The Character Table

Abstract

The definition of a character has been given in Chapter 3. As will be demonstrated in Chapter 5, character tables are necessary for the determination of the selection rules that govern which bands will appear in the infrared and Raman spectra of various molecules and also for the determination of the number of fundamentals of each type of vibration. Table 4–1 shows a typical character table, that for the C 2v point group, and Fig. 4-1 diagrammatically illustrates the significance of the various parts for the character table for C 3v. The character table classifies the displacements of the atoms of molecules from their equilibrium positions according to the irreducible representation of the symmetry group. The first column of the character table lists the types of representations, or species of vibrations, possible for the given point group. The most symmetrical species are placed near the top of the table, and the least symmetrical species near the bottom. The symmetry classes pertinent to the point group form the column headings.