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.
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.
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.
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.
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.
Download or read book Reconstructive Approaches to One and Two electron Density Matrix Theory written by John M. Herbert and published by . This book was released on 2003 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reduced Density Matrix Based Models for Strongly Correlated Electrons written by Mohammad Mostafanejad and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation presents a survey of ab initio models developed based on the merger of multireference (MR) methods and density functional theory (DFT) in order to provide an accurate and efficient description of electron correlation effects in strongly correlated systems. We first introduce a reduced density matrix (RDM)-based formulation of multiconfiguration pair-density functional theory (MC-PDFT) which addresses two of the three common problems in MR+DFT framework: double counting of the electron correlation and symmetry dilemma. MC-PDFT minimizes the double counting of electron correlation by computing the classical effects within MR part while accounting for quantum mechanical interactions via DFT part. Symmetry dilemma is also addressed through a change of variables from spin densities to on-top pair-density (OTPD). In order to resolve the third issue in MR+DFT framework, the computational cost barrier of the MR methods, we adopt the variational two-electron reduced density matrix (v2RDM)-driven complete active-space self-consistent field (CASSCF) approach. The favorable polynomial computational cost of v2RDM-CASSCF allows one to go beyond the active space size limitations of conventional configuration interaction (CI)-based MR methods. In order to reduce the delocalization error (DE) plaguing almost all density functionals, we extend MC-PDFT to its global and range-separated hybrid variants where a fraction of local exchange from OTPD functionals is replaced with its nonlocal counterpart computed by v2RDM-CASSCF reference RDMs. The efficiency and accuracy of our MC-PDFT-based models have also been demonstrated through their application to a wide variety of realistic and challenging molecular systems with dominant MR character such as the calculation of dissociation potential energy curves for di- and polyatomic molecules, reaction energy barriers of 1,3-dipolar cycloaddition reaction of ozone to ethylene and acetylene and singlet/triplet energy gaps of large members of oligocene molecular series. After providing numerical evidence for usefulness of our models for strongly correlated systems, we focus on the sources of errors and metrics for error quantification in DFT. Through introducing constrained search-Kohn-Sham density functional theory (CS-KSDFT), we have addressed two fundamental and controversial problems in KS-DFT: inaccessibility of the exact density within finite basis set and lack of a universal mathematical metric for the density error. Applying CS-KSDFT to strongly correlated systems, such as the triple-bond dissociation of N2, we have numerically showed that non-interacting KS-DFT electron densities can be far more accurate than those calculated by the conventional exchange-correlation (XC) functionals, regardless of the size of the basis set. By applying our basis set-independent metric to rank the performance of conventional density functionals for strongly correlated systems, we have numerically presented that the errors caused by the approximate forms of XC functionals (as opposed to density-driven errors) are the main source of error in KS-DFT. Lastly, we have analyzed the contentious onset of open-shell character in the singlet ground state zig-zag narrow graphene nanoribbons via a variety of metrics such as effectively unpaired electrons, natural orbital occupation numbers, singlet/triplet energy gaps and structural indicator of C-C bond length alternation.
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:
Download or read book Frontiers in Quantum Systems in Chemistry and Physics written by P.J. Grout and published by Springer Science & Business Media. This book was released on 2008-09-12 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume we have collected some of the contributions made to the Twelfth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-XII) in 2007. The workshop was held at Royal Holloway College, the most westerly campusof the University of London,and situated just a stone’s throw from Windsor Great Park. The workshop, which ran from 30 August to 5 September, continued the series that was established by Roy McWeeny in April 1996 with a meeting held at San Miniato, near Pisa. The purpose of the QSCP workshops is to bring together, in an informal atmosphere and with the aim of fostering collaboration, those chemists and physicists who share a common ?eld of interest in the theory of the quantum many-body problem. Quantum mechanics provides a theoretical foundation for our understandingof the structure,propertiesanddynamicsof atoms, moleculesandthe solid state, in terms of their component particles: electrons and nuclei. The study of ‘Quantum Systems in Chemistry and Physics’ therefore underpins many of the emerging?elds in twenty-?rstcenturyscience andtechnology:nanostructure,smart materials, drug design – to name but a few. Members of the workshop were keen to discuss their research and engage in collaboration centred upon the development of fundamental and innovative theory which would lead to the exploration of new concepts. The proceedings of all of the workshops, which have been held annually since 1996, have been published both to disseminate the latest developments within the wider community and to stimulate further collaboration.
