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Many-Electron Densities and Reduced Density Matrices

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 111/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

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

2013-03-09 Science
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Release : 2013-03-09
Genre : Science
Kind : eBook
Book Rating : 090/5 ( reviews)

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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. This book was released on 2013-03-09. 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.

Reduced Density Matrices in Quantum Chemistry

2012-12-02 Science
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Release : 2012-12-02
Genre : Science
Kind : eBook
Book Rating : 022/5 ( reviews)

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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. This book was released on 2012-12-02. 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

2007-04-06 Science
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Release : 2007-04-06
Genre : Science
Kind : eBook
Book Rating : 59X/5 ( reviews)

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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. This book was released on 2007-04-06. 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.

Density Matrices and Density Functionals

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 551/5 ( reviews)

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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. This book was released on 2012-12-06. 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.

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