Course 2024-2025

Mathematical chemistry [SCHIB309]

  • 5 credits
  • 30h+22.5h
  • 2nd quarter
Language of instruction: French / Français

Learning outcomes

Master the essential concepts of quantum mechanics used in chemistry Solving Schrödinger's equation for simple chemical systems (hydrogen atoms, chemical bonding, conjugate systems in Hückel's method) and interpretation of results. Understand the quantum origin of a number of concepts (chemical bonding, aromaticity, ...) and make the link with quantities that can be experimentally measured (bond lengths, absorption wavelengths, ionisation energies, ...)

Objectives

To provide an introduction to quantum chemistry suitable for mathematics training.

Content

After recalling the fundamental principles of quantum mechanics, the electronic structure of the hydrogen atom, light atoms, the hydrogen molecule and diatomic molecules is described. The two essential notions of quantum chemistry are introduced: the theory of orbitals and the LCAO approximation. Before tackling the last chapter, which really deals with molecules, the notions of electronic structure of atoms, of the periodic classification of elements (Mendeleïev's Table), of the Lewis model of chemical bonding and of Gillespie's rules to explain the 3D geometry of molecules are explained in connection with the notions of quantum chemistry seen so far. Finally, the development of Hückel's method allows the study of conjugated organic molecules in relation with their experimental properties. In the course of the course, the concepts of binding energy and resonance are recalled and interpreted. Observable quantities such as bond lengths, ionization potentials, electroaffinities are also discussed. Table of contents 1. Origins of quantum mechanics 2. Principles of quantum mechanics - Dynamics of atomic and molecular (microscopic) systems: A) The postulates of quantum mechanics. B) Particle in a box 3. The hydrogen atom and hydrogenoids: A) Radial and angular equations. B) Interpretation of hydrogenoid wave functions. 4. The He atom and multi-electron atoms: from the independent model to an approximate method. 5. Molecular orbital theory - chemical bonding. A) H2+ and the LCAO approximation. B) Diatomic molecules. 6. Basic concepts in chemistry. 7. Periodic classification of elements. 8. Molecule and chemical bonding. 9. Geometry of molecules. 10. Unsaturated molecules - Hückel's method: A) Principles of Hückel's method. B) Simple molecules.


Teaching methods

The main concepts are presented on the blackboard and illustrated by practical applications in relation to experimental data. Given the specificity of the course for mathematicians, attention is also drawn to areas where the use of advanced mathematics is expected to bring significant breakthroughs.

Evaluations

The examination consists of the written preparation of 4-5 questions (1H30-2H00) followed by an oral presentation and discussion (15 minutes). The examination is conducted in person.

Recommended readings

Atkins' Physical Chemistry, P. Atkins and J. de Paula, Oxford University Press, Oxford, 2006, 8th edition. D.A. McQuarrie and J.D. Simon, Physical Chemistry - A Molecular Approach (University Science Books, Sausalito, California), 1997 C. Cohen-Tannoudji, B. Diu and F. Lalöe, Quantum Mechanics, Volume I, Hermann, Paris, 1977. E. Heilbronner and H. Bock, The HMO-Model and its Applications 1. Basis and Manipulation, English translation, WileyInterscience, New York, 1976. E. Heilbronner and H. Bock, The HMO-Model and its Applications 3. Tables of Hückel Molecular Orbitals, English translation, Wiley-Interscience, New York, 1976. A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Introduction to advanced Electronic Structure Theory,McGrawHill, 1989.

Language of instruction

French / Français

Location for course

NAMUR

Organizer

Faculté des sciences
Rue de Bruxelles, 61
5000 NAMUR

Degree of Reference

Undergraduate Degree