Hypoelectronic atoms

We must now consider two classes of metals, hypoelectronic metals, and hyperelectronic metals [29]. A hypoelectronic metal is one composed of atoms in which the number of outer electrons is less than the number of outer orbitals, and a hyperelectronic metal is one composed of atoms in which the number of outer electrons is greater than the number of outer orbitals. For a metal composed of hypoelectronic atoms, the number of bonds n can take the values v - 1, v, and v + 1, corresponding to M+, M°, and M, respectively, and eqn. (4) yields the following expression for the number of unsynchronized resonance structures per atom ... 

A comparison of eqns. (5) and (6) reveals that the term in square brackets in eqn. (6) is the ratio of the number of unsynchronized resonance structures per atom to the number of synchronized resonance structures per atom for a hypoelectronic atom. Given the reasonable assumption that the energy corresponding to an unsynchronized resonance structure is the same order of magnitude as that for a synchronized resonance structure, the energy of a crystal composed of hypoelectronic atoms is lowered considerably via unsynchronized resonance. Therefore, one predicts that every element with an extra orbital to serve as the metallic orbital should be a metal. With a single possible exception, namely boron, which will be discussed in a succeeding section, this prediction is borne out. 

Hypoelectronic Atoms Atoms with Stable Valence Hyperelectronic Atoms ... 

An additional requirement for high-temperature superconductivity is that such hypo-electronic atoms as La, Y, Ba, or Sr can interact with the hyperelectronic Cu atoms. This results in electron transfer from the Cu atoms to the hypoelectronic atoms, which leads to the formation of covalent bonds that resonate among the Y-Y and Y-Cu positions, conferring electronic conductivity on the substance. These two types of resonance caused by the combination of crest and trough metals couple with the phonons to yield superconductivity at relatively high temperatures. 

In the discussion of hypoelectronic metals in ref. 4, the number of ways of distributing Nv/2 bonds among NL/2 positions in a crystal containing N atoms with valence v and ligancy L was evaluated. The number per atom is the Nth root of this quantity. Structures for which the number of bonds on any atom is other than v-l,v, orv + l were then eliminated with use of the binomial distribution function [only the charge states M+, M°, and M are allowed by the electroneutrality principle (5)]. In this way the following expression for rhypo, the number of resonance structures per atom for a hypoelectronic metal, was obtained ... 

It is evident that the calculation of the number of resonating structures must be made in a different way from that for hypoelectronic metals, because M+ and M form the same number of bonds and are therefore classed together in the calculation of the number of ways of distributing the bonds. We consider first the valence v of a hyperelectronic metal whose neutral atoms form z bonds and whose ions M+ and M" form z + 1 bonds. For any atom, with average valence v, the number of structures, b, having n bonds, is, by the assumption used previously (4), proportional to the probability given by the binomial distribution ... 

The Number of Resonance Structures. In calculating the number of resonance structures per atom, vhypel for hyperelec-tronic metals with v = z+ 1/2, we use the same statistical method as for hypoelectronic metals except that the factor 2m is introduced to correct for the fact that there are two kinds of atoms forming z + I bonds, M+ and M, which differ in that M has an unshared electron pair and M+ does not have one. The equation for vhyper is... 

Several structural features, including electron transfer between atoms of different electronegativity, oxygen deficiency, and unsynchronized resonance of valence bonds, as well as tight binding of atoms and the presence of both hypoelectronic and hyperelectronic elements, cooperate to confer metallic properties and high-temperature superconductivity on compounds such as (Sr.Ba.Y.LahCuO,-,. 

The compound Lajln has Tc = 10.4 K. Because La is hypoelectronic and In is hyperelectronic, I expect electron transfer to take place to the extent allowed by the approximate electroneutrality principle.13 The unit cube would then consist of 2 La, La, and In+, with In+ having no need for a metallic orbital and thus having valence 6 with the bonds showing mainly pivoting resonance among the twelve positions. The increase in valence of In and also of La (to 3 f ) and the assumption of the densely packed A15 structure account for the decrease in volume by 14.3%. Because the holes are fixed on the In + atoms, only the electrons move with the phonon, explaining the increase in Tc. 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

One of the most interesting bare Group 13 metal clusters is the first one to be discovered [66], namely the 11-atom cluster frin in the intermetallic Kglnn-Analogous 11-vertex clusters were subsequently synthesized containing gallium [67] and thallium [68]. The frin cluster has 11+7=18 skeletal electrons = 2 n - 4 for n = 11. It is thus a highly hypoelectronic system relative to the 2n + 2 skeletal electron deltahedral boranes B H . The polyhedron found in Inn is... 

