Rule of mutual exclusion

The rule of mutual exclusion in molecular spectroscopy relates the observation of molecular vibrations to molecular symmetry. It states that no normal modes can be both Infrared and Raman active in a molecule that possesses a center of symmetry. This is a powerful application of group theory to vibrational spectroscopy, and allows one to easily detect the presence of this symmetry element by comparison of the IR and Raman spectra generated by the same molecule.

The rule arises because, in a centrosymmetric point group, a normal mode of vibration must have the same character (i.e. transform similarly, according to the same irreducible representation) under inversion as the property which generates it. IR active modes are generated by one of the components of the dipole moment vector. Vectors transform as spatial coordinates, and are thus of ungerade (u) symmetry, i.e. their character under inversion is -1. Thus, IR active modes must have character -1 under inversion.

Raman active modes, meanwhile, are generated by the polarizability tensor. Since tensor components transform as bilinear products of two spatial coordinates, they are invariant under inversion and are thus of gerade (g) symmetry, i.e. their character under inversion is +1. Thus, in the character table there is no irreducible representation that spans both IR and Raman active modes, and so there is no overlap between the two spectra.

This does not mean that a vibrational mode which is not Raman active must be IR active: in fact, it is still possible that a mode of a particular symmetry is neither Raman nor IR active. Such spectroscopically "silent" or "inactive" modes exist in molecules such as ethylene (C₂H₄), benzene (C₆H₆) and the tetrachloroplatinate ion (PtCl₄²⁻).