Many-Electron Densities and Reduced Density Matrices

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Publisher : Springer Science & Business Media
ISBN 13 : 9780306464546
Total Pages : 320 pages
Book Rating : 4.4/5 (645 download)

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Book Synopsis Many-Electron Densities and Reduced Density Matrices by : Jerzy Cioslowski

Download or read book Many-Electron Densities and Reduced Density Matrices written by Jerzy Cioslowski and published by Springer Science & Business Media. This book was released on 2000-09-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil iary yet essential N-representability conditions turned quite bleak. How ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry.

Reduced Density Matrices in Quantum Chemistry

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Author :
Publisher : Elsevier
ISBN 13 : 0323161022
Total Pages : 144 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Reduced Density Matrices in Quantum Chemistry by : Ernest Davidson

Download or read book Reduced Density Matrices in Quantum Chemistry written by Ernest Davidson and published by Elsevier. This book was released on 2012-12-02 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced Density Matrices in Quantum Chemistry is from a special topics course of the author to graduate students at the Ohio State University. The focus of the book is on the structure of the density matrix as reference to the electronic structure of atoms and molecules. Chapters 1 and 2 discuss and differentiate in detail the ensemble density matrix and reduced density matrices. Ensemble density matrix is discussed in the context of different states, while the energy expressions of reduced density matrices are highlighted together with some examples. Chapter 3 accordingly follows through with a description of the properties of reduced density matrices. The succeeding chapters focus on the first-order and second-order reduced density matrices in terms of their analytic and physical properties. The final chapter discusses and interprets the two-body density matrix. The book is intended for graduate students and researchers in the study of quantum chemistry.

Reduced-Density-Matrix Mechanics

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Publisher : John Wiley & Sons
ISBN 13 : 047010659X
Total Pages : 300 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Reduced-Density-Matrix Mechanics by : David A. Mazziotti

Download or read book Reduced-Density-Matrix Mechanics written by David A. Mazziotti and published by John Wiley & Sons. This book was released on 2007-04-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of this cutting-edge research in a consistent and understandable framework, of special interest to experts in other areas of electronic structure and/or quantum many-body theory. It will serve equally well as a self-contained guide to learning about reduced density matrices either through self-study or in a classroom as well as an invaluable resource for understanding the critical advancements in the field.

Reduced Density Matrices

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540671480
Total Pages : 300 pages
Book Rating : 4.6/5 (714 download)

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Book Synopsis Reduced Density Matrices by : A.J. Coleman

Download or read book Reduced Density Matrices written by A.J. Coleman and published by Springer Science & Business Media. This book was released on 2000-04-14 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors demonstrate that the essential information about order in, and energy levels of physical systems is encapsulated in the second order reduced density matrix. They have discovered an algorithm to obtain a reasonable accurate expression for the 2-matrix of an N-particle state to make nearly all properties of matter which are of interest to chemists and physicists accessible.

Reduced Density Matrices in Quantum Chemistry

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Publisher :
ISBN 13 : 9780122058509
Total Pages : 135 pages
Book Rating : 4.0/5 (585 download)

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Book Synopsis Reduced Density Matrices in Quantum Chemistry by : Ernest R. Davidson

Download or read book Reduced Density Matrices in Quantum Chemistry written by Ernest R. Davidson and published by . This book was released on 1976-01-01 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reduced Density Matrices in Quantum Chemistry

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Publisher :
ISBN 13 : 9780124337732
Total Pages : 0 pages
Book Rating : 4.3/5 (377 download)

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Book Synopsis Reduced Density Matrices in Quantum Chemistry by : Ernest Roy Davidson

Download or read book Reduced Density Matrices in Quantum Chemistry written by Ernest Roy Davidson and published by . This book was released on 1976 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Many-Electron Densities and Reduced Density Matrices

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Publisher : Springer Science & Business Media
ISBN 13 : 1461542111
Total Pages : 311 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Many-Electron Densities and Reduced Density Matrices by : Jerzy Cioslowski

Download or read book Many-Electron Densities and Reduced Density Matrices written by Jerzy Cioslowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science advances by leaps and bounds rather than linearly in time. I t is not uncommon for a new concept or approach to generate a lot of initial interest, only to enter a quiet period of years or decades and then suddenly reemerge as the focus of new exciting investigations. This is certainly the case of the reduced density matrices (a k a N-matrices or RDMs), whose promise of a great simplification of quantum-chemical approaches faded away when the prospects of formulating the auxil iary yet essential N-representability conditions turned quite bleak. How ever, even during the period that followed this initial disappointment, the 2-matrices and their one-particle counterparts have been ubiquitous in the formalisms of modern electronic structure theory, entering the correlated-level expressions for the first-order response properties, giv ing rise to natural spinorbitals employed in the configuration interaction method and in rigorous analysis of electronic wavefunctions, and al lowing direct calculations of ionization potentials through the extended Koopmans'theorem. The recent research of Nakatsuji, Valdemoro, and Mazziotti her alds a renaissance of the concept of RDlvls that promotes them from the role of interpretive tools and auxiliary quantities to that of central variables of new electron correlation formalisms. Thanks to the economy of information offered by RDMs, these formalisms surpass the conven tional approaches in conciseness and elegance of formulation. As such, they hold the promise of opening an entirely new chapter of quantum chemistry.

