Course

Unit I

Introduction to molecular point groups
Definition of a mathematical group, Symmetry in molecules, elements of symmetry, , matrix representation of symmetry operations, molecular point groups, , abelian group, cyclic group, symmetry operations as group elements, similarity transformation and classes, group multiplication table, symmetry classification of molecules into point groups (Schoenflies symbol)

Unit II

Construction and interpretation of character tables
Reducible and irreducible representations, Great Orthogonality Theorem and its consequences, character tables, reduction formula, construction of character tables for point groups with order 6, interpretation of character tables.

Unit III

Applications of Group theory – I (vibrational and electronic spectroscopy)
Infrared and Raman activity of molecular vibrations in H2O, N2F2, BF3, AB4type molecules (Td and D4h) and AB6 type (Oh) of molecules; selection rules; Electronic structure of free atoms and ions, splitting of terms in a chemical environment, construction of energy level diagrams, estimations of orbital energies, selection rules and polarizations, double groups, a brief idea on electronic spectra of transition metal complexes selection rules, Orgel diagrams, Tanabe Sugano diagrams.

Unit IV

Applications of Group theory (Chemical bonding – Hybridization and molecular orbital formation)
Group theory to explain hybridization – wave functions as bases for irreducible representations, construction of hybrid orbitals for AB3 (planar), AB4 (Td), AB5 (D3h) and AB6 (Oh) type of molecules, symmetry adapted linear combinations, projection operators, application of projection operators to pi-bonding in ethylene, cyclopropenyl systems and benzene, application of symmetry to predict polar and chiral compounds;

Unit V

Symmetry in solid state

Symmetry elements and operations in solid state – proper axis of rotation, mirror planes of symmetry, roto-reflection and roto-inversion axes of symmetry, screw axes of symmetry, glide planes; a brief introduction to the crystallographic point groups and space groups

Textbooks

1. F. Albert Cotton, ‘Chemical Applications of Group Theory’, 3^rd Edition, John Wiley, 1990.
2. A Salahuddin Kunju, G Krishnan; ‘Group theory and its application in chemistry’, second edition, PHI Learning private limited – 2015.

References

1. Robert L Carter,‘Molecular symmetry and Group theory’, John Wiley & Sons, Inc.
2. V. Ramakrishnan and M. S. Gopinathan, ‘Group Theory in Chemistry’, 2^{n d}reprint edition, Vishal Publications, 1996.
3. P. H. Walton,“Beginning Group Theory for Chemistry”, Oxford University Press Inc., NewYork, 1998.