- Mathematical review: N-dimensional complex vector space, Matrix representation of operators, Diagonalization and eigenvalue equations, Change of basis, Functions of matrices, Connection between functions and Dirac notation.
- Electron spin: Spin-statistics theorem, He atom, Pauli exclusion principle, Spin angular momentum operators, Slater determinant, Excited determinant, He ground and excited state.
- Many-electron atoms: Addition of angular momentum, Spin-orbit coupling, Atomic term symbol, Energy-level diagram, Atomic Hamiltonian, Selection rule in many-electron atoms.
- Diatomic molecules: Born-Oppenheimer approximation, Approximate treatment of H2+ ground electronic state, MO and VB wave functions of homonuclear diatomics.
- Electronic structure theory: Hartree product, Spin and spatial orbitals, Rules for matrix elements, Hartree-Fock method, Self consistency, Roothaan and Pople-Nesbet equation, Koopmans theorem, Brillouins theorem, Second quantization, Virial theorem, Hellmann-Feynman theorem, Electrostatic theorem.
- Electron-correlation methods: Configuration Interaction, Full CI matrix, Truncated CI and size-consistency, Mller-Plesset Perturbation theory, Perturbation expansion of correlation energy, Coupled cluster theory, Cluster expansion of wave function, Density functional theory, Density matrices and operators, Exchange-correlation hole and functionals, Thomas-Fermi-Dirac-Weizscker theory, Hohenberg-Kohn-Sham theory, Local-density approximation, Generalized gradient approximation.
- Semiempirical methods: Hckel and Extended Hckel theory.
- Introduction to classical computer simulation method: Monte-carlo simulation, Molecular dynamics simulation, Hands on session related to quantum and classical problems.
|