Chemical applications of group theory

Vakinformatie

Given by professor Thomas Jagau in 2021-2022.

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)

1. Given are the following equations: i*i=j*j=k*k=-e i*j*k=-e a. Is the group abelian. Explain your reasoning. b. Is the group cyclic. Explain your reasoning.

Question 2 (10/20)

2. Given is the molecule C4H2N2 (trans) a. What is the point group of this molecule? b. Do a full coordinate analyis. Give the irreps of the rotational, translational and vibrational displacements. c. What irreps will be visible in the IR spectrum? d. There are 10 pi-electrons. Give the irreps of the orbitals involved. (Unsure about this question, but it did involve the pi-system) e. The ground state evolves according to the totally symmetric irrep. What excitations would vibrationally couple with the ground state?

Question 3 (6/20)

3. ML6 with Oh point group and 8 d-electrons. (Similar to Q4 exercise session 5) a. Identify d-electron configuration of lowest energy state. b. 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. c. If we excite 1 electron give the term symbols. Take into account spin. d. What excitations would be optically visible.