Mathematical chemistry

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.