Tensor Numerical Methods In Electronic Structure Calculations

DOWNLOAD

Download Tensor Numerical Methods In Electronic Structure Calculations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Tensor Numerical Methods In Electronic Structure Calculations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Tensor Numerical Methods In Quantum Chemistry

DOWNLOAD
Author : Venera Khoromskaia
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-06-11

Tensor Numerical Methods In Quantum Chemistry written by Venera Khoromskaia and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.

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 Scientific Computing

DOWNLOAD
Author : Boris N. Khoromskij
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-06-11

Tensor Numerical Methods In Scientific Computing written by Boris N. Khoromskij and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.

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

Semiempirical Methods Of Electronic Structure Calculation

DOWNLOAD
Author : Gerald Segal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Semiempirical Methods Of Electronic Structure Calculation written by Gerald Segal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

If one reflects upon the range of chemical problems accessible to the current quantum theoretical methods for calculations on the electronic structure of molecules, one is immediately struck by the rather narrow limits imposed by economic and numerical feasibility. Most of the systems with which experimental photochemists actually work are beyond the grasp of ab initio methods due to the presence of a few reasonably large aromatic ring systems. Potential energy surfaces for all but the smallest molecules are extremely expensive to produce, even over a restricted group of the possible degrees of freedom, and molecules containing the higher elements of the periodic table remain virtually untouched due to the large numbers of electrons involved. Almost the entire class of molecules of real biological interest is simply out of the question. In general, the theoretician is reduced to model systems of variable appositeness in most of these fields. The fundamental problem, from a basic computational point of view, is that large molecules require large numbers of basis functions, whether Slater type orbitals or Gaussian functions suitably contracted, to provide even a modestly accurate description of the molecular electronic environment. This leads to the necessity of dealing with very large matrices and numbers of integrals within the Hartree-Fock approximation and quickly becomes both numerically difficult and uneconomic.

Aeta 2018 Recent Advances In Electrical Engineering And Related Sciences Theory And Application

DOWNLOAD
Author : Ivan Zelinka
language : en
Publisher: Springer
Release Date : 2019-04-13

Aeta 2018 Recent Advances In Electrical Engineering And Related Sciences Theory And Application written by Ivan Zelinka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-13 with Technology & Engineering categories.

These proceedings address a broad range of topic areas, including telecommunication, power systems, digital signal processing, robotics, control systems, renewable energy, power electronics, soft computing and more. Today’s world is based on vitally important technologies that combine e.g. electronics, cybernetics, computer science, telecommunication, and physics. However, since the advent of these technologies, we have been confronted with numerous technological challenges such as finding optimal solutions to various problems regarding controlling technologies, signal processing, power source design, robotics, etc. Readers will find papers on these and other topics, which share fresh ideas and provide state-of-the-art overviews. They will also benefit practitioners, who can easily apply the issues discussed here to solve real-life problems in their own work. Accordingly, the proceedings offer a valuable resource for all scientists and engineers pursuing research and applications in the above-mentioned fields.

Matrix Methods

DOWNLOAD
Author : Vadim Olshevsky
language : en
Publisher: World Scientific
Release Date : 2010

Matrix Methods written by Vadim Olshevsky and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume. --

Advances In Quantum Chemistry

DOWNLOAD
Author :
language : en
Publisher: Elsevier
Release Date : 2005-12-20

Advances In Quantum Chemistry written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Science categories.

Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field that falls between the historically established areas of mathematics, physics, chemistry, and biology. With invited reviews written by leading international researchers, each presenting new results, it provides a single vehicle for following progress in this interdisciplinary area. This volume continues the tradition with high quality and thorough reviews of various aspects of quantum chemistry. It contains a variety of topics on the use of quantum mechanical methods to calculate molecular properties including response properties. Linear and non-linear response methods have been developed and implemented for most of the approximate wave functions used in quantum chemistry, giving a range of computational methods of varying cost and accuracy. Thus it is presently possible to calculate for example excitation energies, linear and nonlinear optical properties, one- and multi-photon transition rates, and magnetically induced transition moments for a wide range of molecules and target accuracies. These calculations aid in the interpretation of a wide range of spectroscopy including electron spin resonance, nuclear magnetic resonance and magnetic circular dichroism and general laser spectroscopy.

State Of The Art Of Molecular Electronic Structure Computations Correlation Methods Basis Sets And More

DOWNLOAD
Author :
language : en
Publisher: Academic Press
Release Date : 2019-09-07

State Of The Art Of Molecular Electronic Structure Computations Correlation Methods Basis Sets And More written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-07 with Science categories.

