| Topic |
Sub-topic |
| Subject I. The Group Theory in Chemistry. |
1. Matrix representations.
2. Character tables. Degeneracy.
3. Basis functions.
4. Direct product representations.
5. Vanishing integrals.
6. Symmetry adapted linear combinations and projection operators.
7. Group Theory and Quantum Chemistry. |
| Subject II. Molecular electronic structure I. |
1. The molecular hamiltonian: the Born-Oppenheimer approximation.
2. Potential energy surfaces.
3. The hydrogen molecule ion H2+: the MO method.
4. The hydrogen molecule H2: the VB method
5. Comparison of the MO and VB methods.
6. The validity of the Born-Oppenheimer approximation. |
| Subject III. Molecular electronic structure II. |
1. Electronic configurations and electronic terms in diatomic molecules.
2. The effect of the spin-orbit interaction.
3. Electron density and bond polarity.
4. The MO and VB methods applied to diatomic molecules.
5. Polyatomic molecules: classification of the electronic states.
6. Application of the MO method to simple polyatomic molecules.
7. Electron population analysis.
8. Localized MOs.
9. Molecules with conjugate bonds: the sigma-pi separation. The free electron MO method.
10. The Hückel MO method.
11. Electron delocalization and aromatic stability.
12. Application of the VB method to polyatomic molecules: types of hybridization.
13. Resonance. |
| Subject IV. Electronic structure and Computational Chemistry. |
1. The Hartree-Fock SCF method applied to molecules.
2. Basis functions in molecular calculations.
3. The Roothaan-Hall and Pople-Nesbet equations.
4. Limitations of the Hartree-Fock SCF method.
5. Post-Hartree-Fock methods.
6. Density Functional Theory (DFT).
7. Relativity in molecular calculations.
8. Semi-empirical methods. |
| Subject V. Interaction of the electromagnetic radiation with matter and molecular spectroscopy. |
1. Interaction of the electromagnetic radiation with matter.
2. Diffusion.
3. Absorption: transition moments and selection rules.
4. The Lambert-Beer law.
5. Broadening of the spectral lines.
6. Raman effect.
7. Laser.
8. Fourier transform.
9. General aspects of the experimental techniques |
| Subject VI. Molecular rotation and rotational spectroscopies. |
1. The polyatomic rigid rotor: results of the classical and quantum treatments.
2. Rotational spectra.
2.1. Selection rules, populations and line intensities
2.2. Stark effect.
2.3. Hyperfine structure and nuclear quadrupole moment.
2.4. Molecules with non-zero electronic angular momentum.
2.5. Type-l doubling.
3. Microwave spectroscopy (MW) and its applications.
4. Rotational Raman spectra.
5. Obtaining the molecular geometry from the rotational constants.
6. Nuclear spin and rotational states. |
| Subject VII. Molecular vibration and vibrational spectroscopies. |
1. Vibration in diatomics.
2. Anharmonicity, vibration-rotation interaction and centrifugal distortion.
3. Vibration and vibration-rotation spectra in diatomic molecules.
4. Line intensity and nuclear spin.
5. Vibration in polyatomic molecules.
6. Vibration-rotation spectra in polyatomic molecules.
7. Analysis based on the symmetry: IR and Raman activities.
8. Anharmonicity and potential energy surfaces.
9. Normal modes with more than a minimum. |
| Subject VIII. Electronic spectra. |
1. Electronic spectra.
2. Diatomic molecules.
2.1 Selection rules.
2.2 Franck-Condon principle and fine structure.
2.3 Dissociation and predissociation.
3. Electronic spectra in polyatomic molecules.
4. Fluorescence and phosphorescence.
5. Non-radiative transitions.
6. Photoelectron spectroscopies
7. Optically active molecules. Circular dicroism.
8. Laser techniques. |
| Subject IX. Resonance spectroscopies |
1. Introduction.
2. Foundations of the RMN and RSE spectroscopies : Chemical shift.
3. Interpretation of the shielding constants.
4. Interpretation of the fine structure.
5. RMN and nuclear exchange processes.
6. RMN for the solid state.
7. Foundations of the pulse techniques and spin relaxation.
8. RSE spectroscopy: hyperfine structure.
9. Quadrupole resonance spectroscopy.
10. Mössbauer spectroscopy. |
