Applications in Vibrational Spectroscopy - Molecular Symmetry

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the irreducible representations for the CO stretching modes and, hence, explain these

observations.

4. Iron tetranitrosyl, Fe(NO) 4 , has been synthesized from Fe(CO) 5 by treatment with NO

under pressure. It is a very reactive complex that decomposes even under an inert atmo-

sphere. It has a suggested structure of [Fe(NO + ) 3 ]NO − , supported by the observation

that it shows two IR absorptions in the NO + stretch region. Possible structures for the

[Fe(NO + ) 3 ] complex include D 3h or C 3v point groups.

(a) Using a suitable basis, identify the irreducible representations for NO + stretching

vibrations that are IR active for each complex geometry and so identify the most

likely geometry.

(b) For each of the irreducible representations you have identified, sketch the motion of

the NO + atoms during the corresponding vibration. Explain your answer in terms of

compliance with the characters of the representation and the spectroscopic selection

rules.

5. (a) Explain why molecules which belong to point groups having centres of inversion

will have IR-active vibrations with only ungerade representations.

(b) Using a basis of six C H vectors, identify the representations for all the ungerade

C H stretching vibrations of benzene.

(c) Two of the ungerade C H stretch vibrations of benzene lead to observable IR

absorption; explain why only one band is seen experimentally.

(d) Using the projection operator, obtain a normalized SALC representation of the

vibrational motion of the C H stretch mode of benzene which is ungerade but

not IR active. Based on your SALC, illustrate the relative phases of motion of the

C H bonds in this vibration using the basis from (b). Why does this mode not give

a transition dipole moment?

6. In Section 6.3.1 and Problem 6.6 the irreducible representations for C

H stretching

modes of 1,4- and 1,2-difluorobenzene are derived.

(a) Using the projection operator method, find normalized SALC representations for all

modes in each case. Confirm that your functions have the expected behaviour for

the group operations by deriving the characters for each mode and comparing with

the relevant irreducible representation. Note : for degenerate modes, the characters

for the individual vibrations should be summed.

(b) Show that the SALC functions you have derived for the C

H stretching modes are

orthogonal to one another.