Bonding energy spectra, gaps

The bonding in solids is similar to that in molecules except that the gap in the bonding energy spectrum is the minimum energy band gap. By analogy with molecules, the chemical hardness for covalent solids equals half the band gap. For metals there is no gap, but in the special case of the alkali metals, the electron affinity is very small, so the hardness is half the ionization energy. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

Thus, we now recognize that the only sure sign of a semiconductor is a gap in the energy spectrum of its electrons. It is the presence of this gap that divides semiconductors from metals and alloys, in which the predominantly metallic bonds result in the overleq) of the valence and the conduction bands. 

Ionic and covalent materials can combine in any group of valence compounds forming a class centered on simple or complex phases with four electrons per atom. Valence compounds with three and five electrons per atom are the nearest nel bors. In each of these subgroups we find that an increase in the atomic weight tends to increase the metallic interaction between the atoms and to alter the structure, However, most of the valence compounds are substances with mixed (ionic-covalent) bonds and with a gap in the electron energy spectrum, i.e., they are semiconductors. 

Dicyclopentadiene forms a radical cation (20 ) in which one of the bonds linking the monomer units is cleaved. The species contains two allyl moieties attached to a C4 spacer . Structure 20 + rests on an unmistakable CIDNP pattem " and is supported by an analysis of the electronic absorption spectmm. The large energy gap in the OS of this ion (AE = 1.67 eV) is incompatible with the photoelectron spectrum of the parent molecule (AE = 0.15 eV), but it fits the ring-opened structure 20 +. 

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