NKEA07017U Group Theory and its Application in Quantum Chemistry
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.
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.
Introduction to Group Theoretical Methods in Quantum Chemistry, Lecture Notes, Sten Rettrup
- Category
- Hours
- Exam
- 20
- Lectures
- 28
- Preparation
- 144
- Theory exercises
- 14
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Written assignment, 2 weeksOral examination, 30 minPass-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.
Course information
- Language
- English
- Course code
- NKEA07017U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 2 blocks
- Placement
- Block 1 And Block 2
- Schedule
- A (Tues 8-12 + Thurs 8-17), B (Mon 8-12 + Tues 13-17 + Fri 8-12) And C (Mon 13-17 + Wednes 8-17)The schedule for the lectures and exercises will be agreed between the attending students and the teacher
- Course capacity
- No admission restriction
- Continuing and further education
- Study board
- Study Board of Physics, Chemistry and Nanoscience
Contracting department
- Department of Chemistry
Course responsibles
- Sten Rettrup (7-7669787876797444676c6971326f7932686f)