Quantum Chemistry B

elective courses

This is the first quantum chemistry course within the chemical studies of the 1st level, the advanced version. Here we take full advantage of the mathematical apparatus which students learned during the I year of the studies. It is assumed that the student is not afraid of mathematics, and, when it is needed, is ready to slightly broaden his knowledge of this discipline.

Remote learning

The purpose: learning the quantum theory of atoms and molecules, and basics of molecular spectroscopy.

The course consists of lectures and proseminars, and the computer laboratory (separately graded).

Lectures: two hours per week (30 hours per semester).

Proseminars: two hours each, some weeks (15 hours per semester).

In the academic year 2020/21 the lectures and proseminars will be presented in a remote mode by using the Google Meet platform.

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:

(I) Wave functions. (II) Operators. (III) The time evolution of a quantum system. The Schrődinger equation. (IV) The interpretation of measurements in the microworld.

The Heisenberg uncertainty principle. The indeterminism of quantum mechanics.

3. One-dimensional systems: free particle, square potential well, potential barrier, harmonic oscillator.

4. Quantum particle in three dimensions. Angular-momentum operators.

5. The postulates of quantum mechanics (cont.):

(V) The particle spin. (VI) The quantization of electric charge. (VII) The magnetic moment of a charged particle. (VIII) Antimatter.

The atomic units.

6. The postulates of quantum mechanics (cont.):

(IX) The 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. 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. Perturbation method. Variation principle and variational method. The Ritz variational method.

10. The postulates of quantum mechanics (cont.):

(X) System of identical particles, quantum statistics (for bosons and fermions).

Many-electron systems and the Pauli exclusion principle.

11. Atoms and molecules as the many-electron systems. The one-electron approximation: the atomic-orbital and molecular-orbital theories. Spinorbitals, determinantal wave function.

12. The Hartree-Fock method and the Hartree-Fock-Roothaan method. Koopmans' theorem. Density-functional theory (DFT) and the Kohn-Sham method.

13. Atomic-structure theory: electronic configurations, the Hund rules, atomic terms. The Mendeleev periodic table of elements.

14. Molecular orbitals (bonding and anti-bonding) in the H2+ ion. The covalent chemical bond formation.

15. The molecular electronic-structure theory in the LCAO MO approximation. Molecular orbitals, canonical and localized, their approximate construction in terms of hybridized atomic orbitals.

16. The electronic-energy hypersurface, the molecular geometry and its determination. The VSEPR model.

17. Molecular vibrations. The harmonic approximation and normal modes. The rotational, vibrational, and electronic energy of a molecule.

18. The pi-electron molecules, the Hűckel model and its applications. The reactivity of the pi-electron molecules. The Woodward-Hoffmann rules.

19. The postulates of quantum mechanics (cont.):

(XI) The decay of excited states. (XII) The quanta of electromagnetic field (photons).

20. The foundations of molecular spectroscopy: transitions induced by electromagnetic waves (the photon absorption and emission). The rotational and vibrational transitions. Transition intensities and selection rules.

21. Vertical electronic transitions: the Franck-Condon rule. The orbital model of electronic excitations - the CIS model.

22. The symmetry of moleculec. The symmetry classification of electronic and vibrational states of multiatomic molecules.

1. Lucjan Piela "Ideas of quantum chemistry", Elsevier, Amsterdam 2007.

2. Włodzimierz Kołos, "Chemia kwantowa", PWN, Warszawa, 1978.

3. Włodzimierz Kołos, Joanna Sadlej, "Atom i cząsteczka", WNT, Warszawa, 2007.

Lecture:

1. Understanding the fundamental theory of the microworld: the quantum mechanics.

2. Learning the quantum description of the basic components of the matter that surrounds us: electrons, atomic nuclei, and the (quantized) electromagnetic field.

3. Understanding the structure of atoms and molecules, and learning their desriptions within the quantum chemistry.

4. Learning certain acpects of the chemical reactivity of molecules. Understanding the interactions of molecules with the electromagnetic field.

The (joint) grade for the lecture and proseminar is based on the result of the written exam.

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