other. As this assumption has been shown in quantum theory to be incorrect the particles in the same state in Bose-Einstein quantum statistics are indistinguishable. Interchanges of two of the par- 

The number of particles ni which in the most probable distribution will be present in the state with energy and statistical weighty (the number of states i) is given by the following expressions for the three forms of statistics mentioned1. 

Each sodium atom contains a 3s valence electron. Metals have a tendency to lose electrons and form positive ions. The valence electrons loosely held in metals are pooled and belong to the crystal structure as a whole. The positive metal ions are continually being formed as they lose their valence electrons, and these electrons are shared among the metal atoms. In this situation, we 

Sodium Ions in a Pool of Delocalized Valence Electrons 

The Na+ ions are surrounded by a pool of delocalized electrons, which acts as the glue that holds the metallic atoms together. This arrangement is referred to as the metallic bond. This mobile pool of electrons accounts for the characteristic properties of metals. For example, because the electrons are loosely attached, rigid bonds are not formed and atoms can easily be shaped because the electrons move freely throughout the structure. 

One feature of metals is well known. Metals tend to lose electrons to nonmetals in a chemical reaction. That is, they tend to have lower electronegativities than nonmetals. This is obvious in compounds formed from metals at the far left of the periodic table and nonmetals from the far right. Sodium (a metal) clearly loses an electron to chlorine (a nonmetal) forming an ionic bond. The resulting compound—table salt—is a water-soluble, white 

But the nature of the compounds formed when the metal and nonmetal are closer to the center of the periodic table is less obvious. Their electronegativities are closer together. And the electronegativity difference between the atoms in a compound determines the nature of the bond. Recall that differences of 1.7 or more result in ionic bonds atoms with differences less than 1.7 form bonds with some covalent character. Lead sulfide (PbS) is an example of such a compound. Lead has an electronegativity of 1.9 sulfur is 2.5. The difference of 0.6 is less than 1.7, so the bond between them should have some covalent character. Like sodium chloride, lead sulfide is a crystalline compound. However, it is dark and shiny, quite unlike salt. It is also insoluble in water, which indicates a high degree of covalency in the lead-sulfur bond, just as one would expect. 

if both sodium and lead are defined as metals and chlorine and sulfur as nonmetals, why is sodium chloride so different from lead sulfide Something appears to be missing in our definition of a metal. It is true that metals tend to lose electrons to nonmetals in a chemical reaction, but that definition turns out to be so broad that it is not very useful. How, then, should a metal be defined The answer was arrived at years before the electronic structure of atoms was known. Simply put, metals are best defined by their common physical properties  

High electrical conductivity. The conductivity of metals is many orders of magnitude higher than that of nonmetals. Sulfur, for example, is considered an electrical insulator, while aluminum, only three places to its left in the periodic table, is a good conductor of electricity. 

High density. Metals are usually much denser than nonmetals. Sodium, for instance, has a density of 0.97 

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We consider first some experimental observations. In general, the initial heats of adsorption on metals tend to follow a common pattern, similar for such common adsorbates as hydrogen, nitrogen, ammonia, carbon monoxide, and ethylene. The usual order of decreasing Q values is Ta > W > Cr > Fe > Ni > Rh > Cu > Au a traditional illustration may be found in Refs. 81, 84, and 165. It appears, first, that transition metals are the most active ones in chemisorption and, second, that the activity correlates with the percent of d character in the metallic bond. What appears to be involved is the ability of a metal to use d orbitals in forming an adsorption bond. An old but still illustrative example is shown in Fig. XVIII-17, for the case of ethylene hydrogenation. 

Fig. XVIII-17. Correlation of catalytic activity toward ethylene dehydrogenation and percent d character of the metallic bond in the metal catalyst. (From Ref. 166.)...

V. K. Grigorovich, The Metallic Bond and the Structure of Metal.s Nova Science, Huntington, NY (1989). 

A weakened carbon—oxygen bond results from the combined ( - and TT-bonding, allowing the metal-bonded carbon monoxide to react more readily... 

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. 

The easy movement of the electrons gives the high electrical conductivity of metals. The metallic bond has no directionality, so that metal ions tend to pack to give simple, high-density structures, like ball-bearings shaken down in a box. 

Metal atoms tend to behave like miniature ball-bearings and tend to pack together as tightly as possible. F.c.c. and c.p.h. give the highest possible packing density, with 74% of the volume of the metal taken up by the atomic spheres. However, in some metals, like iron or chromium, the metallic bond has some directionality and this makes the atoms pack into the more open b.c.c. structure with a packing density of 68%. 

