Hybrids with d-orbital participation

In Section 7.2.1, we have seen that many hybridization schemes involve d orbitals. In fact, we do not anticipate any technical difficulty in the construction of hybrids that have d orbital participation. Let us take octahedral d2sp3 hybrids, directed along Cartesian axes (Fig. 7.1.10), as an example. From Table 7.1.5, 

With these results, we can easily obtain the hybrid wavefunctions 

Lastly, we consider a system with non-equivalent positions. An example of such a system is the trigonal bipyramidal molecule AX5 with symmetry. As discussed previously, one possible scheme is the dsp3 hybridization, where dz2 is the only d orbital participating. 

However, there is no reason at all to assume ha and hb are made up of only pz and dz2 orbitals The dz2 orbital can also contribute to the equatorial hybrids, and the s orbital can also contribute to the axial hybrids. In fact, if we use only the s and pz orbitals for the axial hybrids, and the dz2, px, and p-y for the equatorial hybrids, we then have 

Obviously, both of the matrices in eqs. (7.2.4) and (7.2.5) are limiting cases. A general expression encompassing these two cases is 

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