Learning objectives
Application of some key-concepts in quantum mechanics.
Familiarization with some spectroscopic techniques (UV-vis-NIR-IR absorption, FT-IR, Raman).
Interpretation of spectroscopic data and their use for getting molecular parameters.
Prerequisites
Knowledge of the basic concepts of Quantum Mechanics, of Physics and Mathematics.
Course unit content
Quantum Eraser.
Particle-in-box model: Application to organic dyes.
Introduction to Fourier transform. Michelson interferometer. FT-IR spectrophotometer. Roto-vibrational spectra of diatomic molecules.
Group theory: definition of a group, symmetry groups, symmetry elements, reducible and irreducible representations. Reduction of the representations. Connection to quantum mechanics.
Definition of the vibrational normal modes and their symmetry (with examples). Use of group theory for the evaluation of integrals of interest in quantum mechanics. Selection rules for IR spectroscopy. Raman spectroscopy and its selection rules. Prediction of IR and Raman activity for molecules of different symmetry.
Adiabatic approximation.
Huckel method: approximations, resolution of the problem and calculation of atomic charges, bond orders, dipole moments. The 4n+2 rule; use of symmetry.
Full programme
Lab experiments
- Quantum eraser: wave-particle dualism in photons; the collapse of the wavefunction and its reversibility.
- Electronic spectra of organic dyes.
Recording of the vis-NIR absorption spectrum of organic dyes with increasing chain length. Interpretation of the results based on the particle-in-a-box model. Vibronic structure of the spectra.
- Roto-vibrational spectrum of HCl.
Recording of the IR absorption spectrum of an HCl gas sample with an FT-IF spectrophotometer.
Interpretation of roto-vibrational spectrum. Effects of the centrifugal distortion, anharmonicity, roto-vibrational coupling. Morse potential. Overtones.
Roto-vibrational structure of the fundamental transition: R and P branches. Isotopic effect. Effect of the spectral resolution and use of apodization techniques.
Exploitation of the experimental data to extract some molecular parameters.
- Infrared and Raman spectra of inorganic salts having anions of different symmetry.
Recording of the IR and Raman spectra of solid samples. Interpretation of the spectra via group theory.
- Calculation of the electronic structure of an unsaturated hydrocarbon via the Hückel method.
The exercise consists in the resolution of the pi electronic structure of an unsaturated hydrocarbon with the Hückel method. Determination of energies, bond orders, atomic charges, dipole moments. Determination of the symmetry of molecular orbitals and of ground and excited states though the application of group theory. Prediction of allowed and forbidden electronic transitions.
Bibliography
- P. W. Atkins, Molecular Quantum Mechanics, Oxford University Press.
- F. A. Cotton, Chemical Applications of Group Theory, Wiley 1990.
Teaching methods
Classes, exercises and lab experiments.
Assessment methods and criteria
Learning is evaluated based on the reports and on the final integrated exam of "Physical Chemistry II and Laboratory".
The integrated exam consists of a short written test (according to the calendar published on the Esse3 portal), followed by an oral interview. Only those who pass the written test can access the next stage of the exam. Passing the written test allows access to the corresponding oral exam and not to the ones of the following rounds.
Other information
Attending lessons and participating to the lab experiences is mandatory and will be monitored by collecting the signatures. Each student will have only one possibility to recover an eventually lost experiment (if the absence is notified and justified in due time).
At the end of the course, any student missing one or more lab experiment will not be admitted to the final exam and will have to attend once again the Laboratory Course during the following year.
Each student has to keep a laboratory notebook, to be filled during each lab experiment, reporting the procedures and the data. Moreover, for each experiment, each student (by him/herself or in group) has to prepare a report, where to resume the experiment, the concepts at the basis of it, the results and conclusions. The ensemble of the reports must be delivered at least two weeks before the exam and in any case not later than September 27, 2024. In case the reports are not delivered in due time, the student will not be admitted to the final exam and will have to attend the laboratory course once again during the following year.
The final examination (where you are admitted only if you followed each lab experiment and delivered the reports in due time) is carried out together with Physical Chemistry II.
