Tensor Numerical Methods in Quantum Chemistry

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110391376
Total Pages : 297 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Tensor Numerical Methods in Quantum Chemistry by : Venera Khoromskaia

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.

Tensor Numerical Methods in Electronic Structure Calculations

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Publisher :
ISBN 13 : 9783110365849
Total Pages : 240 pages
Book Rating : 4.3/5 (658 download)

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Book Synopsis Tensor Numerical Methods in Electronic Structure Calculations by : Venera Khoromskaia

Download or read book Tensor Numerical Methods in Electronic Structure Calculations written by Venera Khoromskaia and published by . This book was released on 2016 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Numerical Methods in Scientific Computing

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311036591X
Total Pages : 379 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Tensor Numerical Methods in Scientific Computing by : Boris N. Khoromskij

Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

Tensor Spaces and Numerical Tensor Calculus

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Publisher : Springer Science & Business Media
ISBN 13 : 3642280277
Total Pages : 525 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : Wolfgang Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2012-02-23 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. ​

Tensor Spaces and Numerical Tensor Calculus

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Publisher :
ISBN 13 : 9783030355555
Total Pages : 622 pages
Book Rating : 4.3/5 (555 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : W. Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by W. Hackbusch and published by . This book was released on 2019 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of pde and more.

Computational Methods in Quantum Chemistry

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Publisher : World Scientific
ISBN 13 : 9789810226114
Total Pages : 264 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis Computational Methods in Quantum Chemistry by : Ahmed A. Hasanein

Download or read book Computational Methods in Quantum Chemistry written by Ahmed A. Hasanein and published by World Scientific. This book was released on 1996 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account, from first principles, of the methods of numerical quantum mechanics. Coverage encompasses formulations and fundamental postulates; the Hamiltonian and angular momentum operators; and approximation of the solutions of the Schroedinger equation

Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 3662047500
Total Pages : 557 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum Mechanics by : Louis Marchildon

Download or read book Quantum Mechanics written by Louis Marchildon and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fresh and original text on quantum mechanics focuses on: the development of numerical methods for obtaining specific results; the presentation of group theory and the systematic use of operators; the introduction of the functional integral and its applications in approximation; the discussion of distant correlations and experimental measurements. Numerous exercises with hints and solutions, examples and applications, and a guide to key references help the student to work with the text.

Introduction to Tensor Network Methods

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Publisher : Springer
ISBN 13 : 3030014096
Total Pages : 172 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero

Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Tensor Spaces and Numerical Tensor Calculus

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Publisher : Springer Nature
ISBN 13 : 3030355543
Total Pages : 605 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : Wolfgang Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Nature. This book was released on 2019-12-16 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

From Quantum to Classical Molecular Dynamics

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Publisher : European Mathematical Society
ISBN 13 : 9783037190678
Total Pages : 164 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis From Quantum to Classical Molecular Dynamics by : Christian Lubich

Download or read book From Quantum to Classical Molecular Dynamics written by Christian Lubich and published by European Mathematical Society. This book was released on 2008 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations. This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrodinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.

Tensor Analysis and Nonlinear Tensor Functions

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Publisher : Springer Science & Business Media
ISBN 13 : 9401732213
Total Pages : 680 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Tensor Analysis and Nonlinear Tensor Functions by : Yuriy I. Dimitrienko

Download or read book Tensor Analysis and Nonlinear Tensor Functions written by Yuriy I. Dimitrienko and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space R3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science.

Tensor Analysis

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110404265
Total Pages : 343 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Tensor Analysis by : Heinz Schade

Download or read book Tensor Analysis written by Heinz Schade and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-10-08 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics. ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates

New Methods in Computational Quantum Mechanics

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Publisher : John Wiley & Sons
ISBN 13 : 0470142057
Total Pages : 812 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis New Methods in Computational Quantum Mechanics by : Ilya Prigogine

