UNIT I Molecular Symmetry

Symmetry elements and symmetry operations in molecules. Identity, Rotation, Reflection, Inversion and Improper rotation operation. Examples. Point Groups and their determination. Mathematical group-Definition, Examples, order of a group. Abelian and Cyclic groups, Group Multiplication table. Rearrangement theorem Sub groups and classes in a group. Similarly transformation. Conjugate elements. Matrices, Addition and multiplication of matrices, Inverse of matrix. Character of matrix. Diagonal matrix, Direct sum and direct product of square matrices. Block diagonalized matrices. Solving linear equations by the method of matrices. Matrix form of symmetry operations. Basis.

UNIT II Theory of molecular symmetry

Representation of groups. Basis. Construction of representations using vectors and atomic orbitals as basis. The representation generated by using Cartesian co-ordinates positioned on the atoms of a molecule. (SO2 and H2O may be taken a examples). Reducible and irreducible representations.  Construction of irreducible representations by reduction (similarity transformation). Great orthogonality theorem (GOT) and properties of irreducible representations using GOT, Construction of character Table (C2v, C3v, C2h, C4v). Nomenclature of irreducible representations - Mulliken symbols, Symmetry species. Derivation of reduction formular using GOT, Reduction of reducible representations (e.g. Гcart) using the reduction formula, Direct sum and direct product of irreducible representations. Connection between group theory and quantum mechanics.

UNIT II Application of group theory to Molecular vibrations

Molecular vibrations, symmetry species of normal modes of vibration, Construction of Гcart. Normal coordinates and drawings of normal modes (e.g., H2O and NH3), Selection of rules for IR and Raman activities, complementary character of IR and Raman spectra, Determination of IR active and Raman active modes of molecules (e.g., H2O, NH3, CH4, SF6).

UNIT VI Application of Group theory to Chemical Bonding

i) Vanishing and non varnishing integrals. Transition moment integral and selection rules. Overlap integrals and conditions for overlap. ii) Molecular orbital treatment of molecules using Group theory. Treatment of H2O, Classification of atomic orbital involved into symmetry species, Group orbital, Symmetry adapted linear combination (SALC), Projection Operator, Construction of MOs, Electronic Configuration of H2O, Symmetries of the ground and excited states,  Electronic transitions and selection rules, Laporte selection rule for centro symmetric molecules. iii) Group theoretical treatment of hybidization, Construction of hybrid orbital in BF3 and CH4, Inverse transformation.