Berry Pseudorotation Exercises

As an aid you may wish to use the dos program REDUCE. You can run the program on an Athena machine using the dos emulator "dosemu". Just unzip the REDUCE directory, cd into it, and then type "dosemu REDUCE.EXE" at the command prompt.

1. Determine the number and symmetry types of the normal modes for the C_4v transition state structure for BPR involving SF₄.
2. The energies have been computed for the SF₄ normal modes in the C_4v BPR transition-state structure. Examine the drop-down menu (click here) and identify which are the energies that belong to modes having E symmetry.
3. With reference to the same drop-down menu, determine the symmetry species (Mulliken symbol) of the 490 cm^-1 vibration. To do this by inspection, it will be helpful to note the position and magnitude of the normal mode displacement vectors.
4. Identify the energies of the A₁ vibrations by noting that these are infrared active and so will involve a dipole moment change during vibration.
5. Identify the energy of the B₂ vibration by noting that its displacement vectors have the same phase characteristics as a d_xy orbital.
6. How many A₂ vibrations are found among the normal modes of the C_4v transition state structure for BPR involving SF₄?
7. In the case of the C_2v equilibrium geometry structure of SF₄, how many of the normal modes are IR active?