Lecturer(s)


Nauš Jan, prof. RNDr. CSc.

Course content

Use of theory of symmetries in spectroscopies 1) Groups and their structures, conjugated elements and their classes, the first and the second theorem on isomorphism. 2) Linear representation of groups, reducible and irreducible representations, direct addition of representations, functions generated by representations, construction of representations, base of representation formed by vectors and wave functions, notations and properties of irreducible representations. 3) Character of representation, relation of orthogonality, tables of characters, analysis of reducible representations by characters, direct addition and direct product of representations. 4) General selection rules according to symmetry, allowed and banned transitions, degeneration of states, notation of states of molecules and orbitals, polarization of transitions. 5) Atomic and molecular orbitals from the viewpoint of symmetry, hybrid orbitals, symmetry of electron states of molecules. 6) Symmetry of normal vibrations, symmetrical selection rules in infrared and Raman spectroscopy. 7) Complexes of transition metals, theory of crystal field. 8) Orbital symmetry in reaction kinetics. 9) Relation between theory of special functions and theory of representations.

Learning activities and teaching methods

Lecture
 Homework for Teaching
 40 hours per semester
 Preparation for the Exam
 40 hours per semester
 Attendace
 42 hours per semester

Learning outcomes

The goal of the course is to present a deeper theory of the symmetry effects in spectroscopies. The mathematical group theory is applied to orbitals and the selection rules. The course contains theory of symmetry, group theory and theory of representations, character of representations. Symmetry of molecules, complexes and biological objects is described. The orbitals are introduced based on symmetry. General selection rules are treated by symmetry. The states of atoms and molecules are designated using the symbols of irreducible representations. Polarization of energetic transitions, symmetry of normal vibrations. Crystal filed theory. Complexes of transition metals.
Comprehension Explain the essence of data and be able to interpret them, recognize and classify the given problem, predict the behaviour of the given phenomena.

Prerequisites

Basic course of mathematics and some parts of experimental methods of biophysics

Assessment methods and criteria

Student performance
Acquiring the theoretical derivation of the rules in application of theory of symetry in spectroscopies.

Recommended literature


1. J. Štěpánek : Matematika pro přírodovědece. II. Grupy a tenzory. UK Praha 1992. 2. V. Peřinová : Úvod do teorie speciálních funkcí (část A a B) , UP Olomouc 1995. 3. J. Fišer : Úvod do molekulové symetrie. SNTL, Praha 1980. 4. O. Litzman, M. Sekanina : Užití teorie grup ve fyzice. Academia, Praha 1982. 5. V. Malíšek : Úvod do optické spektroskopie, UP Olomouc 1981..
