Table of Contens

Prerequisites: P103

Evaluation: Examination

Total number of hours: 22.5 h (3ECTS)

16. 
    P205: Numerical simulations of materials
    

Main professor: Dr. Florent Calvayrac (University of Maine, LeMans)

Dr. Florent Calvayrac

Objectives: The aim of this course is to present in general numerical methods in physics and chemistry, from ab-initio to phenomenological modelling, and some applications to the computation of properties of materials. Practical examples are given, and the limits of various methods are discussed. Theoretical developments are kept simplified and a historical approach is used.

Introduction: non-integrable physical equations and the necessity of numerical approximations as intermediate in between theory and experiment. Problems of numerical modelling: choice of equations, accuracy and stability problems, computational cost; example of finite differences to solve partial differential equations.

1. 
   Structure of common materials as a function of the nature of chemical bonding: ionic, covalent and metallic systems. Phenomenological approaches to the structure of materials: molecular dynamics, molecular mechanics, solvent effects, periodic boundaries conditions, thermostats and barostats. Examples with GROMACS software
   
2. 
   Ab-initio approaches to the structure of molecules: Hartree-Fock theory, Gaussians, example of GAMESS software
   
3. 
   Ab-initio approaches to the structure of crystals: Density Functional theory, plane waves, examples of WIEN2K and Quantum Espresso software. Modern extensions of DFT (LDA+U, noncollinear magnetism)
   
4. 
   Some phenomenological ways to compute properties of materials: Ising and Heisenberg models in magnetism, Monte- Carlo/Metropolis simulated annealing, examples of phase transitions
   
5. 
   Extensions: optical properties of materials from time-dependent DFT, transport properties, multiscale modelling and link to continuum problems (finite elements, fluid mechanics)
   

Outline (with number of hours per part)	Lect	PSS	LW
Introduction	2