Download or read book New Methods in Computational Quantum Mechanics written by Ilya Prigogine and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of quantum chemistry for the quantitative prediction of molecular properties has long been frustrated by the technical difficulty of carrying out the needed computations. In the last decade there have been substantial advances in the formalism and computer hardware needed to carry out accurate calculations of molecular properties efficiently. These advances have been sufficient to make quantum chemical calculations a reliable tool for the quantitative interpretation of chemical phenomena and a guide to laboratory experiments. However, the success of these recent developments in computational quantum chemistry is not well known outside the community of practitioners. In order to make the larger community of chemical physicists aware of the current state of the subject, this self-contained volume of Advances in Chemical Physics surveys a number of the recent accomplishments in computational quantum chemistry. This stand-alone work presents the cutting edge of research in computational quantum mechanics. Supplemented with more than 150 illustrations, it provides evaluations of a broad range of methods, including: * Quantum Monte Carlo methods in chemistry * Monte Carlo methods for real-time path integration * The Redfield equation in condensed-phase quantum dynamics * Path-integral centroid methods in quantum statistical mechanics and dynamics * Multiconfigurational perturbation theory-applications in electronic spectroscopy * Electronic structure calculations for molecules containing transition metals * And more Contributors to New Methods in Computational Quantum Mechanics KERSTIN ANDERSSON, Department of Theoretical Chemistry, Chemical Center, Sweden DAVID M. CEPERLEY, National Center for Supercomputing Applications and Department of Physics, University of Illinois at Urbana-Champaign, Illinois MICHAEL A. COLLINS, Research School of Chemistry, Australian National University, Canberra, Australia REINHOLD EGGER, Fakultät für Physik, Universität Freiburg, Freiburg, Germany ANTHONY K. FELTS, Department of Chemistry, Columbia University, New York RICHARD A. FRIESNER, Department of Chemistry, Columbia University, New York MARKUS P. FÜLSCHER, Department of Theoretical Chemistry, Chemical Center, Sweden K. M. HO, Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa C. H. MAK, Department of Chemistry, University of Southern California, Los Angeles, California PER-ÅKE Malmqvist, Department of Theoretical Chemistry, Chemical Center, Sweden MANUELA MERCHán, Departamento de Química Física, Universitat de Valéncia, Spain LUBOS MITAS, National Center for Supercomputing Applications and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Illinois STEFANO OSS, Dipartimento di Fisica, Università di Trento and Istituto Nazionale di Fisica della Materia, Unità di Trento, Italy KRISTINE PIERLOOT, Department of Chemistry, University of Leuven, Belgium W. THOMAS POLLARD, Department of Chemistry, Columbia University, New York BJÖRN O. ROOS, Department of Theoretical Chemistry, Chemical Center, Sweden LUIS SERRANO-ANDRÉS, Department of Theoretical Chemistry, Chemical Center, Sweden PER E. M. SIEGBAHN, Department of Physics, University of Stockholm, Stockholm, Sweden WALTER THIEL, Institut für Organische Chemie, Universität Zürich, Zürich, Switzerland GREGORY A. VOTH, Department of Chemistry, University of Pennsylvania, Pennsylvania C. Z. Wang, Ames Laboratory and Department of Physi

Second Quantization-Based Methods in Quantum Chemistry

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Publisher : Elsevier
ISBN 13 : 0323141099
Total Pages : 184 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Second Quantization-Based Methods in Quantum Chemistry by : Poul Joergensen

Download or read book Second Quantization-Based Methods in Quantum Chemistry written by Poul Joergensen and published by Elsevier. This book was released on 2012-12-02 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second Quantization-Based Methods in Quantum Chemistry presents several modern quantum chemical tools that are being applied to electronic states of atoms and molecules. Organized into six chapters, the book emphasizes the quantum chemical methods whose developments and implementations have been presented in the language of second quantization. The opening chapter of the book examines the representation of the electronic Hamiltonian, other quantum-mechanical operators, and state vectors in the second-quantization language. This chapter also describes the unitary transformations among orthonormal orbitals in an especially convenient manner. In subsequent chapters, various tools of second quantization are used to describe many approximation techniques, such as Hartree-Fock, perturbation theory, configuration interaction, multiconfigurational Hartree-Fock, cluster methods, and Green’s function. This book is an invaluable source for researchers in quantum chemistry and for graduate-level students who have already taken introductory courses that cover the fundamentals of quantum mechanics through the Hartree-Fock method as applied to atoms and molecules.

