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Dear Students,

The aim of the course is to familiarize students with the basic ideas of group theory and representation theory (representation theory of groups) and their application in chemistry (description of molecular symmetry). The effective technics for dealing with hybrid orbitals, molecular orbitals, ligand field theory, vibrational modes and electronic transitions will be demonstrated.

Lecture: Written exam.

The courses on mathematics, physics and fundamental chemistry should be already credited.

Definitions of group theory: symmetry element, symmetry operation. Molecular symmetry. Multiplication of symmetry operations. Multiplication table. Similarity transform. Conjugacy classes of symmetry operations. Point group. Cyclic groups and subgroups. Schoenflies notation and Hermann-Mauguin notation. Platonic solids. Classification of molecules into point groups. Definitions of representation theory. Group representation. Characters of representation. Totally symmetric representation. Matrix representation. Reducible representation and irreducible representation. Character table. Mulliken symbol. Great orthogonality theorem. Group theory and quantum chemistry. Atomic orbitals as basis for irreducible representation in the point group. Direct product. Symmetry of electronic state. Symmetry-adapted linear combination of atomic orbitals. The projection operator. Application of molecular symmetry to problems of molecular orbitals. Lone electron pairs in water and molecular symmetry described by the group theory. Qualitative delocalized MO energy levels. Application of molecular symmetry to problems of vibrational and electron spectroscopy. Polarization of electron transitions. Symmetry of vibrational states.

Knowledge

understands the basics of higher mathematics

Skills

can extract and analyze information from scientific journals and books;

can prepare written reports and visual presentations;

Other competences

understands whole life learning

F. Albert Cotton, "Teoria grup. Zastosowania w chemii", PWN, Warszawa, 1973.

M. T. Pawlikowski, "Wstęp do teoretycznej spektroskopii molekularnej. Teoria grup", Jagiellonian University Press, Warszawa, 1991.

A. Jezierski, A. Ogorzałek, "Symetrie w naukach przyrodniczych. Tom II", Wroclaw University Press, Wrocław, 1993.

H. Weyl, "Symetria", PWN, Warszawa, 1960.

R. L. Carter, "Molecular symmetry and group theory", John Wiley & Sons, Inc., USA, 1997.

S. F. A. Kettle, "Symmetry and structure. Readable group theory for chemists", John Wiley & Sons, Inc., USA, 2007.