# Office of Academic AffairsIndian Institute of Science Education and Research Berhampur

Chemistry

CHM 301: Symmetry and Group Theory (4)

Prerequisites: CHM 102

Learning Objectives:

To learn the basic concepts related to symmetry elements, symmetry operations, point groups and their applications towards the understanding of bonding and spectroscopic characterization in molecules.

Course Contents:

Molecular Symmetry: Symmetry elements and symmetry operations, definition of group and its characteristics, subgroups, classes, similarity transformation. Products of symmetry operations, relations between symmetry elements and operations, symmetry elements and optical activity, classes of symmetry operations, Conventions regarding coordinate system and axes, point group and classification, degenerate point groups, examples, Some properties of matrices, representation of groups, reducible and irreducible representations, the great orthogonality theorem, character tables, position vector and base vector as basis for representation, Wave functions as basis for irreducible representations (p- and d-orbitals) direct product, vanishing integral.

Symmetry adopted linear combinations: Projection operators and some examples, e.g. π-orbitals for the cyclopropenyl group etc.

Applications:

Symmetry Aspects of Molecular Orbital Theory: General Principles, symmetry factoring of secular equations, carbocyclic systems, more general cases of LCAO-MO bonding, examples, Huckel Molecular orbital theory systems, e.g., π-systems and conjugated π-systems, benzene and naphthalene, delocalization energies, resonance energies and aromaticity, the bond order (p) and free valence number (F), three centre bonding.

Hybrid orbitals and Molecular orbitals: transformation properties of atomic orbitals, hybridization schemes for bonding and for π -bonding, hybrid orbitals as LCAO, examples, MO theory for ABn, molecular orbital theory for regular octahedral and tetrahedral molecules.

Molecular Vibrations: Normal Mode analyses via IR and Raman spectroscopy. Selection rules, spectral transition probability, vibronic coupling, electronic spectra of inorganic complexes and ions. Splitting of one electron level in an octahedral and tetrahedral environment.

Suggested Books:

• Chemical Applications of Group Theory, F. A. Cotton, 3rd edition, Wiley InterScience, New York, 1990.
• Molecular Symmetry and Group Theory, R. L. Carter, John Wiley & Sons, India, 2004, 2005.
• Molecular Symmetry and Group Theory, A. Vincent, 2nd Edition, John Wiley & Sons Ltd, England, 2001.
• Symmetry and Spectroscopy of Molecules, K. Veera Reddy, New Age International (P) Ltd, India, 2010.
• Group Theory and Chemistry, D. M. Bishop, Dover Publications, New York, 1993.