Foundations of quantum chemistry 1200-1PCHKW3

The program of the lecture:

1. Mathematical introduction: complex numbers, vector spaces, scalar product, linear transformations (operators) in vector spaces.
2. The postulates of quantum mechanics: wave functions, operators, time evolution of a quantum system, the Schrődinger equation, the interpretation of measurements in the microworld. The Heisenberg uncertainty principle.
3. One-dimensional systems: free particle, square potential well, harmonic oscillator.
4. Quantum particle in three dimensions, angular-momentum operators.
5. The postulates of quantum mechanics (cont.): the particle spin, the quantization of electric charge, the magnetic moment of a charged particle, antiparticles. Atomic units.
6. The postulates of quantum mechanics (cont.): wave functions and operators for a system of many particles.
7. The system of two particles: separation of the center-of-mass motion, and the relative motion. The rigid rotor and the hydrogenlike ion, atomic orbitals.
8. The separation of nuclear and electronic motion in the AB+ ion (A,B = H, D, T): the adiabatic approximation, the Born-Oppenheimer approximation. The approximate additivity of the energies of electronic, vibrational, and rotational motions in the molecule.
9. Variation principle and variation method. Ritz variation method.
6. Molecular orbitals (bonding and anti-bonding) in the H2+ ion, the covalent-bond formation.
7. The postulates of quantum mechanics (cont.): electronic spin, many-electron systems and the Pauli principle. The quantum statistics (for bosons and fermions).
8. Atoms and molecules as many-electron systems, one-electron approximation: atomic-orbital and molecular-orbital theory.
9. Spinorbitals, determinantal wave function. The Hartree- Fock method.
10. Atomic-structure theory: electronic configurations, the Hund rules, atomic terms. The Mendeleev periodic table of elements.
11. The molecular electronic-structure theory in the LCAO MO approximation. Molecular orbitals, canonical and localized, their approximate construction in terms of hybridized atomic orbitals.
12. The electronic-energy hypersurface, the molecular geometry and its determination.
13. Molecular vibrations. Harmonic approximation and normal modes.
14. Rotations of the rigid molecule.
15. The rotational, vibrational, and electronic energy of a molecule.
16. Pi-electron molecules, the Hűckel model and its applications.
17. The reactivity of pi-electron molecules. The Woodward-Hoffmann rules.
18. The foundations of molecular spectroscopy: transitions induced by electromagnetic waves (photon absorption and emission). The orbital model of electronic excitations. Transition intensities and selection rules.