NKEA07017U Group Theory and its Application in Quantum Chemistry

Volume 2013/2014
Education
MSc Programme in Chemistry
Content
The group postulates, Subgroups, Coset decompositions, Lagrange's theorem, Cayley's theorem, Direct product groups, Normalizer groups.
The group algebra, Regular representation, Equivalent representations, Reducible representations, Unitary matrix representations, Schur's lemmas, General form of Orthogonality relations. Irreducible basis for the group algebra, Character projection elements, Irreducible representations of direct product groups.
Symmetry of Many-Electron Wavefunctions, Symmetry operations, Rotation of functions, Classification of stationary states, The Pauli principle. Spin-Free Quantum Chemistry, The spin-free Pauli principle, Configuration state functions. Matrix Elements in Quantum Chemistry, Rotation of operators,
Wigner coefficients, Irreducible tensors and tensor operators, The Wigner-Eckart theorem.
Learning Outcome
The overall goal of the course is to provide a fundamental understanding of finite groups, their associated group algebras, the matrix representation theory from first principles, and to emply group theory in molecular quantum chemistry. In completing the course the students are expected to have aquired    

Competences:
- Understand the concepts of finite groups and their associated group algrbras.
- Discuss the application of group theory in molecular quantum chemitry.
- Employ group theoretical arguments in predicting molecular properties. 

Skills:
- Describe basic properties of finite groups and their group algebras.
- Apply the concepts of finite groups in analyzing the electronic structure of molecules.

Knowledge: 
- Understand the fundamental concepts of group theory and their applications in molecular quantum chemistry.
- Understand the consequence of molecular symmetry in predicting molecular properties.
Literature
Introduction to Group Theoretical Methods in Quantum Chemistry, Lecture Notes, Sten Rettrup
Fundamental knowledge of linear algebra and quantum chemistry corresponding to the levels of MatFysK/AnvMatKem and KemiKS.
Lectures and exercises
  • Category
  • Hours
  • Exam
  • 20
  • Lectures
  • 28
  • Preparation
  • 144
  • Theory exercises
  • 14
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written assignment, 2 weeks
Oral examination, 30 min
Pass-Fail evaluation based on a take-home exam followed by individual oral examination with reference to the contents of the take-home problem.
The evaluation is based on a comprehensive assessment of the take-home exam and the oral exmination.
Internal censorship.
Marking scale
passed/not passed
Censorship form
No external censorship
Exam period
several internal examiners
Criteria for exam assesment
After the course the student should be able to:
  • Explain the fundamental concepts of finite groups and their group algebras.
  • Explain the group theoretical orthogonality relations and their consequences for the application of group theory.
  • Apply group theoretical projection operators in molecular quantum chemistry calculations.
  • Discuss the implications of group theory for the electronic structure and properties of molecules.