Overview

Ce cours est une introduction à la modélisation mathématique et à l'analyse numérique pour la chimie moléculaire quantique, un champ peu connu des mathématiciens et pourtant riche en sujets d'investigation. Le point de vue choisi est celui du mathématicien appliqué. Le cours est construit de manière auto-consistante. Seules des notions de base en analyse fonctionnelle sont requises pour l'aborder. Les outils mathématiques plus élaborés sont introduits progressivement et les connaissances nécessaires en physique et en théorie spectrale sont regroupées dans des annexes. On présente d'abord les modèles les plus utilisés en pratique. Puis, on analyse ces modèles d'un point de vue mathématique (questions d'existence de solutions, d'unicité, ...). On introduit ensuite les différentes stratégies numériques employées pour la résolution pratique, et on fournit, quand ceci est possible, des éléments d'analyse numérique de ces méthodes. Les liens existants entre les modèles de la chimie moléculaire et des sujets connexes sont aussi explorés : modélisation de la phase liquide, physique de l'état cristallin, biologie, simulation des matériaux, ... Le cours peut aussi intéresser le chimiste ou le physicien curieux de comprendre les techniques mathématiques dont relèvent les modèles qu'il utilise, et de découvrir comment de telles techniques peuvent améliorer significativement l'efficacité et la qualité des simulations numériques.

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9783540309963

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Reviews

From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book presents the mathematical foundations of quantum chemistry. To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009)

From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book presents the mathematical foundations of quantum chemistry. To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009)

From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book presents the mathematical foundations of quantum chemistry. To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009) From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book ... presents the mathematical foundations of quantum chemistry. ... To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009) From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book presents the mathematical foundations of quantum chemistry. To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009) From the reviews: This book presents the mathematical foundations of several models of quantum chemistry. It is intended for graduate students in mathematics (and possibly also for scientists from physics or chemistry interested in understanding the formal underpinnings of their models), and introduces techniques and methods from several mathematical fields, in particular variational techniques, nonlinear analysis, spectral theory and partial differential equations theory. (Gabriel Stoltz, Mathematical Reviews, Issue 2009 d) The reviewing book presents the mathematical foundations of quantum chemistry. To summarize, this book is actually a rather broad reflection of the current state of mathematical art of quantum chemistry that deserves to be studied by the readers interested in the mathematical grounds of quantum chemistry and their direct applications in the research. (Eugene Kryachko, Zentralblatt MATH, Vol. 1167, 2009)

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