Corso di laurea in Chimica e Tecnologie Chimiche

Provide formal and conceptual tools for understanding the chemical complexity by introducing a quantum-mechanical approach to chemistry.

Students must acquire the competences listed below, detailed following the Dublin descriptors:

The course provides an introduction to the atomic and molecular quantum theories. It covers the fundamentals of quantum mechanics with its postulates and theorems. We illustrate the reference models (the free particle, the molecule that rotates or vibrates, the hydrogen atom) and techniques (variational method and perturbation theory, group theory). The electronic structure of the molecules (with references to the atomic states and the condensed state) and the information that can be drawn from the rotational and vibrational spectroscopy are the primary focus of the course. The full program is as follows:

• Notes on mathematics and linear algebra.
• Group Theory. Symmetry elements and operations, order of a group. Classes. Multiplication table. Bases and representations. Character tables and their vector interpretation. Reducible Representations (RR) and their decomposition. Symmetry of the translation, rotation and vibration motions of molecules. IR and Raman vibrational activity.
• Introduction to quantum mechanics (QM). The inadequacy of classical mechanics at the atomic scale: black body; photoelectric effect; electron diffraction and wave/particle dualism; atomic emission spectra. The spectrum of the hydrogen atom. Heisenberg's uncertainty principle.
• The quantum wave equation and the Schröedinger equation (EdS). EdS as an eigenvalue problem. Postulates of quantum mechanics and their meaning. Wavefunction and probability. Wavefunction requirements.
• QM applied to simple systems: (a) particle in the box (one- and three-dimensional); (b) the harmonic oscillator (and the vibrations of the molecules); (c) the rigid rotator.
• Approximate methods and perturbation theory. Examples for anharmonic oscillator and H and He atoms. The variational method (linear and non-linear): connections with linear algebra and the use of the calculator. The LCAO method and the H2 molecule.
• Atomic structure. The hydrogen atom (short discussion): EdS; separation of variables; explicit solution of the part in φ. Eigenvalues ​​and eigenvectors, degeneracy and graphical representation. Nodes and nodal surfaces. Atomic orbitals (AO). Angular momentum and connection with the rigid rotator. Meaning of the quantum numbers l and m. The Spin. Level scheme and spectroscopy of the H atom. Representation of wave functions. Polyelectronic atoms: aufbau and construction of the periodic system. Configurations, states and termination symbols. The antisymmetry principle and the Slater determinant.
• The H2+ molecule. Setting the EdS and Born-Oppenheimer approximation. The LCAO method and the molecular orbitals of H2+.
• Simple diatomic homo- (H2, Li2, B2, C2, N2, O2, F2) and hetero-nuclear ( molecules. Hybridization: methane, ethylene and acetylene. Hückel's method. Conjugated systems and electronic delocalization. Aromatic molecules: benzene.
• The matter-radiation interaction. Notes on the theory of time-dependent perturbations. Absorption and emission probabilities and Einstein coefficients. Notes on LASERS. The experimental study of matter-radiation interaction. The electromagnetic spectrum and the main spectroscopic techniques.
• Rotational spectra of diatomic molecules. Number, arrangement and intensity of the bands. Effect of T (Boltzman distribution).
• Vibrational spectra: insights based on the models developed in the first part. Introduction to Raman spectroscopy.
• Electronic spectra. Franck-Condon principle and vibronic structure. Chromophores. Fluorescence and phosphorescence 

Face-to-face lectures in presence with the addition of support slides.

The exam test aims at verifying the basic knowledge acquired by the student on the principles and methods of quantum mechanics and the capabilities (including critical reasoning) in applying it to the description of the structure (electronic configuration, bonds, geometry, etc.) and of the chemical-physical properties (stability, electrical properties, chemical properties, spectroscopy, etc.) of atoms and molecules.

The exam consists of a written test and an oral exam. The written test is computerized and multiple-choice, with a duration of 60 minutes. Each question and/or exercise is assigned a partial score that reflects its specific difficulty, both in terms of the knowledge required and the time needed to answer. A penalty will be applied for incorrect answers. The test score is the sum of the partial scores, up to a maximum of 30/30, and will account for 30% of the final grade. Students who achieve a score of ≥18 will be admitted to the oral exam, which will take place either on the same day as the written test or in the following days, depending on the number of students who passed the written part.

The oral test is aimed at verifying students’ understanding of the material covered in lectures and will account for 70% of the final grade. It will assess the ability to organize knowledge both discursively and through the use of formulas, diagrams, and schematics, as well as the ability to solve simple exercises. The evaluation will consider critical reasoning on the topics studied and the use of appropriate technical vocabulary.

Each student may attend a maximum of 3 exam sessions per academic year.

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Textbooks:

- Peter Atkins, Julio de Paula, James Keeler, "Physical Chemistry", 11th edition, 2017, Oxford University Press, ISBN: 9788808620521

- Slides presented in class.

Further reading:

- G. K. Vemulapalli, "Physical Chemistry", 1993, ‎Prentice Hall, ISBN: 9780136731207.

- D. A. McQuarrie, J. D. Simon, "Physical Chemistry: A molecular approach", 1997, University Science Books, ISBN: 978-0198769866

Attendance: not required, but strongly recommended.

Students with specific learning disabilities (SLD) or disabilities are requested to review the support (https://www.unito.it/servizi/lo-studio/studenti-e-studentesse-con-disabilita) and reception (https://www.unito.it/accoglienza-studenti-con-disabilita-e-dsa) procedures of the University, and in particular the procedures necessary for support during exams (https://www.unito.it/servizi/lo-studio/studenti-e-studentesse-con-disturbi-specifici-di-apprendimento-dsa/supporto)."