Required in stage
Optional in stage
First term
Second term
Both terms
Not organised
This year
Next year
Alternating years
External
Prerequisites
Taught by
Language of instruction
Duration
Identical coursesChemical Applications of Group Theory (B-KUL-G0I17A)
Aims
Group theory is an important mathematical aid in the study of molecules and molecular phenomena. The aim of the course is to help students to independantly apply group theoretical techniques and methods on scientific questions from their own research domain.
Is included in these courses of study
Activities
3 ects. Chemical Applications of Group Theory (B-KUL-G0I17a)
Content
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
Course material
handbook: A. Ceulemans, Group Theory Applied to Chemistry, Springer, London, August 2013
Language of instruction: more information
The course is given in English as part of the compulsory program for the Erasmus Mundus TCCM master. It is also
an elective course of the general Master of Chemistry program.
Format: more information
3 ects. Chemical Applications of Group Theory: Exercises (B-KUL-G0I18a)
Content
After each lecture the students receive a number of assignments related to the content of the lecture.
In the practical sessions they represent their results and discuss possible way outs or alternatives for exercises that appeared to be more difficult than expected.
The sessions also include working with molecular models to identify symmetry groups and the role of substituents and nuclear displacements.
Each chapter of the handbook for the course contains several study questions. Solutions to all these problems are provided at the end of the handbook.
Course material
The handbook that is used for the lectures also contains many study questions, and also the solutions.
The students also have access to molecular ball and stick models to identify point groups.
Evaluation
Evaluation: Chemical Applications of Group Theory (B-KUL-G2I17a)
Explanation
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.