Increased-valence structure approximation

If Cl and C2 in the molecular orbitals of Eqn. (2) have similar magnitudes, i.e. if y and / have similar energies, then the primary component of P(CI) will be given by Eqn. (8). Therefore, increased-valence structure (1) (which is equivalent to resonance between the Lewis structures (2) and (3)) is the primary valence-bond stractme for this approximate molecular orbital scheme when configuration interaction is invoked. 

Because I2 has a single bond, the extra electron of I must occupy an antibonding molecular orbital. Therefore, the valence-bond structure for 1 must be the Pauling 3-electron bond structure ("I I ). By spin-pairing the unpaired electrons of Ij and McjN", we may represent MejN — 1 by the increased-valence structure (3), and describe (approximately) the electronie stmcture of the complex in terms of resonance between structures (2) and (3). 

It has been dednced " that the Mulliken wave-function for the complex, namely Eqn. (1), is equivalent to the wave-function of Eqn. (4) for the increased-valence structure (13). Therefore, the Mulliken wave-function of Eqn. (1) implies, but conceals an (approximate) description of the intermolecular bond as a 1-electron bond. 

Since instability to distortions increases as the size of the metal ion becomes smaller, it is possible to arrange the various ions of high valency in approximate order of size from a comparison of the crystal structures of their oxides. We shall not carry out this analysis in detail but shall draw attention to a number of important features. 

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. 

A theoretical interpretation relating the valence electron concentration and the structure was put forward by H. Jones. If we start from copper and add more and more zinc, the valence electron concentration increases. The added electrons have to occupy higher energy levels, i.e. the energy of the Fermi limit is raised and comes closer to the limits of the first Brillouin zone. This is approached at about VEC = 1.36. Higher values of the VEC require the occupation of antibonding states now the body-centered cubic lattice becomes more favorable as it allows a higher VEC within the first Brillouin zone, up to approximately VEC = 1.48. 

The structures of the prototype borides, carbides, and nitrides yield high values for the valence electron densities of these compounds. This accounts for their high elastic stiffnesses, and hardnesses. As a first approximation, they may be considered to be metals with extra valence electrons (from the metalloids) that increase their average valence electron densities. The evidence for this is that their bulk modili fall on the same correlation line (B versus VED) as the simple metals. This correlation line is given in Gilman (2003). 

Fig. 3.13 Left-hand panel The electronic structure of an sp-valent diatomic molecule as a function of the internuclear separation. Labels Et and Ep mark the positions of the free-atomic valence s and p levels respectively and = ( s + p). The quantity Rx is the distance at which the and upper tr9 levels cross. The region between the upper and lower n levels has been shaded to emphasize the increase in their separation with decreasing distance that is responsible for this crossing. Right-hand panel The self-consistent local density approximation electronic structure for C2 and Si2 whose equilibrium internuclear separations are marked by RCz and RSa respectively. (After Harris 1984.)...

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