Mathematical Models and Methods for Ab Initio Quantum Chemistry

Mathematical Models and Methods for Ab Initio Quantum Chemistry

Author: M. Defranceschi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 247

ISBN-13: 3642572375

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On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.


An Introduction to Mathematical Modeling

An Introduction to Mathematical Modeling

Author: J. Tinsley Oden

Publisher: John Wiley & Sons

Published: 2012-02-23

Total Pages: 348

ISBN-13: 1118105745

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A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study. Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.


Acta Numerica 2005: Volume 14

Acta Numerica 2005: Volume 14

Author: Arieh Iserles

Publisher: Cambridge University Press

Published: 2005-06-30

Total Pages: 584

ISBN-13: 9780521858076

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A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.


High-Dimensional Partial Differential Equations in Science and Engineering

High-Dimensional Partial Differential Equations in Science and Engineering

Author: André D. Bandrauk

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 210

ISBN-13: 0821838539

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High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker-Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled. The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.


Mathematical Challenges from Theoretical/Computational Chemistry

Mathematical Challenges from Theoretical/Computational Chemistry

Author: National Research Council

Publisher: National Academies Press

Published: 1995-03-29

Total Pages: 143

ISBN-13: 030917662X

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Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.


Quantum Mechanics: Genesis and Achievements

Quantum Mechanics: Genesis and Achievements

Author: Alexander Komech

Publisher: Springer Science & Business Media

Published: 2012-10-24

Total Pages: 294

ISBN-13: 9400755414

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The focus of the present work is nonrelativistic and relativistic quantum mechanics with standard applications to the hydrogen atom. The author has aimed at presenting quantum mechanics in a comprehensive yet accessible for mathematicians and other non-physicists. The genesis of quantum mechanics, its applications to basic quantum phenomena, and detailed explanations of the corresponding mathematical methods are presented. The exposition is formalized (whenever possible) on the basis of the coupled Schroedinger, Dirac and Maxwell equations. Aimed at upper graduate and graduate students in mathematical and physical science studies.


Computational Chemistry

Computational Chemistry

Author: Philippe G. Ciarlet

Publisher: Gulf Professional Publishing

Published: 1990

Total Pages: 928

ISBN-13: 9780444512482

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Aiming to provide the reader with a general overview of the mathematical and numerical techniques used for the simulation of matter at the microscopic scale, this book lays the emphasis on the numerics, but modelling aspects are also addressed. The contributors come from different scientific communities: physics, theoretical chemistry, mathematical analysis, stochastic analysis, numerical analysis, and the text should be suitable for graduate students in mathematics, sciences and engineering and technology.


Essential Computational Modeling in Chemistry

Essential Computational Modeling in Chemistry

Author: Philippe G. Ciarlet

Publisher: Elsevier

Published: 2010-12-07

Total Pages: 399

ISBN-13: 0444537619

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Essential Computational Modeling in Chemistry presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling in Chemistry Vol. 10(2005). Computational Modeling is an active field of scientific computing at the crossroads between Physics, Chemistry, Applied Mathematics and Computer Science. Sophisticated mathematical models are increasingly complex and extensive computer simulations are on the rise. Numerical Analysis and scientific software have emerged as essential steps for validating mathematical models and simulations based on these models. This guide provides a quick reference of computational methods for use in understanding chemical reactions and how to control them. By demonstrating various computational methods in research, scientists can predict such things as molecular properties. The reference offers a number of techniques and the numerical analysis needed to perform rigorously founded computations. Various viewpoints of methods and applications are available for researchers to chose and experiment with; Numerical analysis and open problems is useful for experimentation; Most commonly used models and techniques for the molecular case is quickly accessible


Lectures On Quantum Mechanics And Attractors

Lectures On Quantum Mechanics And Attractors

Author: Alexander Komech

Publisher: World Scientific

Published: 2022-02-18

Total Pages: 272

ISBN-13: 9811248915

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This book gives a concise introduction to Quantum Mechanics with a systematic, coherent, and in-depth explanation of related mathematical methods from the scattering theory and the theory of Partial Differential Equations.The book is aimed at graduate and advanced undergraduate students in mathematics, physics, and chemistry, as well as at the readers specializing in quantum mechanics, theoretical physics and quantum chemistry, and applications to solid state physics, optics, superconductivity, and quantum and high-frequency electronic devices.The book utilizes elementary mathematical derivations. The presentation assumes only basic knowledge of the origin of Hamiltonian mechanics, Maxwell equations, calculus, Ordinary Differential Equations and basic PDEs. Key topics include the Schrödinger, Pauli, and Dirac equations, the corresponding conservation laws, spin, the hydrogen spectrum, and the Zeeman effect, scattering of light and particles, photoelectric effect, electron diffraction, and relations of quantum postulates with attractors of nonlinear Hamiltonian PDEs. Featuring problem sets and accompanied by extensive contemporary and historical references, this book could be used for the course on Quantum Mechanics and is also suitable for individual study.


Computational Quantum Chemistry

Computational Quantum Chemistry

Author: Joseph J W McDouall

Publisher: Royal Society of Chemistry

Published: 2015-11-09

Total Pages: 252

ISBN-13: 1782625860

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Computational Quantum Chemistry presents computational electronic structure theory as practised in terms of ab initio waveform methods and density functional approaches. Getting a full grasp of the field can often prove difficult, since essential topics fall outside of the scope of conventional chemistry education. This professional reference book provides a comprehensive introduction to the field. Postgraduate students and experienced researchers alike will appreciate Joseph McDouall's engaging writing style. The book is divided into five chapters, each providing a major aspect of the field. Electronic structure methods, the computation of molecular properties, methods for analysing the output from computations and the importance of relativistic effects on molecular properties are also discussed. Links to the websites of widely used software packages are provided so that the reader can gain first hand experience of using the techniques described in the book.