This course is a comprehensive treatment of application of Group Theory in chemistry

The topics covered:

• Symmetry elements and symmetry operations

How to write down all the symmetry operations associated with a symmetry element

• Group postulates

Closure property, existence of identity, associativity property and Inverse property

• Types of groups -abelian, nonabelian and cyclic groups

• Multiplication tables

• Similarity transformations, order and class of a group

Separation of operations of a group into classes using similarity transformations

• Point group – Schoenflies notation

Assigning point groups to molecules -systematic procedure

• Sub Groups, cyclic Groups and isomorphic Groups

• Transformation matrices for symmetry operations

• Representations of a group – reducible and irreducible representations

• Great orthogonality theorem and construction of character tables (C2v , C3v , C2h)

• Assignment of symmetry species to translational motion, rotational motion and d-orbitals

• Standard reduction formula

• Molecular vibrations-symmetries of normal modes of vibration of molecules and predicting their IR and Raman activity

• Wave functions as basis for irreducible representations

• Direct product representations

• Symmetry selection rules for electronic transitions in simple molecules

• Symmetry selection rules for IR and Raman spectra – rule of mutual exclusion

• Projection operators

• Simplification of Huckel’s Molecular orbital calculation using group theory-

Molecular wave functions and their energies for ethylene, Molecular wave functions and delocalization energy for butadiene and cyclopropenyl systems

• Hybridization scheme for sigma orbitals

• Practice exercises are given wherever necessary