Some Connections Between the Representation Table and Molecular Orbitals

Q 13-10 Some Connections Between the Representation Table and Molecular Orbitals 

The representation table also tells us which basis AOs can appear in the various MOs. For instance, if we used a set of valence AOs for NH3, we would have a 2p AO on nitrogen, oriented along the C3 axis of the molecule, and also 2px and Ipy AOs perpendicular to C3. Now 2px,2py, and 2pz transform like x, y, and z, respectively (if they are centered at a common point on the C3 axis) just as z is symmetric for all symmetry operations of the group, so is 2pz. This means that the 2pz AO can be expected to appear only in MOs with ai symmetry. Ipx and Ipy must appear together 

---