Licence 2 CPES Modeling and Numerics in Material Sciences

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The oscillator is an essential concept in physics: matter is often modeled by a collection of oscillators (harmonic or not) interacting with each other and with the external environment. The latter acts on the matter through a wave, such as an acoustic or electromagnetic wave. This makes it possible to lay the theoretical foundations of the problems of radiation-matter interaction and thus to build one of the fundamental tools for the study of matter (in the broad sense): spectroscopy.

Spectroscopy is indeed the basic tool for the study of the physical properties of objects that surround us, such as a molecule, a crystal, a star, a galaxy. These properties are deduced either from their spontaneous emission or from their response to an external excitation. For example we measure the properties of absorption, reflection, transmission of an applied electromagnetic radiation (visible, infra-red, X, neutrons, ...). The response to this radiation is then a way to discover which are the various types of oscillators constituting the studied medium.

 In short, the study of the physical media that surround us requires the use of two fundamental theoretical tools: oscillators and waves, which are the subject of this course.  

The principle adopted here is a step-by-step progression from the harmonic oscillator, then from coupled oscillators, to waves treated in the framework of discrete systems: infinite and then finite coupled oscillators with different edge conditions.

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This module completes and formalizes the notions of thermodynamics introduced by the EU Thermodynamics 1, by deepening several aspects: thermodynamic potentials defined from Legendre transformations, thermodynamics of open systems, phase transitions of the pure body and irreversible processes, with incursions at the microscopic level in order to give an overview of the physical foundations of the theory.

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The first part of this course presents the basics of quantum chemistry for chemists and physical chemists. It begins by reviewing the principles of quantum mechanics and its master equation, the Schrödinger equation. The resolution of the Schrödinger equation in simple cases and the notions of wave functions and quantization are presented and illustrated in simple cases. The hydrogen atom is then studied.

The teaching also focuses on approximation methods to determine the properties of complex systems where the Schrödinger equation cannot be solved directly. The effect of spin on the electronic properties of atoms and molecules will also be discussed.

The second part of this teaching focuses on the quantum description of molecular properties and reactivity. The qualitative construction of molecular orbitals using symmetry properties will be introduced and the link between molecular orbital diagram and chemical bonding is made. The link between molecular geometry and electronic structure will be discussed. This teaching will then focus on Huckel's method of obtaining molecular orbital diagrams of π systems. The classical notions of conjugation, delocalization, donor or acceptor character and aromaticity will be studied in this approach. The theory of boundary orbitals is used to rationalize molecular reactivity (cycloadditions, electrocyclisation) and molecular geometries.

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This module constitutes an introduction to the approach of using computer tools in Physics: it is a question of analyzing a phenomenon, of idealizing/modeling it, then of studying it on computer. The critical interpretation of the results is also part of it. The examples are chosen in relation with the other current subjects in the training.

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