The sp n 1-3 hybrid orbitals

Recalling from Section 3.4.1, we use the s orbital and the pz orbital to form two equivalent hybrid orbitals, one pointing in the +z direction and the other in the —z direction. These two orbitals are called sp hybrids, since they are formed by one s and one p orbital. The wavefunctions of the sp hybrid orbitals are given by eqs. (3.4.6) and (3.4.7). In matrix form the wavefunction are 

We now use this 2x2 coefficient matrix to illustrate the relationships among the coefficients  

If we use the s orbital and the px and py orbitals to form three equivalent orbitals h 1, ft2, and ft3, these orbitals are called sp2 hybrids. Furthermore, they lie in the xy plane and form 120° angles between them. Now the hybrids have the wavefunctions 

If the three hybrids have the orientations as shown in Fig. 3.4.8, we then get the following results for the coefficients. Since the s orbital is (equally) split among the three equivalent hybrids, 

Note that both e and j are negative because hi and hs project on the -x direction. 

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