**Course Objectives:**

Recognize the most significant and elementary solutions of Schrodinger equation in molecular quantum mechanics through a study of time independent perturbation theory, valence bond and molecular orbital theories.

Apply the concept of linear combination of atomic orbitals to hybridization and directed bonding in polyatomic molecules.

Solve the real-world problem using advanced numerical programs through Gaussian orbitals.

Show that molecular symmetry operations form a group and can be characterized by fundamental representations of groups known as irreducible representations.

Apply the great orthogonality theorem to derive simple point groups and illustrate its use in the applications in crystal field theory, pericyclic reactions and molecular spectroscopy.

**Learning Outcomes**: At the end of the course, the learners should be able to:

**Apply **time independent perturbation theory to complex problems of molecular energy levels in the presence of external electric and magnetic fields

**Distinguish **different types of hybridization based on geometries of the complex and to calculate for a one-electron and two electron system, all the necessary integrals due to coulombic forces.

**Determine **the symmetry operations of any small and medium-sized molecule and apply point group theory to the study of electrical, optical and magnetic properties and selection rules for absorption.

**Course Contents:**

- Time-independent perturbation theory, degenerate states, variational method, Hellmann-Feynman theorem Spectra and structure of helium atom, term symbols for atoms.
- Born-Oppenheimer approximation, hydrogen molecule ion, hydrogen molecule: valence bond and molecular orbital methods: Detailed calculations for energies and overlaps.
- Polyatomic molecules and hybridisation. Conjugated pi-systems and Huckel theory, frontier orbital theory, configuration interaction.
- Hartree-Fock method, self-consistent field method and derivation of Hartree-Fock, Roothaan Equations.
- Polyatomic basis sets, Gaussian, double-zeta and polarized basis sets, population analysis and dipole moments. The Thomas-Fermi model of the atom.

**Group Theory in Chemistry**

- The concept of groups, symmetry operations and symmetry elements in molecules, matrix representations of symmetry operations, point groups, irreducible representations and character tables.
- Great orthogonality theorem and its proof.
- Application of group theory to atomic orbitals in ligand fields, molecular orbitals, hybridization.
- Classification of normal vibrational modes, selection rules in vibrational and electronic spectroscopy. Woodward-Hoffmann rules.

**Text Books:**

- A. McQuarrie, Quantum Chemistry, University Science Books, 1983.
- W. Atkins, Molecular Quantum Mechanics, 2nd edition, Oxford University Press, 1983.
- N. Levine, Quantum Chemistry, 3rd edition, Allyn and Bacon, 1983.
- Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover, 1996.
- McWeeney, Coulson’s Valence, Oxford University Press, 1979.
- A. Cotton, Chemical Applications of Group Theory, Wiley, 1996.
- M. Bishop, Group theory and Chemistry, Dover, 1989.