Details of Program of 3rd Summer School of Theoretical and Computational Chemistry

1. Basic approximations used for solving more-electrons stationary Schrodinger equation
   • approximations concerning Hamiltonian, approximations concerning wavefunction
   • Born-Oppenheimer approximation, perturbation theory, variational principle, MO LCAO approximation, independent electrons model
2. Hierarchy of quantum chemistry methods
   • ab initio methods, semi-empirical methods, empirical methods

1. Hartree-Fock method
• HF equations for two--electron system, coulombic and exchange integral, SCF equations
• Closed- and open-shell systems, Hartree-Fock-Roothan equation
• Basis for MO-LCAO expansion
• Hartree-Fock limit, correlation energy definition, Koopman's and Brillouin theorem
2. Post Hartree-Fock methods
• Configuration interaction method, Moller-Plesset perturbation theory method, coupled-cluster method

1. Introduction to the system
2. Filesystem and basic commands (tree hierarchy, file and directory related commands), Midnight Commander
3. Text files commands (more, grep, tail, cat)
4. Text editing with mcedit

1. Molecular symmetry and spectroscopy
• Introduction to group theory, molecular Hamiltonian and its symmetry
2. Rovibronic states calculations
• Harmonic approximation and rigid rotor model, normal coordinates
• Anharmonicity and rovibronic interaction, perturbation theory, effective Hamiltonians, spctroscopy constants, variational calculations of rovibronic states, spectra calculations of large molecules and clusters
• Nonrigid molecules, failure of the harmonic approximation
3. Current trends in theoretical molecular spectroscopy

1. Classical molecular dynamics
2. Quantum molecular dynamics

1. Resonance phenomenon: open and closed resonator
2. Resonances due to wave character of particles (electrons or atoms)
   • in spectroscopy
   • in collision processes
3. Fingerprints of resonance phenomenon in measurables
4. Interactions which lead to resonance phenomenon
   • Feshbach type of resonance
   • Shape type of resonance
5. Methods to calculate resonance positions and widths

1. What is statistical thermodynamics?
• Axioms, statistical ensembles, partition function and thermodynamic quantities
2. Simple models
• Ideal gas, ideal crystal
3. Intermolecular interactions
• Pair-additive potentials: models and quantum chemistry results, three-particle potentials
4. Real gas
• Virial expansion, pros and cons
5. Dense liquid and gas
• Inner structure of liquid - pair distribution function, computer pseudo-experiments, theory of integral equations, perturbation theory, pair-distribution function and thermodynamic quantities
6. Some philosophical aspects of statistical thermodynamics
• Probability and entropy, third law of thermodynamics: axiom or proof?, negative absolute temperatures, arrow of time

• How to create (build) a molecule in computer?, structure visualization, 3D visualization (3D glases, virtual reality), rendering and raytracing, computer animations

1. General aspcts of programming languages for scientific applications
2. Hardware for computational chemistry
3. The most often used quantum chemistry codes
4. Gaussian program, its computational capabilities, comparison to other codes

1. Theorems leading to the formulation of DFT methods
2. Exchange and correlation density functionals
• LDA (LSD) approximation
• GGA and hybrid functionals
3. Pros and cons of DFT

1. Theoretical foundations: Born-Oppenheimer approximation
2. Critical points on the energy hypersurface, optimization methods, coordinate systems
3. Energy derivatives
4. Equilibrium and rate processes
5. Critical points on the energy hypersurface occuring during the electronic state change
6. Photophysical and photochemistry processes
7. Problem of multiple local minima
8. Superposition error
9. Molecular dynamics and energy hypersurface

1. Covalent and non-covalent interactions
2. Non-covalent interactions in natural sciences
3. Origin of non-covalent interactions
4. Perturbation and variational calculations of non-covalent interactions, their advantages and disadvantages
5. Energy, entropy and free (Gibbs) energy and molecular complexes, energy surfaces
6. Experimental detection of molecular clusters