Description:

Consideration of atomic system symmetry allows, without any quantitative calculations, rigorously and precisely determine how many energy states there are and what interactions and transitions between them may occur. Therefore, the main purpose of this course is to describe the methods by which we can extract the information on the object that symmetry alone will provide. The application of these methods is illustrated by an example of molecular orbitals, inner orbitals of ions in the crystal field environment, normal modes of molecular vibrations, and selection rules for optical absorption transitions.

Contents:

1. Definitions and theorems of group theory.
2. Molecular symmetry.
3. The symmetry point groups, classes of symmetry operations.
4. Reducible and irreducible representations of groups, properties of irreducible representations, decomposition of reducible representations.
5. Character tables.
6. Wave functions as bases for irreducible representations.
7. The direct product and its use.
8. Molecular orbital theory - transformation properties of atomic orbitals, complete and incomplete projection operator.
9. Molecular orbitals for sigma and pi bonding.
10. Ligand field theory - splitting of the terms of free ions in a crystalline environment.
11. Construction of energy level diagrams for ions in a crystalline environment by using the method of descending symmetry.
12. Selection rules and polarizations of optical transitions.

Recommended literature:

Key references:
[1] F. A. Cotton: Chemical applications of group theory, 1990, John Willey & Sons, New York.

Recommended references:
[2] M. S. Dresselhaus, G. Dresselhaus, A. Jorio: Group theory: application to the physics of condensed matter, 2008, Springer-Verlag, Berlin.

Keywords:

Group theory, symmetry point groups, representations of groups, molecular orbitals, ligand field theory

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar