C4v point group

Figure 6-14. The symmetry operations of the C4v point group applied to the 2p orbitals.

In some cases, it is possible for a d orbital to be polarized by the s orbital and simultaneously by a p orbital. This happens, for example, to the z orbital in ML5 complexes with an SBP geometry ( 2.3.1.2). This orbital does indeed have the same symmetry as the s and pz orbitals (ai in the C4V point group). The z orbital of the d block has antibonding interactions with the ligands (z — I, 2.A9) the s andp contributions mix in so that ... 

The entries 2C4, and 2aj in the top row of the character table for the C4V point group mean that this point group has two independent symmetry operations in each of the C4, a and a classes. The C4 class includes both the C4 operation itself, and the inverse of this operation, C4 , which is the same as 4. The basis functions for the two-dimensional irreducible representation (E) in the last row are pairs of coordinate values (x, y) or pairs of products of these values. The character 2 here means that the identity symmehy preserves both values, as it should, and the character -2 indicates that the C2 operation changes the sign of both values. 

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