From complex chemistry to new physics 0800-PA-COMCHEM

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 (non-interacting 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