A review of the unsynchronized-resonating-covalent-bond theory of metals in presented. Key concepts, such as unsynchronous resonance, hypoelectronic elements, buffer elements, and hyperelectronic elements, are discussed in detail. Application of the theory is discussed for such things as the atomic volume of the constituents in alloys, the structure of boron, and superconductivity. These ideas represent Linus Pauling s understanding of the nature of the chemical bond in metals, alloys, and intermetallic compounds. 

In Table 1 the number of unsynchronized resonance structures per atom for hypoelectronic metals with various values of the ligancy L and valence v are given. These are also shown in Figure 3, from which it is seen that a maximum in the number of unsynchronized resonance structures per atom for hypoelectronic metals occurs at v = L/2. As will be... 

Table 1. Number of unsynchronized resonance structures per atom as a function of valence v and ligancy L for hypoelectronic metals.

Figure 3. The number of resonance structures per atom for hypoelectronic metals ( ) and for hyperelectronic metals (A) as a function of unit increase in valence v and ligancy L. Note that the maximum for each L occurs at v = L/2.

With this assumption that v = z + 1/2, the statistical treatment is the same as for hypoelectronic metals, except that the factor 21/2 must be introduced to account for the fact that there now exist two kinds of atoms (M+ and M ), forming z + 1 bends. These differ in that M+ does not have an unshared electron pair whereas M- does have one. Under these conditions, the equation for the number of unsynchronized resonance structures per atom for hyperelectronic metals is ... 

For a hypoelectronic metal with valency v and ligancy L, the theoretical value of u>, the amount of metallic orbital per atom, is... 

The discussion of metallic valence and of electron transfer from hyperelectronic elements to hypoelectronic elements for metals, both in bulk alloys and on surfaces, is complicated somewhat by the need for consideration of the effect of the metallic orbital. As pointed out earlier, the metallic orbital, 0.72 per atom, on average, is required for the unsynchronized resonance of valence bonds characteristic of metals. For example, tantalum is hypoelectronic and copper is hyperelectronic, and accordingly, electron transfer from copper to tantalum is expected, leading to an increase in valence for both Ta and Cu and to increased strength of bonds [29]. This increased strength of bonds shows up in bulk alloys as an effect independent of the electron transfer induced by difference in electronegativity. 

Let us first consider a hypoelectronic metal, such as Al, which has three valence electrons and four available orbitals. The Al atom can accept an additional bonding electron,... 

L. Pauling and B. Kamb, Comparison of theoretical and experimental values for the number of metallic orbitals per atom in hypoelectronic and hyperelectronic metals. Proc. Natl. Acad. Sci. (USA) 82, 8286-8287 (1985). 

The extreme hypoelectronicity of the indium and thallium clusters can be relieved by d-orbital participation from some of the vertex metal atoms. In the case of a normal bare post-transition metal vertex in a metal cluster sucb as those discussed in Section 10.6.1, tbe 12 external electrons may be divided into two types, namely, tbe 10 nonbonding d electrons and tbe 2 electrons of an external lone pair analogous to tbe B-H bonding pair in the polyhedral boranes B H (6 < n < 12). In this way a normal post-transition metal vertex such as indium may be considered to use a four-orbital sp bonding manifold just like light vertex atoms such as boron or carbon. However,... 

Comparison of theoretical and experimental values of the number of metallic orbitals per atom in hypoelectronic and hyperelectronic metals. Proc. Natl. Acad. Sci. 82 (1985) 8286—8287. (Linus Pauling and Barclay Kamb). [86-11] A revised set of values of single-bond radii derived from the observed interatomic distances in metals by correction for bond number and resonance energy. Proc. Natl. Acad. Sci. 83 (1986) 3569—3571. (Linus Pauling and Barclay Kamb). 

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