State of the Art of Molecular Electronic Structure Computations: Correlation Methods, Basis Sets and More, Volume 79 in the Advances in Quantum Chemistry series, presents surveys of current topics in this rapidly developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology. Chapters in this new release include Computing accurate molecular properties in real space using multiresolution analysis, Self-consistent electron-nucleus cusp correction for molecular orbitals, Correlated methods for computational spectroscopy, Potential energy curves for the NaH molecule and its cation with the cock space coupled cluster method, and much more. - Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology - Features detailed reviews written by leading international researchers

Nitroxides

DOWNLOAD
Author : Olivier Ouari
language : en
Publisher: Royal Society of Chemistry
Release Date : 2021-05-13

Nitroxides written by Olivier Ouari and has been published by Royal Society of Chemistry this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-13 with Science categories.

Nitroxides are versatile small organic molecules possessing a stabilised free radical. With their unpaired electron spin they display a unique reactivity towards various environmental factors, enabling a diverse range of applications. They have uses as synthetic tools, such as catalysts or building blocks; imaging agents and probes in biomedicine and materials science; for medicinal antioxidant applications; and in energy storage. Polynitroxides (polymers bearing pendant nitroxide sidechains) have been used in organic radical batteries, oxidation catalysts and in exchange reactions for constructing complex architectures. Chapters in this book cover the synthesis of nitroxides, EPR studies and magnetic resonance applications, physiochemical studies, and applications including in batteries, imaging and organic synthesis. With contributions from leaders in the field, Nitroxides will be of interest to graduate students and researchers across chemistry, physics, biology and materials science.

High Performance Tensor Computations In Scientific Computing And Data Science

DOWNLOAD
Author : Edoardo Angelo Di Napoli
language : en
Publisher: Frontiers Media SA
Release Date : 2022-11-08

High Performance Tensor Computations In Scientific Computing And Data Science written by Edoardo Angelo Di Napoli and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Science categories.

Nmr Crystallography

DOWNLOAD
Author : Robin K. Harris
language : en
Publisher: John Wiley & Sons
Release Date : 2012-12-19

Nmr Crystallography written by Robin K. Harris and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-19 with Science categories.

The content of this volume has been added to eMagRes (formerly Encyclopedia of Magnetic Resonance) - the ultimate online resource for NMR and MRI. The term "NMR Crystallography" has only recently come into common usage, and even now causes raised eyebrows within some parts of the diffraction community. The power of solid-state NMR to give crystallographic information has considerably increased since the CPMAS suite of techniques was introduced in 1976. In the first years of the 21st century, the ability of NMR to provide information to support and facilitate the analysis of single-crystal and powder diffraction patterns has become widely accepted. Indeed, NMR can now be used to refine diffraction results and, in favorable cases, to solve crystal structures with minimal (or even no) diffraction data. The increasing ability to relate chemical shifts (including the tensor components) to the crystallographic location of relevant atoms in the unit cell via computational methods has added significantly to the practice of NMR crystallography. Diffraction experts will increasingly welcome NMR as an allied technique in their structural analyses. Indeed, it may be that in the future crystal structures will be determined by simultaneously fitting diffraction patterns and NMR spectra. This Handbook is organised into six sections. The first contains an overview and some articles on fundamental NMR topics, followed by a section concentrating on chemical shifts, and one on coupling interactions. The fourth section contains articles describing how NMR results relate to fundamental crystallography concepts and to diffraction methods. The fifth section concerns specific aspects of structure, such as hydrogen bonding. Finally, four articles in the sixth section give applications of NMR crystallography to structural biology, organic & pharmaceutical chemistry, inorganic & materials chemistry, and geochemistry. About EMR Handbooks / eMagRes Handbooks The Encyclopedia of Magnetic Resonance (up to 2012) and eMagRes (from 2013 onward) publish a wide range of online articles on all aspects of magnetic resonance in physics, chemistry, biology and medicine. The existence of this large number of articles, written by experts in various fields, is enabling the publication of a series of EMR Handbooks / eMagRes Handbooks on specific areas of NMR and MRI. The chapters of each of these handbooks will comprise a carefully chosen selection of articles from eMagRes. In consultation with the eMagRes Editorial Board, the EMR Handbooks / eMagRes Handbooks are coherently planned in advance by specially-selected Editors, and new articles are written (together with updates of some already existing articles) to give appropriate complete coverage. The handbooks are intended to be of value and interest to research students, postdoctoral fellows and other researchers learning about the scientific area in question and undertaking relevant experiments, whether in academia or industry. Have the content of this Handbook and the complete content of eMagRes at your fingertips! Visit: www.wileyonlinelibrary.com/ref/eMagRes View other eMagRes publications here