The Indian Institute of Technology, Madras, is among the foremost of institutes of national importance in higher technological education and in basic and applied research.

The department of chemistry in IITM or Indian Institute of Technology Madras constitutes one such center for of academic excellence.

Since its start in 1959, the department is engaged in imparting the highest level and quality of academic education and has focused upon addressing key scientific problems, which have gathered universal admiration and acknowledgment.

CY 5017 - Principles Of Quantum Mechanics

Review of vectors and vector spaces, matrices and determinants, eigenvalues and eigenvectors, similarity transformations, ordinary differential equations- first and second order.

Solution of differential equations by power series method: solutions of Hermite equation in detail. Orthogonality properties and recurrence relations. Introduction to the solutions of Legendre and Laguerre differential equations, Spherical Harmonics. Introduction to Fourier series and Fourier transforms, convolution theorem.

Solution of the Schrodinger equation for exactly solvable problems such as particle-in-a- box, particle-in-a-ring, harmonic oscillator and rigid rotor. Tunneling, one dimensional potential barriers and wells.

Postulates of quantum mechanics, wave functions and probabilities, operators, matrix representations, commutation relationships. Hermitian operators, Commutators and results of measurements in Quantum Mechanics. Eigenfunctions and eigenvalues of operators and superposition principle. States as probability distributions and expectation values. The expansion of arbitrary states in terms of complete set.

Angular momentum, commutation relationships, basis functions and representation of angular momentum operators, Coupling (addition) of angular momenta, Clebsch-Gordan coefficients and Wigner-Eckart theorem.

Solution of the Schrodinger equation for the hydrogen atom, radial and angular probability distributions, atomic orbitals and electron spin, Pauli’s exclusion principle and Aufbau principle.

The time dependent Schrödinger equation. Co-ordinate and momentum space representation of operators and eigenstates; Properties of eigenstates – single-valuedness, double differentiability, continuity, boundedness / square integrability. Discrete and continuous distributions; Unitary evolution and reversibility. Schrodinger and Heisenberg representations. Projections and irreversibility.

Time-independent perturbation theory, degenerate states, variational method, Hellmann-Feynman theorem Spectra and structure of helium atom, term symbols for atoms.

Text Books:
1. E. Kreyszig, Advanced Engineering Mathematics, 5th edition, Wiley Eastern, 1989.
2. G. Arfken and Hans J. Weber, Mathematical methods for physicists, Prism Indian Edition, 1995.
3. D. A. McQuarrie, Quantum Chemistry, University Science Books, 1983.
4. P. W. Atkins, Molecular Quantum Mechanics, 2nd edition, Oxford University Press, 1983.
5. I. N. Levine, Quantum Chemistry, 3rd edition, Allyn and Bacon, 1983.
6. D. J. Griffiths, Introduction to Quantum Mechanics, Pearson Education, 2005.
7. H. Kuhn, H.-D. Försterling, and D.H. Waldeck, Principles of Physical Chemistry, 2nd Edn., Wiley, (2009).
8. J. P. Lowe, Quantum Chemistry, K. A. Peterson, Third edition, Academic Press, 2006.

CY 5018 - Quantum Chemistry and Group Theory

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.

The metallic bond. Bloch theory, free electron and tight binding model. Effective crystal field Hamiltonian: Steven's equivalent operator method.

Electric and magnetic properties of molecules. Introduction to multipole expansion, dipole moments, static polarizability and hyperpolarizability, magnetic susceptibility, vector functions and vector potential: shielding constants, spin-spin coupling and hyperfine interactions.

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:
1. D. A. McQuarrie, Quantum Chemistry, University Science Books, 1983.
2. P. W. Atkins, Molecular Quantum Mechanics, 2nd edition, Oxford University Press, 1983.
3. I. N. Levine, Quantum Chemistry, 3rd edition, Allyn and Bacon, 1983.
4. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover, 1996.
5. R. McWeeney, Coulson's Valence, Oxford University Press, 1979.
6. F. A. Cotton, Chemical Applications of Group Theory, Wiley, 1996.
7. David M. Bishop, Group theory and Chemistry, Dover, 1989.