Atoms with s and p valence electrons

The next level of complexity in crystal structure arises from atoms that have both s and p valence electrons. The individual p states are not spherically symmetric so they can form linear combinations with the s states that have directional character a single p state has two lobes of opposite sign pointing in diametrically opposite directions. The s and p states, illustrated in Fig. 1.8, can then serve as the new basis for representing electron wavefunctions, and their overlap with neighboring wavefunctions of the same type can lead to interesting ways of arranging the atoms into a stable crystalline lattice (see Appendix B on the character of atomic orbitals). 

The possibility of combining these atomic orbitals to form covalent bonds in a crystal is illustrated by the following two-dimensional example. For an atom, labeled A, with states s, p, Py, pf which are orthonormal, we consider first the linear combinations which constitute a new orthonormal basis of atomic orbitals  

The first three orbitals, / f, point along three directions on the xy plane 

Imagine next that we repeat this exercise we take another atom with the same linear combinations of orbitals as A, which we will call A, and place it in the direction of the vector relative to the position of atom B, and at the 

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