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Symmetry and Group Theory

Module CH3337

This Module is offered by TUM Department of Chemistry.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2021/2 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2021/2SS 2018

Basic Information

CH3337 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

  • Focus Area Theoretical Quantum Science & Technology in M.Sc. Quantum Science & Technology
  • Catalogue of non-physics elective courses
Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Content, Learning Outcome and Preconditions


1. Foundations of group theory
2. molecular symmetry and point symmetry groups
3. representation theory
4. symmetry and quantum mechanics
5. MO theory and symmetry in inorganic and organic chemistry
6. ligand field theory and spectroscopy
7. molecular vibrations
8. solid state and crystal symmetry

Learning Outcome

Upon successful completion of the module students know the required mathematical foundations and methods from group theory which are required for symmetry considerations. They are able to apply them to simplify and solve problems from diverse areas in chemistry and quantum mechanics after they have successfully worked on the given practical exercises. They know the most important applications of symmetry and group theory in chemistry after attending the module.


The modules Mathematics (CH0105, CH0112), Quantum Mechanics (CH4108), and Molecular Structure and Statistical Mechanics (CH4113) from the TUM Chemistry Bachelor Degree Program.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

The module consists of a lecture with inegrated exercise classes. The presence time in lectures and exercises is comparable in order to balance the acquisition of conceptual knowledge with that of practical skills. Lectures introduce the various topical units. The students deepen their understanding during guided self-study time, based on the material provided in the e-learning course. Practical exercises allow students to self-assess their competence level, apply their knowledge to jointly solve representative example problems, and receive immediate feedback from a instructor.


Scripts, e-learning course, exercise portfolio, blackboard, PowerPoint


F.A. Cotton, Chemical Applications of Group Theory, Wiley-Interscience; Edition: 3 (2. March 1990)

Module Exam

Description of exams and course work

The module examination consists of a single written exam (90 minutes) in which the students have to recall different group theoretical approaches and methods and symmetry concepts as well as their respective applicability to problems in chemistry and physics. They have to solve simple problems by computation without any external aids. The answers to questions for background knowledge can be given partially as free text or in multiple choice form. The free text allows students to express their understanding at their personal competence level in their own words. Through the computational problems students can show that they can formalize and apply this understanding in mathematical language.

Exam Repetition

There is a possibility to take the exam in the following semester.

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