Polar covalent bands

In the previous chapters, we discussed various models of bonding for covalent and polar covalent molecules (the VSEPR and LCP models, valence bond theory, and molecular orbital theory). We shall now turn our focus to a discussion of models describing metallic bonding. We begin with the free electron model, which assumes that the ionized electrons in a metallic solid have been completely removed from the influence of the atoms in the crystal and exist essentially as an electron gas. Freshman chemistry books typically describe this simplified version of metallic bonding as a sea of electrons that is delocalized over all the metal atoms in the crystalline solid. We shall then progress to the band theory of solids, which results from introducing the periodic potential of the crystalline lattice. 

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. 

When methyl fluoride was absorbed into neat antimony pentafluoride at room temperature a low field band at —12-5 p.p.m. appears. The relative intensity of this species compared with the covalently polarized methyl fluoride complex is, however, small and it could originate from impurities in the system. 

The same disciission may apply to the anodic dissolution of semiconductor electrodes of covalently bonded compounds such as gallium arsenide. In general, covalent compoimd semiconductors contain varying ionic polarity, in which the component atoms of positive polarity re likely to become surface cations and the component atoms of negative polarity are likely to become surface radicals. For such compound semiconductors in anodic dissolution, the valence band mechanism predominates over the conduction band mechanism with increasing band gap and increasing polarity of the compounds. 

K.4 At one time die melting points of the fluorides of the lhud-row elements were taken to indicate a discontinuity between tonic banding (AJFj) and covalent bonding (SiFJ. Explain the observed trend assuming that the bond polarity decreases uniformly from NaF to SF6. 

In covalently bonded non-polar semiconductors the higher levels of the valence band are formed by electrons that are shared between neighbouring atoms and which have ground state energy levels similar to those in isolated atoms. In silicon, for instance, each silicon atom has four sp3 electrons which it shares with four similar atoms at the comers of a surrounding tetrahedron. As a result each silicon atom has, effectively, an outer shell of eight electrons. The... 

Figure 7. Ground-state wave function of plastocyanin. A HOMO wave function contour for plastocyanin (28). B HOMO wave function contour for the thiolate copper complex tet b (34/ C Copper L-edge (38) and sulfur K-edge (34) spectra as probes of metal-ligand covalency. D Absorption, single-crystal polarized absorption, and low-temperature MCD spectra of plastocyanin. The absorption spectrum has been Gaussian resolved into its component bands as in reference 33.

Bond orbitals are constructed ft om s/r hybrids for the simple covalent tetrahedral structure energies are written in terms of a eovalent energy V2 and a polar energy K3. There are matrix elements between bond orbitals that broaden the electron levels into bands. In a preliminary study of the bands for perfect crystals, the energies for all bands at k = 0 arc written in terms of matrix elements from the Solid State Tabic. For calculation of other properties, a Bond Orbital Approximation eliminates the need to find the bands themselves and permits the description of bonds in imperfect and noncrystalline solids. Errors in the Bond Orbital Approximation can be corrected by using perturbation theory to construct extended bond orbitals. Two major trends in covalent bonds over the periodic table, polarity and metallicity, arc both defined in terms of parameters from the Solid State Table. This representation of the electronic structure extends to covalent planar and filamentary structures. 

---