Group Theory for Chemists, 2nd Edition

2

Groups and Representations

While Chapter 1 outlined the concept of symmetry in a descriptive manner, this chapter will aim to place the concept on a more quantitative basis. Transformation matrices – the numerical descriptors of individual symmetry operations – will be introduced, as will numerical representations for the point group symmetry operations. These will allow group theory to be applied in a more quantitative way to the analysis of vibrational spectra and molecular orbital theory (Parts II and III).

2.1 GROUPS

A “group” can be thought of as an exclusive club to which only a number of members belong. These members must, in turn, agree to abide by certain rules. The collection of symmetry operations which make up a point group form ...