QUANTUM MECHANICS (ATOM)
Introduction (atom models)
The wave function (meaning, expectation value, factorization, perturbation theory)
Schrodinger equation, Hamilton operator, atomic units
Particle in the box
Harmonic oscillator
Quantization of the angular momentum
The hydrogen atom (incl. spectroscopy of the H atom, series, fine structure, hyperfine structure, Dirac vs. Schrodinger equation)
Atomic orbitals
2-electron Systems (He atom)
Slater determinant (independent electrons)
Spin-orbit interaction
Correlation
Many-electron systems (relativistic effects)
Atoms in external fields (Zeeman, Stark effects)
CHEMICAL BOND (MOLECULE)
The H2+ molecule
The H2 molecule
MO theory (LCAO ansatz)
Systems with many atoms (diatomic, triatomic, many-atomic molecules, Walsh diagrams)
pi-electron systems (Huckel MO theory)
Electron deficiency and electron excess compounds, d electron systems
Intermolecular interactions (van der Waals etc.)
Molecules in external fields
The solid state (bands, band structures, periodicity, density of states, reciprocal space, Brillouin zone, k points)
METHODS OF ELECTRONIC-STRUCTURE CALCULATIONS
The quantum mechanical many-body problem, Schrodinger equation, Born-Oppenheimer approximation
Hartree-/Hartree-Fock-/Hartree-Fock-Roothaan methods
Semi empirical methods (INDO, NDDO etc.)
Including correlation (CI, MCSCF, Coupled-Cluster, Moller-Plesset)
Density-functional theory (Thomas-Fermi, Xa, Hohenberg-Kohn theorems, Kohn-Sham method, functionals, DFTB)
Technical details
Structure and energetics
COMPUTER SIMULATIONS
Introduction
Techniques (periodic boundary conditions, Ewald summation, super cells, convergence)
Geometry optimization (local und global Geometry optimization, steepest descent, conjugate gradient)
Molecular dynamics (Newtons equations of motion, Born-Oppenheimer MD, Car-Parinello MD, statistical ensembles, multi-scale modeling: QMMM and accelerated MD)
Monte-Carlo simulations
Special modeling approaches (modeling of reactions, transition-path sampling)
Appendices
