Solids hybrid levels

Figure 4.9. Origin of the bands in sp bonded solids the levels s, p and s, p correspond to the atoms A, B the5/t hybrids in each case aredenoted by = 1,2, 3,4),...

The concepts which we need for understanding the structural trends within covalently bonded solids are most easily introduced by first considering the much simpler system of diatomic molecules. They are well described within the molecular orbital (MO) framework that is based on the overlapping of atomic wave functions. This picture, therefore, makes direct contact with the properties of the individual free atoms which we discussed in the previous chapter, in particular the atomic energy levels and angular character of the valence orbitals. We will see that ubiquitous quantum mechanical concepts such as the covalent bond, overlap repulsion, hybrid orbitals, and the relative degree of covalency versus ionicity all arise naturally from solutions of the one-electron Schrodinger equation for diatomic molecules such as H2, N2, and LiH. 

Fig. 7.5 The hybrid NFE-TB band structure of fee and bee iron in the nonmagnetic state. The solid circles represent the first principles energy levels of Wood (1962). (From Pettifor (1970e).)...

Figure 13.4 Torsional potential energy surfaces about the two C-O bonds linking the anomeric centers of sucrose at the MM3 level (a), 2-tetrahydrofuranyl-2-tetrahydropyranyl ether at the MM3 level (b), the same ether at the HF/6-31G(d) level (c), and the sum of the difference between the last two with the first (d). Thus, the last surface may be viewed either as the effect of the sucrose hydroxyl groups on the energy surface, evaluated at the MM3 level, added to the framework surface calculated at the ab initio level, or as an MM3 surface that has been partially conected quantum mechanically. Solid triangles represent anomeric torsions in sucrose units found in various X-ray crystal structures. Note that the hybrid surface is the only one that clusters the large majority of these triangles within low-energy contours...

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