Quantum Chemistry and Group theory

Schrodinger equation, postulates of quantum mechanics, operators, Hamiltonian and Hermitian operator, discussion of solutions of the Schrodinger equation of some model systems:  particle in a box and its extension to 3D box, quantization of energy levels, degeneracy, zero point energy and justification for Heisenberg uncertainity principle, simple harmonic oscillator and its solution using series solution or factorization method, calculation of various average values using ladder operator and recursion relation of hermite polynomial, rigid rotor, hydrogen atom, radial distribution function of 1s, 2s, 2p, 3s, 3p and 3d orbitals and polar plots, node, nodal plane and nodal sphere.

The variation theorem, linear variation principle, perturbation theory (first order and non – degenerate), application of variation method and perturbation theory to helium atom. Ordinary and generalized angular momentum, eigen functions and eigen values for angular momentum operator using ladder operators, spin, antisymmetry and Pauli’s exclusion principle.

Extension of MO theory to homonuclear and heteronuclear diatomic molecules, Qualitative MO theory and its applications to AH₂ type molecule, Huckel theory of conjugate systems, bond order and charge density calculations. Applications to ethylene, butadiene, cyclobutadiene, benzene, allyl system and cyclopropenyl system. Introduction to extended Huckel theory.

Symmetry elements and symmetry operations, definition of group and subgroup, conjugacy relation and classes, product of symmetry operations, relation between symmetry elements and symmetry operations, orders of a finite group and its subgroup, point group symmetry, schonfiles symbols, representations of groups by reducible and irreducible presentations and relation between them (representation for the C_n, C_nv, D_nh etc. groups to be worked out explicitly), character of a representation, the great orthogonality theorem (without proof) and its importance, character tables of C_2v and C_3v and their use.

Formation of hybrid orbitals: sigma bonding in linear structure (BeCl₂), trigonal planar (BF₃), tetrahedral (CH₄), square pyramid (BrF₅) and square planar (XeF₄), octahedral and square planar complexes, π bonding in complex compounds: square planar molecule and tetrahedral molecule.

Molecules with delocalized π orbitals, cyclopropenyl system, cyclobutenyl system, cyclopentadienyl system and benzene.