CHE216
Assessed coursework 3
Deadline for submission 16:00 Tuesday may 13th
These questions are on the two remaining topics not yet assessed – (a) molecular bonding through symmetry adapted linear combinations, and (b) spectroscopic transitions.
They are written in the style. of what will appear in your exam. These are not your exam questions, but they are written as if they were actual exam questions on these topics. In your exam, there will be 4 questions, worth 25 marks each. Hence, the questions below are worth 25 marks each. In that way, the marks reflect actual marks in an exam. However, your coursework mark will be reported out of 100.
In attempting these questions keep in mind that your exam will be 120 minutes along. Hence, as these two questions represent half of an exam, one hour would be available to complete them in an exam (~30 minutes each). You might initially try to attempt these questions under timed exam conditions as a test of where you are now. You can then use the two-working week period to polish your answers, and then during revision re-try to complete them within the hour.
Question 1
Consider planar molecule with D3h symmetry of the type AB3. A and B are elements of the periodic table. Elements A and B have s and p valance electrons. In this question, you will determine the symmetry-adapted linear combinations (SALCs) of thep atomic orbitals of element B that can participate in σ bonding with the s atomic orbitals on the central atom A.
|
D3h
|
E
|
2C3
|
3C2
|
σh
|
2S3
|
3σv
|
|
|
|
A1′
|
1
|
1
|
1
|
1
|
1
|
1
|
|
x2+y2, z2
|
|
A2 ′
|
1
|
1
|
-1
|
1
|
1
|
-1
|
Rz
|
|
|
E′
|
2
|
-1
|
0
|
2
|
-1
|
0
|
(xy)
|
(x2-y2, xy)
|
|
A1 ′′
|
1
|
1
|
1
|
-1
|
-1
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-1
|
|
|
|
A2 ′′
|
1
|
1
|
-1
|
-1
|
-1
|
1
|
z
|
|
|
E ′′
|
2
|
-1
|
0
|
-2
|
1
|
0
|
(Rx,Ry)
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(xz,yz)
|
(a) Considering only the Bp orbitals (one from each B atom) directed toward the central A atom, and only s orbitals on atom A, construct the reducible representation (Γred) for their combination using the D₃h character table. Clearly explain how each character in Γred is obtained. [7 marks]
(b) Reduce your reducible representation into a sum of irreducible representations. [6 marks]
(c) With a brief explanation of your reasons, identify the valence orbitals (s and p) on A that can participate in σ bonding. For each orbital, state its symmetry under D₃h. [6 marks]
(d) Using the results from parts (b) and (c), determine which SALCs ofthe B atoms can
combine with which A orbitals to form. bonding molecular orbitals. Indicate which interactions are symmetry-allowed and explain why. [6 marks]
Question 2
(a) In the context of molecular electronic spectroscopy (e.g., UV-vis absorption spectroscopy), explain what is meant by saying that an electronic excitation within a molecule is electric dipole allowed. [3 marks]
(b) In what ways does molecular symmetry influence whether such a transition can occur? [2 marks]
(c) State the two main selection rules that determine whether an electronic transition is electric dipole-allowed in a molecule with a centre of inversion. Give a brief explanation of each. [5 marks]
(d) Explain how group theory can be used to determine whether a transition is dipole-allowed. [5 marks]
(e) Describe how the direct product of irreducible representations is used in this context. [5 marks]
(f) Consider a transition between an A2u ground state to a T1u excited state of an Oh complex.
With an explanation of your method, use group theory to prove that this transition is dipole forbidden. Hint: You do not need the character table to prove this. [5 marks]