Silver is a white metal it is softer than copper and harder than gold. One use of the pure metal (about 99.99%) is as a liner bonded to stronger or cheaper metals. The metallic bond is usually of high thermal conductivity. 

What is the nature of the metallic bond This bond, like all others, forms because the electrons can move in such a way that they are simultaneously near two or more positive nuclei. Our problem is to obtain some insight into the special way in which electrons in metals do this. 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

In summary we can say that the metallic bond is a sort of nondirectional covalent bond. It occurs when atoms have few valence electrons compared with vacant valence orbitals and when these valence electrons are not held strongly. 

It is interesting that a straight line drawn through the tetrahedral radii passes through the metallic radius for calcium this suggests that the metallic bonding orbitals for calcium are sp orbitals, and that those for scandium begin to involve d-orbital hybridization. 

Forty six years ago, on the basis mainly of empirical arguments, I formulated a description of the interatomic forces in metals (2) that had some novel features. I pointed out that according to this view the metallic bond is very closely related to the ordinary covalent (shared-electron-pair) bond some of the electrons in each atom in a metal are involved with those of neighboring atoms in an interaction described as covalent-bond... 

With increasing B content, the covalent component of the bonding in boride lattices increases owing to the appearance of direct B—B bonds and a decrease in the metallic bond character, e.g., in the structural series of the CUAI2 family ... 

The metallic bond can be understood by extending the orbital picture we sketched above. The metals all have extended outer s or p orbitals, which ensure large overlap. The formation of the metallic bond from such s and p levels is illustrated in Fig. 6.9. 

Unsually short NMR T, relaxation values were observed for the metal-bonded H-ligands in HCo(dppe)2, [Co(H2)(dppe)]+ (dppe = l,2-bis(diphenylphosphino)ethane), and CoH(CO) (PPh3)3.176 A theoretical analysis incorporating proton-meta) dipole-dipole interactions was able to reproduce these 7) values if an rCo H distance of 1.5 A was present, a value consistent with X-ray crystallographic experiments. A detailed structural and thermodynamic study of the complexes [H2Co(dppe)2]+, HCo(dppe)2, [HCo(dppe)2(MeCN)]+, and [Co(dppe)2(MeCN)]2+ has been reported.177 Equilibrium and electrochemical measurements enabled a thorough thermodynamic description of the system. Disproportionation of divalent [HCo(dppe)2]+ to [Co(dppe)2]+ and [H2Co(dppe)2]+ was examined as well as the reaction of [Co(dppe)2]+ with H2. 

Fig. 1. Catalytic activities of metals for ethane hydrogenolysis in relation to the percentage d character of the metallic bond. The closed points represent activities compared at a temperature of 205°C and ethane and hydrogen pressures of 0.030 and 0.20 atm, respectively, and the open points represent percentage d character. Three separate fields are shown in the figure to distinguish the metals in the different long periods of the periodic table.

Fig. 7. Percentage d character of the metallic bond in copper-nickel alloys as a function of composition (74, 84).

Fig. 4. Hydrogen isotope exchange between C6H and C6D6. Correlation of randomisation rate constant kF, with percentage d-character of the metallic bonds (4). 

The articles by J. R. Anderson, J. H. Sinfelt, and R. B. Moyes and P. B. Wells, on the other hand, deal with a classical field, namely hydrocarbons on metals. The pattern of modem wTork here still very much reflects the important role in the academic studies of deuterium exchange reactions and the mechanisms advanced by pioneers like Horiuti and Polanyi, the Farkas brothers, Rideal, Tw igg, H. S. Taylor, and Turkevich. Using this method, Anderson takes ultrathin metal films with their separated crystallites as idealized models for supported metal catalysts. Sinfelt is concerned with hydrogcnolysis on supported metals and relates the activity to the percentage d character of the metallic bond. Moyes and Wells deal with the modes of chemisorption of benzene, drawing on the results of physical techniques and the ideas of the organometallic chemists in their discussions. 

Certain transition metal complexes catalyze the decomposition of diazo compounds. The metal-bonded carbene intermediates behave differently from the free species generated via photolysis or thermolysis of the corresponding carbene precursor. The first catalytic asymmetric cyclopropanation reaction was reported in 1966 when Nozaki et al.93 showed that the cyclopropane compound trans- 182 was obtained as the major product from the cyclopropanation of styrene with diazoacetate with an ee value of 6% (Scheme 5-56). This reaction was effected by a copper(II) complex 181 that bears a salicyladimine ligand. 

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