Symmetry and Elements of Group Theory

Abstract

Abstract This chapter covers the rudiments of group theory, with emphasis on the use of the character tables of molecular point groups. The chapter begins with the identification of the symmetry elements a molecule possesses, and the symmetry operations these elements generate. With such knowledge at hand, the symmetry point group of a given molecule can be readily determined. The character tables of the point groups are then introduced, and the Mulliken notation for the irreducible representations is discussed in detail. Finally, the direct product of two irreducible representations is covered. The result of the direct product is used to identify the non-zero integrals in quantum chemistry and derive the selection rules in electronic spectroscopy. No rigorous mathematics is used in treating the various theories in this chapter. Instead, abstract concepts are often illustrated with examples based on real chemical compounds or practical applications.