Chapter 5, Problem 5.29P

The projection operator method has applications beyond the deduction of group orbitalSALCs. Deduce the wave function equations for the six $\pi$ molecular orbitals of benzene, usingthe labels specified for each ${\text{2P}}_{\text{z}}$ orbital. First, derive initial SALCs using each representation ofthe ${\text{D}}_{\text{6h}}$ point group; some combinations will afford zero. Using sketches of the deduced orbitals,symmetry characteristics of the representations, and a coefficient table like that in Section 5.4.4, deduce the SALCs not derived initially from the character table analysis.Provide normalized equations and a sketch for each molecular orbital.