Rule of mutual exclusion

Centrosymmetric Molecule Example: Carbon Dioxide (CO2) The rule of mutual exclusion applies to molecules that possess a center of inversion. Carbon dioxide (CO2) is a classic example that belongs to the D∞h point group and is centrosymmetric. Carbon dioxide has four fundamental vibrational modes: • Symmetric stretch • Two degenerate bending modes • Asymmetric stretch These vibrations can be classified as either gerade (g) or ungerade (u), depending on how they behave after inversion has been applied. • Symmetric stretch is gerade meaning that it is Raman active but IR inactive • Asymmetric stretch is ungerade meaning that it is IR active, but Raman inactive • Bending modes are also ungerade meaning that they are IR active, but Raman inactive It is because of the rule of mutual exclusion that a strict separation of activity can be demonstrated between infrared and Raman spectroscopy. Non-centrosymmetric Molecule Example: Water (H2O) Molecules that do not have a center of inversion do not follow the rule of mutual exclusion. An example would be water (H2O) which belongs to the C2V point group. Water has three vibrational modes: • Symmetric stretch (A1) • Bending Mode (A1) • Asymmetric stretch (B2) Using the C2V character table we can see specific markers that show us IR and Raman activity: • IR activity corresponds to x, y, or z • Raman activity corresponds to quadratic functions (x2, y2, z2, xy, xz, yz) Both IR and Raman activity can be seen in all three vibrational modes. Both A1 and B2 modes are active in both IR and Raman spectra. For A1, IR active is represented as z that is listed in the linear functions section of the character table. Raman is represented by x2, y2, z2 in the quadratic functions section of the character table. For B2, y is representing IR active while yz is representing Raman active. This illustrates that the mutual exclusion rule does not apply to non-centrosymmetric molecules due to all vibrational modes of water being both IR and Raman active. == References ==