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# TSS

**Course:** Symmetry Theory in Spectroscopy

**Department/Abbreviation:** KBF/TSS

**Year:** 2021

**Guarantee:** 'prof. RNDr. Jan Nauš, CSc.'

**Annotation:** 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.

**Course review:**

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.