CY6121 : Advanced Electronic Structure and Density Functional Theory for Molecules

The Hartree – Fock method, derivation and interpretation of HF equations, Roothaan equations. Basis sets – Gaussian and Slater type orbitals Independent electron pair approximation, coupled cluster approximation, cluster expansion of a wave function. Configuration interactions. Many body approach Moller – Plesset perturbation theory. Diagrammatic representation, one particles perturbation. Static electric and magnetic properties of molecules and multiple expansions.

Density matrices, reduced density operators, Thomas – Fermis model, Hobenberg – Kohn theorem. Chemical potential. Hardness and softness, Kohn – Sham method – basic principles, local density and Xa approximation, spin density functional and local spin density approximation. Exchange correlation energy-functional. Introductory account of popular functionals – B3LYP and MPW1PW91.

Simple applications of density functional theory for electronic structure. Or

Electrons in the periodic lattice. Bloch states and Wannier functions.

Dynamics of interacting quantum spin systems in the presence of external fields – Ising and Heisenberg Hamiltonians. Theory of Ferromagnetism. Quantum phase transitions.

Text Books:

  1. Szabo, A. and Ostlund, N.S., Quantum Chemistry, Dover, New York 1996.
  2. Helagaker, T., Jorgenson, P. nad Oslen. J. Molecular Electronic Structure Theory, John Wiley & Sons, New York, 2000.
  3. Cook, D.B., Handbook of Computational Quantum Chemistry, Dover, New York, 2005.
  4. Parr, R.G. and Yang, W. Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford, 1989.
  5. Mc Weeny, R., Methods of Molecular Quantum Mechanics, Academic Press, San Diego, 2001.
  6. Koch, W.C. and Holthausen, M.C., A Chemist‘s Guide to Density Functional Theory, Wiley-VCH, Germany, 2000
  7. Aurerbach, A. Interacting Electrons and Quantum Magnetism, Springer, 1994.
  8. Mattis, D.C., Theory of Magnetism, World Scientific, Singapore, 2006
  9. Van Vleck, J. H., theory of Electric and Magnetic Susceptibilities, Oxford, U.S.A., 1932