High-Performance Tensor Computations in Scientific Computing and Data Science

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Publisher : Frontiers Media SA
ISBN 13 : 2832504256
Total Pages : 192 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis High-Performance Tensor Computations in Scientific Computing and Data Science by : Edoardo Angelo Di Napoli

Download or read book High-Performance Tensor Computations in Scientific Computing and Data Science written by Edoardo Angelo Di Napoli and published by Frontiers Media SA. This book was released on 2022-11-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 0470143371
Total Pages : 568 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Ab Initio Methods in Quantum Chemistry, Volume 67, Part 1 by : K. P. Lawley

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.

New Methods in Computational Quantum Mechanics, Volume 93

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Publisher : Wiley-Interscience
ISBN 13 : 9780471143215
Total Pages : 0 pages
Book Rating : 4.1/5 (432 download)

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Book Synopsis New Methods in Computational Quantum Mechanics, Volume 93 by : Ilya Prigogine

Download or read book New Methods in Computational Quantum Mechanics, Volume 93 written by Ilya Prigogine and published by Wiley-Interscience. This book was released on 1996-04-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of quantum chemistry for the quantitative prediction of molecular properties has long been frustrated by the technical difficulty of carrying out the needed computations. In the last decade there have been substantial advances in the formalism and computer hardware needed to carry out accurate calculations of molecular properties efficiently. These advances have been sufficient to make quantum chemical calculations a reliable tool for the quantitative interpretation of chemical phenomena and a guide to laboratory experiments. However, the success of these recent developments in computational quantum chemistry is not well known outside the community of practitioners. In order to make the larger community of chemical physicists aware of the current state of the subject, this self-contained volume of Advances in Chemical Physics surveys a number of the recent accomplishments in computational quantum chemistry. This stand-alone work presents the cutting edge of research in computational quantum mechanics. Supplemented with more than 150 illustrations, it provides evaluations of a broad range of methods, including: * Quantum Monte Carlo methods in chemistry * Monte Carlo methods for real-time path integration * The Redfield equation in condensed-phase quantum dynamics * Path-integral centroid methods in quantum statistical mechanics and dynamics * Multiconfigurational perturbation theory-applications in electronic spectroscopy * Electronic structure calculations for molecules containing transition metals * And more Contributors to New Methods in Computational Quantum Mechanics KERSTIN ANDERSSON, Department of Theoretical Chemistry, Chemical Center, Sweden DAVID M. CEPERLEY, National Center for Supercomputing Applications and Department of Physics, University of Illinois at Urbana-Champaign, Illinois MICHAEL A. COLLINS, Research School of Chemistry, Australian National University, Canberra, Australia REINHOLD EGGER, Fakultät für Physik, Universität Freiburg, Freiburg, Germany ANTHONY K. FELTS, Department of Chemistry, Columbia University, New York RICHARD A. FRIESNER, Department of Chemistry, Columbia University, New York MARKUS P. FÜLSCHER, Department of Theoretical Chemistry, Chemical Center, Sweden K. M. HO, Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa C. H. MAK, Department of Chemistry, University of Southern California, Los Angeles, California PER-ÅKE Malmqvist, Department of Theoretical Chemistry, Chemical Center, Sweden MANUELA MERCHán, Departamento de Química Física, Universitat de Valéncia, Spain LUBOS MITAS, National Center for Supercomputing Applications and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Illinois STEFANO OSS, Dipartimento di Fisica, Università di Trento and Istituto Nazionale di Fisica della Materia, Unità di Trento, Italy KRISTINE PIERLOOT, Department of Chemistry, University of Leuven, Belgium W. THOMAS POLLARD, Department of Chemistry, Columbia University, New York BJÖRN O. ROOS, Department of Theoretical Chemistry, Chemical Center, Sweden LUIS SERRANO-ANDRÉS, Department of Theoretical Chemistry, Chemical Center, Sweden PER E. M. SIEGBAHN, Department of Physics, University of Stockholm, Stockholm, Sweden WALTER THIEL, Institut für Organische Chemie, Universität Zürich, Zürich, Switzerland GREGORY A. VOTH, Department of Chemistry, University of Pennsylvania, Pennsylvania C. Z. Wang, Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa