Quantum Chemistry 1200-1CHMCHKW3

Lecture and proseminar program:

- Mathematical introduction: complex numbers, vector spaces, scalar product, linear transformations (operators) in vector spaces,
- Postulates of quantum mechanics and Heisenberg's uncertainty principle. Indeterminism in quantum mechanics.
- One-dimensional systems: free particle, potential well, potential barrier, harmonic oscillator.
- Quantum particle in three dimensions. angular momentum operators.
- Two-particle system: separation of center of mass motion and relative motion; rigid rotator; hydrogen-like ion.
- Separation of the motion of nuclei and electrons, adiabatic approximation and Born-Oppenheimer approximation.
- Perturbation theory.
- Variational principle and variational method. Ritz variational method.
- Systems of identical particles, quantum statistics for bosons and fermions; multielectron systems and the Pauli exclusion principle.
- Atoms and molecules as multi-electron systems; one-electron approximation: atomic and molecular orbital theory, spinorbitals, Slater determinants.
- Hartree-Fock method and Hartree-Fock-Roothaan method; canonical orbitals and orbital energies.
- Density functional theory (DFT) and Kohn-Sham method.
- Atomic structure theory: electron configurations, Hund's rules, terms; periodic table.
- Molecular orbitals (bonding and antibonding) in the H2+ ion; formation of a covalent chemical bond. - Theory of molecular electron structure in the LCAO MO approximation; Koopmans' theorem; localized molecular orbitals.
- Potential energy hypersurface, molecule geometry and its determination; VSEPR model.
- Molecular vibrations: harmonic approximation and normal vibrations; rotational, vibrational, and electronic energy of molecules.
- Fundamentals of molecular spectroscopy: radiation quanta (photons); excited states; transitions induced by electromagnetic waves (photon absorption and emission); rotational, vibrational, and electronic transitions; intensity of transitions and selection rules; molecular symmetry (classification of symmetry of electronic states and molecular vibrations of polyatomic molecules).
- Vertical electron transitions: Franck-Condon rule; orbital model of electron excitations - CIS method.
- Pi-electron molecules - Hückel method.

Total student workload: 138 hours, including:
- participation in classes 45 hours;
- preparation to classes 75 hours;
- exam 3 hours,
- consultations with the lecturer 15 hours