Chemical applications of group theory

Vakinformatie

This course is given by Thomas Jagau. The exam consists of questions that are similar to the ones seen in the exercise sessions. You can bring these exercises, your course notes, the book by Ceulemans and just about anything else you might need.

Examenvragen

Exam 29th January, 2024

Question 1

Give the point group for these molecules

1. (E)-2-Butenedinitrile（(CN)CHCH(CN)）
2. cyclobutane (C4H8)
3. tri（oxalato）ferrate Fe(C₂O₄)₃（3-） （chiral)
4. Give a molecule that is chiral but is not C1 group, draw the structure of it.

Question 2

Give the Z-matrix representation for calculation of the following molecules, write the degree of freedom.

1. Allene (H2CCCH2) (D2d)
2. Boric Acid (B(OH)3) (C3h)
3. Hexacarbonyl Chromium (Cr(CO)6) (Oh)

Question 3

Considering (para)dichlorobenzene (ClC6H4Cl) (D2h)

1. Give the irreps for the s orbitals of the hydrogen
2. Construct SALCs of the s orbitals of the hydrogen
3. Rank there energy according to the nodal structure.

Question 4

For octahedral complex CoF6(4-)(that have 7 electrons in the d orbitals), given that it is high spin, answer the question below.

1. Draw a sketch of the energy splitting, give the electron configuration.
2. Give term symbols for this configuration. You should solve direct product first and consider the symmetry of spatial and spin functions.
3. Give the term symbol that has the lowest energy.
4. If we look at Co(H2O)(2+), the point group is Th. Answer the first three question for this molecules.(You do not have to evaluate direct product again, but only need to look at the relation between Oh and Th.)

Exam 30th January

Question 1

1. Give the point group of 3 molecules
2. Which molecules are chiral?

Question 2

Given is a multiplication table (6x6) like the one from exercise session 1 Q.1

1. What is the order of the group?
2. Is the group cyclic?
3. Is the group abelian?
4. What are the classes?

Question 3

1. What are the irreps of the pz-orbitals of trimethylenemethane (D3h)?
2. Derive the SALCs.
3. Order the SALCs in terms of energy by looking at the amount of nodes.
4. Derive the term symbols.

Question 4

1. Perform a normal coordinate analysis on SF6 (Oh). What are the irreps of the translational, rotational and vibrational modes?
2. Does removal of an electron from the HOMO (SF6+) affect the symmetry?

Exam 20th January

The exam is open book. You can take the book by prof. Ceulemans and the printed pages of the exercise sessions.

Question 1 (6/20)

1. Give the point groups of 4 molecules.
2. Construct the multiplication table of a D2h molecule.

Question 2 (9/20)

1. Give the point group of allene.
2. Construct the matrix representation for this point group looking at the 4 hydrogens.
3. Perform a normal coordinate analysis. Give the irreps of the rotational, translational and vibrational displacements.
4. Imagine a fully planar allene. Perform a normal coordinate analysis.
5. Are these visible in the IR spectrum? If so, are they distinguishable?

Question 3 (5/20)

1. Give the point group of C8F8, (synthesized in 2022 for the first time)
2. Give the term symbols of the excitations HOMO --> LUMO and HOMO --> LUMO+1. The HOMO is a fully occupied t2u orbital and the LUMO and LUMO+1 are a1g and t1u respectively.
3. Are these visible in the UV/VIS spectrum?

Exam 26th August 2022

The exam is open book. You can take the book by prof. Ceulemans and the printed pages of the exercise sessions.

Question 1 (4/20)

Given are the following equations:

• i*i=j*j=k*k=-e
• i*j*k=-e

1. Is the group abelian. Explain your reasoning.
2. Is the group cyclic. Explain your reasoning.

Question 2 (10/20)

Given is the molecule C4H2N2 (trans)

1. What is the point group of this molecule?
2. Do a full coordinate analyis. Give the irreps of the rotational, translational and vibrational displacements.
3. What irreps will be visible in the IR spectrum?
4. There are 10 pi-electrons. Give the irreps of the orbitals involved. (Unsure about this question, but it did involve the pi-system)
5. The ground state evolves according to the totally symmetric irrep. What excitations would vibrationally couple with the ground state?

Question 3 (6/20)

ML6 with Oh point group and 8 d-electrons. (Similar to Q4 exercise session 5)

1. Identify d-electron configuration of lowest energy state.
2. Give the term symbols of the ground state. Start from the character table and work out the necessary direct products. No need to take spin into account.
3. If we excite 1 electron give the term symbols. Take into account spin.
4. What excitations would be optically visible.