The Metallic Orbital

One of the lasting practical results of treating metals in this model has been the tabulation of atomic radii and interatomic distances in metals [39-42]. Another interesting application of the unsynchronized-resonating-covalent-bond-theory of metal is its use in the elucidation of the to the structure and properties of elemental boron and the boranes [43]. 

Ten years later, in 1948, Pauling realized that this apparently unused atomic orbital has an important function [24, 27, 30], Consider a metal consisting of N identical atoms M with valence v, that is, each atom forms v covalent bonds with adjacent atoms. Now, if the number of bond positions were greater than the number of bonds, then the bonds could resonate from one position to another only synchronously, with pairs of bonds changing positions simultaneously  

However, the principle of approximate electroneutrality [45, 46] allows for the occurrence of M+ and M, with valences v - 1 and nil, respectively. Therefore, under the condition that there is an available orbital, unsynchronous resonance, involving the shift of a single covalent bond about an atom from one position to another, can then occur  

In order for unsynchronous resonance to occur, the atoms M+ and M° must have an unoccupied orbital available so that they can accept an additional bond. M does not require such an unoccupied orbital because the electroneutrality principle rules out its accepting an additional bond, which would convert it to M2. Accordingly, the structural requirement for a system to possess metallic character is that the fraction of the atoms M+ and M° have available an unoccupied orbital, called the metallic orbital. The average value of 0.72 orbital per atom for the metallic orbital, as deduced from the Slater-Pauling curve, implies that, with unsynchronous resonance of the covalent bonds, the metal consists of 28% M+, 44% M°, and 28% M.  

As will be seen in the statistical theory described in the following section, there exist far more unsynchronized resonating structures per atom than there are synchronized resonating structures. Associated with this increase in the number of resonating structures is an increase in stability for the system, with the increased resonance stabilization energy being approximately proportional to the number of additional resonating structures per atom for unsynchronous resonance, less 1. One is consequently led to conclude that unsynchronized resonance of the covalent bonds between the atoms in metallic systems occurs 

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Figure 19.23 SchemalicillDslralionofpossiblecom-binplions of orbitals in the rr-allyiic complexes. The bonding dirccrion is taken lo be the z-axis with the M aiom below the Cj plane Approprisle combinations of p, orbitals on the 3 C arc shown in the top half of Ihe figure, and beneath them are the metal orbitals with which Ihey arc mosl likely to form bonding inieraciions.

The ligands interact with the two orbitals of cr-symmetry modifying the ordering somewhat (Figure 2.37b). As has been pointed out, altering the relative positions of the metal orbitals relative to those of the carboxylates affects the final scheme considerably (Figure 2.38). 

Finally, the use of simple valence bond theory has led recently to a significant discovery concerning the nature of metals. Many years ago one of us noticed, based on an analysis of the experimental values of the saturation ferromagnetic moment per atom of the metals of the iron group and their alloys, that for a substance to have metallic properties, 0.72 orbital per atom, the metallic orbital, must be available to permit the unsynchronized resonance that confers metallic properties on a substance.34 38 Using lithium as an example, unsynchronized resonance refers to such structures as follows. 

Successive pivoting resonances of a covalent bond allows for electrical conduction to occur, as shown in Figure 1-1. A test of this theory was provided by gray and white tin. Gray tin is not metallic because all its valence orbitals are used for bonding and there is no metallic orbital available. White tin, on the other hand, has the metallic orbital available and therefore has metallic properties. 

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 fundamental structural feature of a metallic system the metallic orbital ... 

However, this uninhibited resonance, involving the conversion of atoms into ions (or the transfer of ionic charges to atoms), requires that the atom receiving a bond have an orbital available for its reception. It is the possession of this extra orbital (the metallic orbital), in addition to the orbitals required on the average for occupancy by unshared... 

Tin has fourteen electrons outside of its krypton-like core. These may occupy the nine orbitals in the following three most stable ways (atomic electrons are indicated by spin vectors, bonding electrons by dots, the metallic orbitals by open circles) ... 

White tin, on the other hand, has metallic properties. Each atom in the crystal forms six bonds, four with length 3.016 A and two with length 3.175 A. When I first made a thorough study of bond lengths in metals (9) I interpreted these values as showing the valence to be 2.44 later (5) the value was recalculated to be 2.50, and then 10) to be 2.56. This value is explained by use of the metallic orbital. The atoms Sn+, Sn, and Sn- have the structures... 

Here the broken circle represents the metallic orbital. 

A requirement for metallic character is that unsynchronized resonance of covalent bonds occur, which means that M and M° have an unoccupied orbital available to accept an additional bond, changing them to M° and M, respectively. M does not need the extra orbital, because it cannot change to M2-. A hyperelectronic metal is one in which the number of outer electrons is greater than the number of outer orbitals, not including the metallic orbital. An example is metallic tin, with 14 outer electrons and 9 outer orbitals (6j, three 6p, five 5d). Sn+ and Sn° have five unshared electron pairs, and Sn has six. Sn+ and Sn form three covalent bonds, and Sn° forms two. Sn+ and Sn° have a metallic orbital, and Sn does not. They may be represented as... 

Accordingly, the mechanism of conduction in metals is different from that for the ring currents in benzene, other aromatic molecules, and graphite, in which the atoms do not have the metallic orbital.16 16... 

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