1) Introduction: Operators, atomic units, molecular Hamiltonian, and Born-Oppenheimer approximation. 2) General introduction to the many-electron theory • The Hartree-Fock (HF) method (self-consistent field approach, canonical orbitals, Slater-Condon rules, and Koopman's theorem) • Density Functional Theory (DFT) (the Hohenberg–Kohn theorems, v- and N-representability, and Kohn–Sham Density Functional Theory (noninteracting kinetic energy and the Kohn–Sham equations) • Gaussian basis sets (Gaussian and Slater-type orbitals, spherical and cartesian Gaussians, extrapolation techniques), molecular orbitals, electron density-their interpretation and visualization • A brief introduction to the post-Hartree-Fock methods: Moller-Plesset perturbation theory, Configuration Interaction, and Coupled-Cluster Ansatz • Time-dependent HF and DFT methods • Atomic and molecular properties (dipole moments, electronic spectra, transition dipole moments, and dipole polarizabilities) • Technical aspects of electronic structure calculations: convergence difficulties, point group symmetries, convergence acceleration (damping, level shifting, and the direct inverse iterative subspace (DIIS) technique), scans of potential energy surfaces and analysis of dissociation energy limits • Example calculations: singlet-triplet excitations, local, charge-transfer, and Rydberg excited states 3) Nuclear motion • Potential energy curves of diatomic molecules • Bound state energies: discrete variable representation (DVR) and Numerov methods • Rotational spectroscopy • Vibrational transitions in diatomic molecules • Polyatomic molecules: vibrational SCF • Cold collisions and near-threshold bound states 4) Case studies • Chemical reaction energies, reactivity, and formation of simple amino acids • Spectroscopy of simple molecules: NH and SrF • Hyperfine structure, isotopic effects in spectroscopy, and standard model violation effects
