Chem3140 Extra Practice
I. Provide the total Reducible Representation for the x,y,z rotational, translational, and vibrational
modes of the following molecules:
1. PF5 (D3h) D
3h E 2C3 3C2 σh 2S3 3σv
18 -2 4 4
2. ClF4I (I is axial, C4v) C4v E 2C4 C
2 2σv 2σd
18 2 -2 4 2
3. C6H12 (“chair”, D3d) D3d E 2C3 3C2 i 2S6 3σd
54 0 0 0 0 6
II. Determine the total Reducible Representation for the C-O stretching vibrations in the following
molecules:
4. Fe(CO)5 (D3h) D3h E 2C3 3C2 σh 2S3 3σv
5 2 1 3 0 3
5. Cr(CO)6 (Oh) Oh E 8C3 6C2 (6C4 3C2) i 6S4 8S6 3σh 6σd
6 0 0 2 2 0 0 0 4 2
III. Vibrational Spectroscopy: Determine the symmetry point group of the molecule trans-Cl2SeF4 (Se is
central atom). Then, using the x, y, and z coordinates for each atom determine the reducible
representation, reduce it, and classify the representations into translational, rotational, and
vibrational modes and decide which modes will be IR-active.
trans-Cl2SeF4
D
4h E (2C4 C
2) 2C2’ 2C2” i 2S4 σh 2σv 2σd
21 3 -3 -3 -1 -3 -1 5 5 3
2A1g + A2g + B1g + B2g + 2Eg + 3A2u + B2u + 4Eu
-A2u (z) and –Eu (x,y) as translational modes
- A
2g (Rz) and –Eg (Rx, Ry) as rotational modes
2A
1g + B1g + B2g + Eg + 2A2u + B2u + 3Eu vibrational modes (remaining)
Only 5 modes are IR active (5 peaks): 2A2u (z) + 3Eu (x,y)
