Symmetry

Abstract

A crucial reason for the importance of group theory in chemistry is that it provides a quantitative description of the symmetry properties of atoms, molecules, and solids. It would be incorrect, however, to think that group theory is only, or even mainly, a theory of geometric symmetry, because group theory also describes the processes of ordinary arithmetic. Indeed the source of the power of group theory in dealing with phenomena that depend on symmetry is its establishment of a link between symmetries and numbers. It is the power of this analogy, which provides arithmetic representations of geometrical operations, that makes it possible to derive geometric conclusions from simple numerical calculations.