3 ECTS credits
90 h study time
Offer 1 with catalog number 1023186BER for all students in the 2nd semester of even academic years (e.g. 2012-2013) at a (B) Bachelor - advanced level.
(from the book “Chemical Applications of Group Theory” by F. A. Cotton)
1. Introduction: group theory in chemistry
2. Definitions and theorems of group theory.
2.1. The defining properties of a group
2.2. Some examples of groups
2.3. Subgroups
2.4. Classes
3. Molecular symmetry and the symmetry of groups
3.1. General remarks
3.2. Symmetry elements and operations
3.3. Symmetry planes and reflections
3.4. The inversion centre
3.5. Proper axes and proper rotations
3.6. Improper axes and improper rotations
3.7. Products of symmetry operations
3.8. Equivalent symmetry elements and equivalent atoms
3.9. General relations among symmetry elements and operations
3.10. Symmetry elements and optical isomerism
3.11. The symmetry point groups
3.12. Symmetries with multiple higher order axes
3.13. Classes of symmetry operations
3.14. A systematic procedure for symmetry classification of molecules
3.15. Illustrative examples
4. Representations of groups
4.1. Introductory comments on matrices and vectos
4.2. Representations of groups
4.3. The “Great Orthogonality Theorem” and its consequences
4.4. Character tables
4.5. Representations for cyclic groups
5. Group Theory and quantum mechanics
5.1. Wave functions as bases for irreducible representations
5.2. The direct product
5.3. Identifying nonzero matrix elements
6. Symmetry-adapted linear combinations
6.1. Derivation of projection operations
6.2. Using projection operators to construct SALCs
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The student will gain insight on how molecular symmetry can simplify many problems in the theoretical description of molecules and on the importance of character tables in this aspect.
Learning outcomes:
Knowledge of elementary group theory and insight into its relationship with molecular symmetry;
Knowledge of the concepts “irreducible representation” and character tables and their importance in the application of group theory in the study of molecular properties;
Competent use of character tables to solve problems in the study of molecular properties.
The final grade is composed based on the following categories:
Oral Exam determines 100% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Oral exam after a written preparation.
The exam consists of an exercise (with use of the course material and character tables), testing the problem solving attitude of the students. Next, a more general question (without the use of the course material) is given to test analysis and synthesis.
This offer is part of the following study plans:
Bachelor of Chemistry: Default track (only offered in Dutch)