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.