Character Tables

Question 1
Give the transformation matrix for the following symmetry operations:

1. E [Solution]
2. C₂(x) [Solution]
3. C₃ [Solution]
4. σ_h [Solution]
5. C₄ [Solution]
6. i [Solution]

Question 2
Construct the Character Table for the D_3h Point Group. The table has the following operations:
E, 2C₃, 3C₂, σ_h, 2S₃ and 3σ_v. [Solution]

Question 3
A Character Table has the following operations: E, 2C₃, C₂, 3σ_v, 3σ_d and one other operation (with 2 equivalent operations). What is the missing operation? [Solution]

Vibrational Spectroscopy

Question 1
For the following molecules determine the number of IR and Raman active vibrations:

1. SiCl₄ [Solution]
2. trans-SF₂Cl₄ [Solution]
3. SbCl₅ [Solution]
4. CH₂Cl₂ [Solution]

Resonance Spectroscopy

Question 1
For the following molecules give the expected coupling pattern that would be observed in a ¹⁹F NMR spectrum (ignore any J_CF and J_HF):

1. PF₆^- [Solution]
2. cis-¹⁹⁵PtF₂Cl₂^2- [Solution]
3. fac-MoF₃(PMe₃)₃ [Solution]
4. DF [Solution]
5. SiFCl₃ [Solution]
6. SeF₄ [Solution]
7. mer-PF₃Cl₃^- [Solution]
8. ⁵⁷FeF₄^- [Solution]
9. AgFPMe₃ [Solution]
10. AlF₄^- [Solution]