RESONATING VALENCE BOND THEORY

Linus Pauling, A Resonating-Valence-Bond Theory of Metals and Intermetallic Com-... 

A resonating-valence-bond theory of metals and intermetallic compounds... 

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. 

Brillouin zones and the resonating-valence-bond theory... 

The generally accepted theory of electric superconductivity of metals is based upon an assumed interaction between the conduction electrons and phonons in the crystal.1-3 The resonating-valence-bond theory, which is a theoiy of the electronic structure of metals developed about 20 years ago,4-6 provides the basis for a detailed description of the electron-phonon interaction, in relation to the atomic numbers of elements and the composition of alloys, and leads, as described below, to the conclusion that there are two classes of superconductors, crest superconductors and trough superconductors. 

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... 

This approach explains satisfactorily the decrease in bond length with increasing valency in the sequences of elements K —> Cr, Rb — Mo, and Co — W. The number of electrons available for bond formation in these metals increases with valency, and therefore, according to the resonating valence bond theory, the number of bonds resonating about the available positions increases, resulting in smaller bond lengths. 

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... 

D. J. Klein, in Valence Bond Theory, D. L. Cooper, Ed., Elsevier, Amsterdam, The Netherlands, 2002, pp. 447-502. Resonating Valence Bond Theories for Carbon ir-Networks and Classical/Quantum Connections. 

Resonating Valence-Bond theories for carbon -networks and classical/quantum connections... 

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. 

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. 

Many solid-state physicists discuss the structure and properties of metals and alloys with use of the band theory, in its several modifications. This theory is also a quantum mechanical theory, which starts with a solution of the wave equation for a single electron, and introduces electron-electron correlation in one or another of several ways. The resonating-valence-bond theory introduces electron-electron correlation in several stages, one of which is by the formation of covalent bonds between adjacent atoms, and another the application of the electroneutrality principle to restrict the acceptable structures to those that involve only M+, M°, and M-. It should be possible to find a relationship between the band-theory calculations and the resonating-covalent-bond theory, but I have been largely unsuccessful in finding such a correlation. I have, for example, not been able to find any trace of the metallic orbital in the band-theory calculations, which thus stand in contrast to the resonating-valence-bond theory, in which the metallic orbital plays a predominant role."... 

L. Pauling, A resonating-valence-bond theory of metals and intermetallic compounds. Proc. Roy. Soc. (London) A196, 343-362 (1949). 

L. Pauling and B. Kamb, The discussion of tetragonal boron by the resonating-valence-bond theory of electron-deficient substances. Z. Kristall. 112, 472-478 (1959). 

L. Pauling, The resonating-valence-bond theory of superconductivity Crest superconductors and trough superconductors. Proc. Natl. Acad. Sci. (USA) 60, 59-65 (1968). 

P. W. Anderson G. Baskaran, Z. Zou, and T. Hsu, Resonating-valence-bond theory of phase transitions and superconductivity in La2Cu04-based compounds. Phys. Rev. Lett. 58, 2790-2793 (1987). 

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