In a molecule with a center of symmetry, an antisymmetric vibration will be active in:a) Infrared andb) Ramanc) Infrared and Ramand) not active (neither in Infrared nor in Raman)

The mutual exclusion rule states that for certain molecules, vibrations that are IR-active are not Raman-active, and vice versa. Molecules must have a certain symmetry element in order for the mutual exclusion rule to apply. Examine the character tables in Appendix 3 and determine what that symmetry element is.

Linearly polarized light can be assigned a specific irreducible representation of a symmetry point group. If the electronic ground state of benzene has A1g symmetry and y- polarized light has the label E1u, what are the symmetry labels of allowed excited electronic states? Use the D6h character table in Appendix 3.

True or False: It is possible for a molecule to have a mirror plane that is parallel to the principal rotation axis, and a mirror plane that is perpendicular to the principal rotation axis. (If true, give an example. If false, briefly explain why.)

3. How many vibrational modes do each of the following have? a) Azulene, C₁0H8: b) Ammonia, NH3:

For the chlorate anion (CI03-) For the chlorate anion, please give the type of rotational axis and number of mirror planes found in the molecule. O C3, no mirror planes C3, three mirror planes C2, two mirror planes C1, no mirror planes

The harmonic oscillator model is a good approximation of atomic stretching. (1) Use an energy level diagram to explain typical vibration absorbance observed in IR spectroscopy.

For selected molecule identify: a) all the symmetry elements present b) appropriate point group c) which of the symmetry elements listed in (a) are sufficient to determine the point group.

How many vibrational modes does an SO3 molecule have a) in the plane of the nuclei, b) perpendicular to the molecular plane? c) Classify them by their symmetry type.

For the Acetone molecule, using each of the symmetry operations of the C2v molecule (E, C2, σx,z, σy,z), confirm that this deformation does have the same symmetry as the B1representation in the character table. Do each symmetry operation and write down the sequence of 1s and -1s.