Density Matrix Theory and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 1461568080
Total Pages : 217 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Density Matrix Theory and Applications by : Karl Blum

Download or read book Density Matrix Theory and Applications written by Karl Blum and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Quantum Chemistry and Dynamics of Excited States

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Publisher : John Wiley & Sons
ISBN 13 : 1119417759
Total Pages : 52 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Quantum Chemistry and Dynamics of Excited States by : Leticia González

Download or read book Quantum Chemistry and Dynamics of Excited States written by Leticia González and published by John Wiley & Sons. This book was released on 2021-02-01 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

Density Matrices and Density Functionals

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Publisher : Springer Science & Business Media
ISBN 13 : 9400938551
Total Pages : 718 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Density Matrices and Density Functionals by : R.M. Erdahl

Download or read book Density Matrices and Density Functionals written by R.M. Erdahl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE COLEMAN SYMPOSIUM This collection of papers is dedicated to Albert John Coleman for his enthusiastic devotion to teaching and research and his many scientific accomplishments. John was born in Toronto on May 20, 1918 and 21 years later graduated from the University of Toronto in mathematics. Along the way he teamed up with Irving Kaplansky and Nathan Mendelson to win the first William Lowell Putnam Mathematical Competition in 1938. He earned his M.A. at Princeton in 1942 and then his Ph.D. at Toronto in 1943 in relativistic quantum mechanics under the direction of Leopold Infeld. During this period he was secretary of the Student Christian Movement in Toronto. Later, in 1945, he became traveling secretary of the World's Student Christian Federation in Geneva and in this capacity visited some 100 universities in 20 countries in the next four years. He spent the 50's as a member of the faculty at the University of Toronto and for 20 years, starting in 1960, he served as Dupuis Professor of Mathematics and Head of the Department at Queen's University. Since 1983 he has been Professor Emeritus at Queen's.

Energy Density Functional Theory of Many-Electron Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 9400919700
Total Pages : 862 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Energy Density Functional Theory of Many-Electron Systems by : Eugene S. Kryachko

Download or read book Energy Density Functional Theory of Many-Electron Systems written by Eugene S. Kryachko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State

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Publisher : Springer Science & Business Media
ISBN 13 : 9401704090
Total Pages : 233 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State by : N.I. Gidopoulos

Download or read book The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State written by N.I. Gidopoulos and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume records the proceedings of a Forum on The Fundamentals of Electron Density, Density Matrix and Density Functional Theory in Atoms, Molecules and the Solid State held at the Coseners' House, Abingdon-on-Thames, Oxon. over the period 31st May - 2nd June, 2002. The forum consisted of 26 oral and poster presentations followed by a discussion structure around questions and comments submitted by the participants (and others who had expressed an interest) in advance of the meeting. Quantum mechanics provides a theoretical foundation for our under standing of the structure and properties of atoms, molecules and the solid state in terms their component particles, electrons and nuclei. (Rel ativistic quantum mechanics is required for molecular systems contain ing heavy atoms.) However, the solution of the equations of quantum mechanics yields a function, a wave function, which depends on the co ordinates, both space and spin, of all of the particles in the system. This functions contains much more information than is required to yield the energy or other property.

Modern Quantum Chemistry

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Publisher : Courier Corporation
ISBN 13 : 0486134598
Total Pages : 480 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Modern Quantum Chemistry by : Attila Szabo

Download or read book Modern Quantum Chemistry written by Attila Szabo and published by Courier Corporation. This book was released on 2012-06-08 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text explains the modern in-depth approaches to the calculation of electronic structure and the properties of molecules. Largely self-contained, it features more than 150 exercises. 1989 edition.

Reduced Density Matrices with Applications to Physical and Chemical Systems

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Publisher : Kingston, Ont. : Queen's College
ISBN 13 :
Total Pages : 468 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis Reduced Density Matrices with Applications to Physical and Chemical Systems by : United States. Air Force. Office of Scientific Research

Download or read book Reduced Density Matrices with Applications to Physical and Chemical Systems written by United States. Air Force. Office of Scientific Research and published by Kingston, Ont. : Queen's College. This book was released on 1968 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Consistent Quantum Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521539296
Total Pages : 412 pages
Book Rating : 4.5/5 (392 download)

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Book Synopsis Consistent Quantum Theory by : Robert B. Griffiths

Download or read book Consistent Quantum Theory written by Robert B. Griffiths and published by Cambridge University Press. This book was released on 2003-11-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

Ideas of Quantum Chemistry

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Publisher : Elsevier
ISBN 13 : 0080466761
Total Pages : 1122 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Ideas of Quantum Chemistry by : Lucjan Piela

Download or read book Ideas of Quantum Chemistry written by Lucjan Piela and published by Elsevier. This book was released on 2006-11-28 with total page 1122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field.Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestable sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. The book is supplemented by an appendix on the Internet. * Presents the widest range of quantum chemical problems covered in one book * Unique structure allows material to be tailored to the specific needs of the reader * Informal language facilitates the understanding of difficult topics

Tensor Network Contractions

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Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.