Faculty of Science

Objectives

To introduce some ideas and mathematical techniques which are essential for understanding the structures and properties of molecules and the crystal structure and emphazise the notions of molecular symmetry and symmetry groups.

Contents

Definitions and theorems of Group Theory: properties of a Group; examples of Groups; subgroups; classes; Molecular symmetry and the symmetry groups: symmetry elements and operations; symmetry planes and reflections; inversion centre; proper axes and rotations; products of symmetry operations; equivalent symmetry elements and equivalent atoms; general relations among symmetry elements and operations; symmetry elements and optical isomerism; symmetry point groups; systematic procedure for symmetry classification of molecules; classes of symmetry operations; representation of groups; properties of matrices and vectors; the “Great Orthogonality Theorem” and its consequences; Character Tables; representations for cyclic groups; Group theory and quantum mechanics; wave functions as bases for irreducible representations; the Direct Product; identifying non-zero matrix elements; Applications in chemical systems.

Prerequisite: