This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH _n (n = 2-6) molecules and cyclic conjugated polyenes (with and without d-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.
Keywords: carbonyl stretching modes, cyclic conjugated polyenes, hybridization schemes, infrared activity, molecular orbital theory, molecular vibrations, normal modes, Raman activity, rule of mutual exclusion, vibrational spectra