Introduction

The determination of the structures of chemical species is an important and absorbing aspect of physical chemistry. Many methods have been devised as the subject of structure determination has developed, but among the most rewarding techniques currently in practice are those based either on spectroscopic or on diffraction methods. The extent of each of these fields is considerable, and here we shall introduce only parts of them. It is important in structure determination to acquire a knowledge of symmetry, and the application of symmetry principles in chemistry is far reaching. We give first a brief introduction to the symmetry of three-dimensional, finite bodies and its application in chemistry.

Symmetry concepts

We can see evidence of symmetry all around us; it is not just a feature of molecules and crystals. The emblems associated with the National Westminster Bank plc, the Isle of Man and Mercedes-Benz cars all reveal threefold symmetry; the latter shows other symmetry as well. The splendid Dobermann in Figure 3.1 illustrates reflection symmetry about a vertical, medial plane through her.

A symmetry operation applied to a molecule, or other body, moves it into a state that is indistinguishable from its initial state, thereby revealing the symmetry inherent in the body. We may link a symmetry operation with a symmetry element, which is a conceptual geometrical entity (point, line or plane) with respect to which a symmetry operation may be said to be performed.