ABSTRACT
For the purpose of developing concepts needed for chiroptical spectroscopy, molecules can be categorized into two different groups. The criterion needed to distinguish these two groups of molecules is to ask whether a given molecule possesses certain symmetry properties. The symmetry properties to consider are (a) reection symmetry (also referred to as plane of symmetry), (b) rotationreection symmetry (also referred to as improper rotation axis), and (c) inversion symmetry (or a point of inversion). If all atoms in a given molecule reside on a plane, then that molecule is said to have a plane of symmetry. Alternately, if identical atoms in a given molecule reect on to each other through a plane, then that molecule is also said to have a plane of symmetry. If a rotation of the molecule about an axis followed by a reection perpendicular to that rotation axis brings the identical atoms in that molecule into each other, then the molecule is said to have an improper rotation axis (or rotation-reection symmetry). A point of inversion symmetry is a point through which the identical atoms invert into each other (vide infra). The planes, axes, and point of symmetry are referred to as the symmetry elements. Although we are only concerned here with the three symmetry elements mentioned above, additional symmetry elements can also be present in a molecule. These additional symmetry elements and associated material can be found in books on group theory (Cotton 1971), but they are not necessary for the present discussion.
