The Normal Modes and Frequencies of Vibration of the Regular Plane Hexagon Model of the Benzene Molecule

The thirty modes of vibration of the regular plane hexagon model for the benzene molecule, including both the hydrogen and carbon atoms, are derived by the group theory method described by Wigner. From these the twenty frequencies of vibration are calculated in terms of a simple potential function involving six force constants. Selection rules for the Raman and infrared spectra are listed. Seven fundamentals are permitted in the Raman spectrum and four fundamentals in the infrared. Both analytical and graphical descriptions of the modes of vibration are given. These depend largely on the symmetry of the molecule and are only in part influenced by the choice of potential function adopted.