Resonating valence bond

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

Extension of the Statistical Theory of Resonating Valence Bonds... 

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. 

In the course of the further investigation of resonating valence bonds in metals the nature and significance of this previously puzzling unstable orbital have been discovered, and it has become possible to formulate a rational theory of metallic valence and of the structure of metals and intermetallic compounds. 

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

Instead of formulating the wave function for a crystal as a sum of functions describing various ways of distributing the electron-pair bonds among the interatomic positions, as was done in the first section of this paper, let us formulate it in terms of two-electron functions describing a single resonating valence bond. A bond between two adjacent atoms ai and cq- may be described by a function < i3-(l, 2) in which 1 and 2 represent two electrons and the function i may have the simple Heitler-London form... 

Extension of the statistical theory of resonating valence bonds to hyperelectronic metals... 

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... 

Pal SK, Itkis ME, Tham PS, Reed RW, Oakley RT, Haddon RC (2005) Resonating valence-bond ground state in a phenalenyl-based neutral radical conductor. Science 309 281-284... 

Anderson PW (1973) Resonating valence bonds a new kind of insulator Mater Res Bull 8 153-160... 

Delocalization of electrons can be pictured by utilizing either the resonance (valence bond, VB) or assumed delocalization (molecular orbital, MO) concepts. This is illustrated in Figure 6.2 fora two-unit (biphenylene) repeating segment of polyphenylene. 

There appears to be no theory, other than that of resonating valence bonds, that can account for this behaviour. 

A further non-metallic state without antiferromagnetic order is that with resonating valence bonds , proposed by Anderson (1987). This has been described in Chapter 3. 

X This has of course been put in doubt by Anderson s proposal of resonating valence bond states (see Chapter 9). 

Further developments in the fundamental approach to the electronic structure of catalysts were made possible by the development of the quantum mechanical treatments of solids which followed the work of Sommerfeld, Bloch and others. Similarly, Pauling s resonating valence bond treatment has lent further impetus to consideration of metallic catalysts. 

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. 

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