The valence-bond theory of metals

So far we have discussed metal systems on the basis of the molecular-orbital theory. We now proceed to a brief discussion of the treatment of these systems in terms of the alternative valence-bond theory, as developed principally by Pauling. 

It is well known that certain univalent metals (for example, lithium) form diatomic molecules in the vapour in which the interatomic binding is presumably covalent in character. On the valence-bond theory it is assumed that such bonds also operate in the solid state, but since the number of electrons available is inadequate to give rise to covalent bonds between each atom and all its neighbours (eight in lithium) resonance is assumed to take place throughout the solid in a way which may be symbolized, in two dimensions, thus  

This mechanism involves the synchronized resonance of pairs of bonds, but much greater stability will result if we countenance the far more numerous structures arising from unsynchronized resonance between arrangements in which ions are also involved, thus  

This process will be possible only if a vacant orbital is available in the lithium atom to accept the extra electron present in the Li ion. In fact this is so, for the three vacant zp orbitals are energetically little above the zs orbital occupied by the valency electron. We can thus regard the 

Li ion as having the structure is2, 2s12p with the 2s orbital and one of the 2p orbitals, probably hybridized, as available for the formation of two covalent bonds. 

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The valence-bond theory of metals is of importance in that it enables us to form a qualitative picture of the properties of these elements. In the first place it explains the close relationship, already mentioned in 5.07, between metallic and covalent radii, since it treats metallic binding as being essentially covalent in origin. A second important feature is that it enables us to understand the distribution of the metallic elements in the Periodic Table, as we may now show. 

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... 

The resonating-valence-bond theory of metals discussed in this paper differs from the older theory in making use of all nine stable outer orbitals of the transition metals, for occupancy by unshared electrons and for use in bond formation the number of valency electrons is consequently considered to be much larger for these metals than has been hitherto accepted. The metallic orbital, an extra orbital necessary for unsynchronized resonance of valence bonds, is considered to be the characteristic structural feature of a metal. It has been found possible to develop a system of metallic radii that permits a detailed discussion to be given of the observed interatomic distances of a metal in terms of its electronic structure. Some peculiar metallic structures can be understood by use of the postulate that the most simple fractional bond orders correspond to the most stable modes of resonance of bonds. The existence of Brillouin zones is compatible with the resonating-valence-bond theory, and the new metallic valencies for metals and alloys with filled-zone properties can be correlated with the electron numbers for important Brillouin polyhedra. 

The principal innovations that have been made in the discussion of the theory of the chemical bond in this edition are the wide application of the electroneutrality principle and the use of an empirical equation (Sec. 7-10) for the evaluation of the bond numbers of fractional bonds from the observed bond lengths. A new theory of the structure of electron-deficient substances, the resonating-valence-bond theory, is described and used in the discussion of the boranes, ferrocene, and other substances. A detailed discussion of the valence-bond theory of the electronic structure of metals and intermetallic compounds is also presented. 

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... 

In a footnote to his 1949 paper entitled A Resonating-Valence-Bond Theory of Metals and Intermetallic Compounds, Linus Pauling gave an example of a simple statistical treatment to derive the metallic orbital [27]. Nevertheless, it took him three and one-half decades to publish the detailed statistical treatment [34-36], which is given in the following. 

L. Pauling, The resonating-valence-bond theory of metals. Physica 15, 23-28 (1949). 

The application of the (8—n) rule to elements preceding group 4 implies the availability of (8—n) electrons per atom for covalent bond formation and is to this extent artificial unless a mechanism for the provision of these electrons can be proposed. A possible mechanism in the case of zinc, based on the valence-bond treatment of metal theory, has already been outlined in 5.28, but it is difficult to feel satisfied that this is more than an ad hoc explanation designed to explain the observed crystal structure of the element if the structure of zinc were unknown there would be few grounds for treating it as other than a simple divalent element. 

In the resonating valence-bond theory of metallic solids, Pauling has suggested that alkali metals use their p as well as their s atomic orbitals for bonding. Pauling designated the p orbitals as metallic orbitals . When both s and p orbitals are used for bonding in the solid alkali metal lithium, the electronic structure of the metal involves resonance between the diatomic Lij structures of structure (6)... 

The resonating-valence-bond theory of the electronic structure of metals is based upon the idea that pairs of electrons, occupying bond positions between adjacent pairs of atoms, are able to carry out unsynchronized or partially unsynchronized resonance through the crystal.4 In the course of the development of the theory a wave function was formulated describing the crystal in terms of two-electron functions in the various bond positions, with use of Bloch factors corresponding to different values of the electron-pair momentum.5 The part of the wave function corresponding to the electron pair was given as... 

As noted in Section 9.1, there are three closely related theories of the electronic structures of transition metal complexes, all making quite explicit use of the symmetry aspects of the problem but employing different physical models of the interaction of the ion with its surroundings as a basis for computations. These three theories, it will be recalled, are the crystal field, ligand field, and MO theories. There is also the valence bond theory, which makes less explicit use of symmetry but is nevertheless in accord with the essential symmetry requirements of the problem. We shall now briefly outline the crystal field and ligand field treatments and comment on their relationship to the MO theory. 

According to the valence bond theory (Section 7.10), the bonding in metal complexes arises when a filled ligand orbital containing a pair of electrons overlaps a vacant hybrid orbital on the metal ion to give a coordinate covalent bond ... 

Much has still to be clarified in the resonating-valence-bond theory of the metals, especially is it not yet clear how the various valences and properties of atoms in different states could ever be derived in an independent way. 

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. 

L. Pauling and Z. S. Herman, The unsynchronized-resonating-covalent-bond theory of metals, alloys, and intermetallic compounds, in Valence Bond Theory and Chemical Structure, D. J. Klein and N. Trinastic, eds., Elsevier, Amsterdam, 1990, pp. 569-610. 

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