Unsynchronized resonance

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. 

The development during the past year of a statistical theory of unsynchronized resonance of covalent bonds in a metal, with atoms restricted by the electroneutrality principle to forming bonds only in number u — 1, u, and v + 1, with u the metallic valence, has led directly to the value 0.70 0.02 for the number of metallic orbitals per atom.39 This theory also has led to the conclusions that stability of a metal or alloy increases with increase in the ligancy and that for a given value of the ligancy, stability is a maxi-... 

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 energy of the synchronized resonance between structures of this sort would contribute to the stabilization of the crystal, but far greater stabilization would result if there were also unsynchronized resonance to structures such as... 

The significance of unsynchronized resonance can be assessed by a simple theoretical treatment. 

The ratio of the number of structures per atom for unsynchronized resonance to that for synchronized resonance is given by the expression in parentheses in Eq. 4. Its value increases from 2.33 for L = 6, v = 1 to 2.78 for L = 16, v = 8, with average about 2.65. The amount of resonance stabilization for unsynchronized resonance is... 

The calculated number of resonance structures per atom (Eq. 4) is 2.50 for synchronized resonance and 6.25 for unsynchronized resonance. The second number is so much greater than the first that there is no doubt that the structure is one involving unsynchronized resonance, with 28% B+, 44% B°, and 28% B". 

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... 

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... 

The foregoing discussion leads to the conclusion that static deformations as well as phonons should be stabilized for superconducting metals by the change in effective radius associated with unsynchronized resonance of electron-pair bonds. Deformation from cubic to tetragonal symmetry, presumably the result of this interaction, has been reported for VsSi at temperatures below 21 K26- 27 and for Nb2Sn at temperatures below 43°K.28... 

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,-,. 

A reasonable interpretation of the 0.72 metallic orbital per atom was not formulated until ten years later.8 It was then suggested that the metallic orbital permits the unsynchronized resonance of electron-pair bonds from one interatomic position to another by the jump of one electron from one atom to an adjacent atom, leading to great stabilization of the metal b3r resonance energy, and to the characteristic properties of metals,... 

This unsynchronized resonance would require the use of an additional orbital on the atom receiving an extra bond. It is assumed that this additional orbital is the metallic orbital. 

According to Pauling [6-9], valence bond theory can also be used to describe metallic systems. At a first glance, this seems to be contradictory, since VB deals with localized chemical bonds and a metallic bond is thought of as completely delocalized. Pauling s argument is that the metal atoms in the crystal have an available orbital to receive an extra electron and thus form an extra covalent bond, through a mechanism he called unsynchronized resonance. 

In the unsynchronized resonance, just one bond is broken, with the concomitant transfer of one electron from one molecule to another and the formation of a new bond (Fig.2). In order for this to occur, one atom has to lose an electron, say atom 4, becoming a positive ion, and another atom must have an extra orbital to receive the extra electron, say atom 2, becoming a negative ion. Thus we form the structure (1-2 2 -3), that we will call metallic structure, where 2 , the metallic orbital, is the extra atomic orbital on atom 2. In a molecular hydrogen crystal, the unsynchronized resonance would provide a mechanism for charge transport and confer metallic properties to the system. 

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. 

One of the salient features of the unsynchronized-resonating-covalent-bond-theory of metals, alloys, and intermetallic compounds is that, on average, 0.72 of an orbital per... 

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]. 

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... 

THE DETAILED ANALYSIS OF THE STATISTICAL THEORY OF UNSYNCHRONIZED RESONANCE OF COVALENT BONDS... 

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. 

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... 

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