3 ECTS credits
90 u studietijd
Aanbieding 1 met studiegidsnummer 1023186BER voor alle studenten in het 2e semester van een even academiejaar (bvb. 2012-2013) met een verdiepend bachelor niveau.
(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.
De beoordeling bestaat uit volgende opdrachtcategorieën:
Examen Mondeling bepaalt 100% van het eindcijfer
Binnen de categorie Examen Mondeling dient men volgende opdrachten af te werken:
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.
Deze aanbieding maakt deel uit van de volgende studieplannen:
Bachelor in de chemie: Standaard traject