6 ECTS credits
165 u studietijd
Aanbieding 1 met studiegidsnummer 4023196FNR voor alle studenten in het 1e semester met een gespecialiseerd master niveau.
Group theory is an important mathematical tool in the study of molecules and molecular phenomena. The aim of the course is to help students to apply symmetry-based principles and methods in their own research projects. At the start the students should have a basic knowledge of matrix algebra, elementary trigonometry, and complex numbers. In addition they should have had an introduction to quantum mechanics. More advanced mathematical concepts are introduced gradually during the course.
The course is based on the sequence: operations, representations, interactions.
In the first part the precise meaning of a symmetry operation is defined. An overview of the point groups is given, and numerous examples of symmetry in molecules are reviewed, often illustrated with ball and stick models. Then the operations in real space are transferred to transformations in a function space, using matrix representations. Finally these representations are coupled to describe interactions between molecules and molecules and electromagnetic fields. Several applications are discussed, involving electronic structure theory, electronic and vibrational spectroscopy, and vibronic interactions.
Contents:
1. Operations
2. Function spaces and matrices
3. Groups
4. Representations
5. What has Quantum Chemistry got to do with it?
6. Interactions
7. Spherical symmetry and Spins
.
Students can independently apply group theoretical techniques and methods on scientific questions.
De beoordeling bestaat uit volgende opdrachtcategorieën:
Examen Andere bepaalt 100% van het eindcijfer
Binnen de categorie Examen Andere dient men volgende opdrachten af te werken:
Open book examination, based on the handbook and lecture notes of the student. The examination always includes the identification of point group symmetries of molecular structures and processes, based on figures and/or 3D molecule models. Then there are two applied exercises, similar to the ones discussed during the semester. Finally the student is asked to derive or prove a group-theoretical proposition.
To each of the questions a number of points is assigned, e.g. four questions of five points each, and the total score is simply the sum of the partial scores.
Deze aanbieding maakt deel uit van de volgende studieplannen:
Master of Chemistry: Analytical and Environmental Chemistry (enkel aangeboden in het Engels)
Master of Chemistry: Chemical Theory, (Bio)Molecular Design and Synthesis (enkel aangeboden in het Engels)