Mathematical Models And Methods For Ab Initio Quantum Chemistry

Author : M. Defranceschi
Publisher : Springer Science & Business Media
ISBN 13 : 3642572375
Total Pages : 247 pages
Book Rating : 4.71/5 ( download)

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Download or read book Mathematical Models and Methods for Ab Initio Quantum Chemistry written by M. Defranceschi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : K. P. Lawley
Publisher : John Wiley & Sons
ISBN 13 : 0470143371
Total Pages : 568 pages
Book Rating : 4.77/5 ( download)

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Download or read book Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1 written by K. P. Lawley and published by John Wiley & Sons. This book was released on 2009-09-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.

Author : Eric Cancès
Publisher : Springer Nature
ISBN 13 : 3031223403
Total Pages : 595 pages
Book Rating : 4.02/5 ( download)

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Download or read book Density Functional Theory written by Eric Cancès and published by Springer Nature. This book was released on 2023-07-18 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2. DFT overcomes this problem by 1) reformulating the N-body problem involving functions of 3N variables in terms of the density, a function of 3 variables, 2) approximating it by a pioneering hybrid approach which keeps important ab initio contributions and re-models the remainder in a data-driven way. This book intends to be an accessible, yet state-of-art text on DFT for graduate students and researchers in applied and computational mathematics, physics, chemistry, and materials science. It introduces and reviews the main models of DFT, covering their derivation and mathematical properties, numerical treatment, and applications.

Author : Venera Khoromskaia
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110391376
Total Pages : 297 pages
Book Rating : 4.74/5 ( download)

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Download or read book Tensor Numerical Methods in Quantum Chemistry written by Venera Khoromskaia and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.

Author : J. Tinsley Oden
Publisher : John Wiley & Sons
ISBN 13 : 1118105745
Total Pages : 348 pages
Book Rating : 4.40/5 ( download)

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Download or read book An Introduction to Mathematical Modeling written by J. Tinsley Oden and published by John Wiley & Sons. This book was released on 2012-02-23 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : André D. Bandrauk
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870372
Total Pages : 212 pages
Book Rating : 4.78/5 ( download)

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Download or read book High-dimensional Partial Differential Equations in Science and Engineering written by André D. Bandrauk and published by American Mathematical Soc.. This book was released on 2007-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : B. L. Hammond
Publisher : World Scientific
ISBN 13 : 9810203217
Total Pages : 320 pages
Book Rating : 4.14/5 ( download)

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Download or read book Monte Carlo Methods in Ab Initio Quantum Chemistry written by B. L. Hammond and published by World Scientific. This book was released on 1994 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential.Some distinguishing features of this book are:

Author : Henry F. Schaefer III
Publisher : Courier Corporation
ISBN 13 : 0486151417
Total Pages : 180 pages
Book Rating : 4.10/5 ( download)

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Download or read book Quantum Chemistry written by Henry F. Schaefer III and published by Courier Corporation. This book was released on 2012-11-14 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: For each of 150 landmark papers in ab initio molecular electronic structure methods, the author provides a lucid commentary that focuses on methodology, rather than particular chemical problems. 1984 edition.

Author : Arieh Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521858076
Total Pages : 584 pages
Book Rating : 4.70/5 ( download)

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Download or read book Acta Numerica 2005: Volume 14 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2005-06-30 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Author : Darrin M. York
Publisher : Springer Science & Business Media
ISBN 13 : 1402099568
Total Pages : 426 pages
Book Rating : 4.64/5 ( download)

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Download or read book Multi-scale Quantum Models for Biocatalysis written by Darrin M. York and published by Springer Science & Business Media. This book was released on 2009-05-30 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Multi-scale Quantum Models for Biocatalysis” explores various molecular modelling techniques and their applications in providing an understanding of the detailed mechanisms at play during biocatalysis in enzyme and ribozyme systems. These areas are reviewed by an international team of experts in theoretical, computational chemistry, and biophysics. This book presents detailed reviews concerning the development of various techniques, including ab initio molecular dynamics, density functional theory, combined QM/MM methods, solvation models, force field methods, and free-energy estimation techniques, as well as successful applications of multi-scale methods in the biocatalysis systems including several protein enzymes and ribozymes. This book is an excellent source of information for research professionals involved in computational chemistry and physics, material science, nanotechnology, rational drug design and molecular biology and for students exposed to these research areas.