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Course, academic year 2023/2024
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Symmetry of Molecules - NBCM027
Title: Symetrie molekul
Guaranteed by: Department of Chemical Physics and Optics (32-KCHFO)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Ing. Pavel Soldán, Dr.
doc. Ing. Lucie Augustovičová, Ph.D.
Mgr. Jiří Klimeš, Ph.D.
Classification: Physics > Biophysics and Chemical Physics
Annotation -
Analysis of molecular symmetry by means of group theory. Groups of symmetry transformations and their representations. Laws of conservation. Symmetry adapted functions. Factorization of Hamiltonian. Quantum states classification in terms of symmetry. Selection rules. Energy levels splitting caused by lower degree of symmetry. Applications to studies of electronic structure and vibrations of molecules. The lecture is meant mainly for the students of physics of molecular and biological systems.
Last update: SOLDAN/MFF.CUNI.CZ (07.01.2010)
Course completion requirements -

Class credit and exam.

Class credit will be given to a student if and only if he/she

a) attends at least 70% of tutorials


b) solves correctly at least 50% of homework


c) obtains at least 2/3 of maximum possible points from two written control exercises.

Student is allowed to take the exam if and only if he/she obtains the class credit.

Last update: Soldán Pavel, doc. Ing., Dr. (30.04.2020)
Literature -

Fišer J.: Úvod do molekulové symetrie. SNTL, Praha 1980.

Fišer J.: Úvod do kvantové chemie. Academia, Praha 1983.

Litzman O. a Sekanina M.: Užití grup ve fyzice. Academia, Praha 1982.

Ferraro J. R. and Ziomek J. S.: Introductory group theory and its applications to molecular structure. Plenum Press, NY 1969.

Carter R. L.: Molecular symmetry and group theory. John Wiley & Sons, 1998.

Last update: SOLDAN/MFF.CUNI.CZ (07.01.2010)
Teaching methods -

Lectures and tutorials covering the following topics:

1. Minimal intro to the group theory

2. Examples of finite groups used in physics

3. Group representations

4. Characters

5. The Euclidean group

6. Point groups

7. Symmetry adapted linear combinations, block diagonalization of Hamiltonians

8. Selection rules

9. Point-group representations

10. Group theory applications in quantum chemistry

Last update: Soldán Pavel, doc. Ing., Dr. (30.04.2020)
Requirements to the exam -

Class credit is necessary in order for a student to take the exam.

The exam is oral.

Exam requirements correspond to the scope of the course subject presented in the current academic year.

Last update: Soldán Pavel, doc. Ing., Dr. (30.04.2020)
Syllabus -

Groups and subgroups, group order, left and right classes, classes of conjugated elements, group homomorphisms and isomorphism. Direct product of groups. Group representations. Reducible and irreducible representations. Characters. Orthogonality relations. Symmetry in Quantum theory. Hamiltonian invariance under coordinate transformations. Molecular symmetry group and symmetry elements. Point groups. Tables of irreducible point-group representations. Vector space of molecular states and its decomposition into subspaces invariant under the action of molecular symmetry group. Use of projection operators for construction of symmetry adapted bases. Hamiltonian matrix factorization. Classification of quantum states with respect to irreducible representations. Symmetry and energy level degenarations. Splitting of energy levels caused by lower degree of symmetry. Selection rules. Molecule vibrations. Infrared spectra. This course is suitable for diploma students and doctoral students.

Last update: Soldán Pavel, doc. Ing., Dr. (29.10.2021)
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