Advanced Inorganic Spectroscopy Mock Exam Questions
Dr. N. A. Young
The exam paper consists of four question, two from Dr Bridgeman, and two from myself. Of my two
questions, one requires 3 short essays chosen from a total of four topics, whilst the other is a 'problem' type
question.
The revision seminar will take place on Friday morning of week 13.
Question 1.
Although the actual paper only has four topics to choose three from or the short essay question, given below
are a selection of the type of questions and topics that might occur.
Discuss three of the following topics, including relevant examples.
The Heisenberg Uncertainty Principle.
The Born-Oppenheimer Approximation.
Hermite polynomials and the vibrational wavefunction
Raman polarization experiments
Anharmonicity and its effects
Fermi resonance.
Isotopic subsitution.
Coriolis Coupling.
Q branches in vapour phase IR spectra
Question 2.
The question given below is representative of the type of problem question that I am in the habit of asking. It
is a little more tricky than you might encounter on the exam, but it is an interesting problem.
White phosphorus (P4) exists as discrete molecules containing the 4 phosphorus atoms at the vertices of a
tetrahedron, each bound to the three other P atoms.
(a) How many vibrational modes do you expect for this molecule, and how many of these can be described
as stretching modes?
(b) Using this information calculate vib and str for P4
(c) Determine the number of IR and Raman active vibrational modes for P4.
(d) Indicate the polarization ratios you would for the bands in the Raman spectrum.
(e) Would you expect to observe more bands in the experimental spectrum than you calculated, and if so
why?
(f) For the A1 vibrational mode use projection operators and the stretching modes to determine the
symmetry coordinate for this mode, and hence sketch the form of the normal mode.
For more practice at Group Theory type questions I have included below some from the old symmetry
course that you have probably seen before. Whilst not as detailed as the 4th year questions, they will give
you practice. In square brackets are exercises more related to the 4th year course.
1996 Symmetry Paper
When RuCl3 is reacted with a mixture of HCl, HCOOH (formic acid) and CsCl a yellow precipitate is
formed. Analysis of the precipitate gave 23.8% Ru, 31.3% Cs and 25.1% Cl. The mass spectrum of the
mono-anion gave a cluster of peaks at 292m/z, with three successive losses of 28. Using the C-O region of
the IR and Raman spectra, show how Group Theory could be used to determine the shapes of the isomers
formed. Indicate which you think is most likely.
Show all your workings.
1997 Symmetry Paper
Show how vibrational spectroscopy (use only the Xe-F stretching modes) and Group Theory can be used to
differentiate between the two isomers of [XeF3]+ shown below. Which of these is the most likely and why?
+
+
F
F
Xe
F
F
Xe
F
F
D3h
C2v
[You could also calculate vib and the symmetry coordinates for the stretching modes for both of these
isomers. What kind of isotope patterns would you expect if the F was replaced by Cl?]
1998 Symmetry Paper
Caesium perchlorate is thought to exist in the vapour phase as a molecular species with either tridentate or
bidentate coordination of the caesium. Show how a combination of Group Theory and vibrational
spectroscopy (consider the Cl-O stretching modes only) could be used to differentiate between these two
isomers.
O
Cl
O
O
O
O
Cl
O
Cs
C3v
[You could calculating vib]
C2v
O
O
Cs
1999 Symmetry Paper
(i)
(ii)
(iii)
(iv)
(v)
Using Group Theory determine str for the two isomers of VF5 shown below.
Which of these irreducible representations are IR and/or Raman active?
How many IR and Raman bands will be observed for each isomer?
How many of the Raman bands will be polarised?
The gas phase IR spectrum of VF5 had bands in the V-F stretching region at 810 and 784
cm-1, whereas the Raman spectrum had bands at 810, 719 and 608 cm-1, the last two being
polarised. Using this information, identify the molecular shape of VF5.
F
F
V
F
F
F
F
D3h
V
F
F
F
F
C4v
[For extra practice work out vib for both, and the symmetry coordinates for the D3h isomer.]