Download or read book A Trajectory Description of Quantum Processes II Applications written by Ángel S. Sanz and published by Springer. This book was released on 2013-09-13 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.
Download or read book Applied Bohmian Mechanics written by Xavier Oriols Pladevall and published by CRC Press. This book was released on 2019-05-24 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.
Download or read book Density Functional Methods for Excited States written by Nicolas Ferré and published by Springer. This book was released on 2015-08-26 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series Topics in Current Chemistry presents critical reviews of the present and future trends in modern chemical research. The scope of coverage is all areas of chemical science including the interfaces with related disciplines such as biology, medicine and materials science. The goal of each thematic volume is to give the non-specialist reader, whether in academia or industry, a comprehensive insight into an area where new research is emerging which is of interest to a larger scientific audience. Each review within the volume critically surveys one aspect of that topic and places it within the context of the volume as a whole. The most significant developments of the last 5 to 10 years are presented using selected examples to illustrate the principles discussed. The coverage is not intended to be an exhaustive summary of the field or include large quantities of data, but should rather be conceptual, concentrating on the methodological thinking that will allow the non-specialist reader to understand the information presented. Contributions also offer an outlook on potential future developments in the field. Review articles for the individual volumes are invited by the volume editors. Readership: research chemists at universities or in industry, graduate students
Download or read book Theoretical and Quantum Chemistry at the Dawn of the 21st Century written by Tanmoy Chakraborty and published by CRC Press. This book was released on 2018-06-19 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, edited by a well-known specialist in the field of theoretical chemistry, gathers together a selection of papers on theoretical chemistry within the themes of mathematical, computational, and quantum chemistry. The authors present a rich assembly of some of the most important current research in the field of quantum chemistry in modern times. In Quantum Chemistry at the Dawn of the 21st Century, the editors aim to replicate the tradition of the fruitful Girona Workshops and Seminars, held at the University of Girona, Italy, annually for many years, which offered important scientific gatherings focusing on quantum chemistry. This volume, like the workshops, showcases a large variety of quantum chemical contributions from different points of view from some of the leading scientists in the field today. This unique volume does not pretend to provide a complete overview of quantum chemistry, but it does provide a broad set of contributions by some of the leading scientists on the field, under the expert editorship of two leaders in the field.
Download or read book Condensed Matter Theories written by Virulh Sa-yakanit and published by World Scientific. This book was released on 2009 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Thirty-First International Workshop on Condensed Matter Theories (CMT31) held in Bangkok focused on the many roles played by ab initio theory, modeling, and high-performance computing in condensed matter and materials science, providing a forum for the discussion of recent advances and exploration of new problems. Fifty-six invited papers were presented, of which 38 appear as chapters in this volume. Reports of recent results generated lively debate on two-dimensional electron systems, the metal-insulator transition, dilute magnetic semiconductors, effects of disorder, magnetoresistence phenomena, ferromagnetic stripes, quantum Hall systems, strongly correlated Fermi systems, superconductivity, dilute fermionic and bosonic gases, nanostructured materials, plasma instabilities, quantum fluid mixtures, and helium in reduced geometries.
Download or read book Density Functional Theory written by C. Amador and published by Springer. This book was released on 1983-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the International Workshop on Electronic Density Functionals, Mexico City.
Download or read book Density Matrices and Density Functionals written by R.M. Erdahl and published by Springer. This book was released on 1987-04-30 with total page 722 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.
Download or read book Reviews of Modern Quantum Chemistry written by K. D. Sen and published by World Scientific. This book was released on 2002 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book collects together state?of?the?art reviews of diverse topics covering almost all the major areas of modern quantum chemistry. The current focus in the discipline of chemistry ? synthesis, structure, reactivity and dynamics ? is mainly on control. A variety of essential computational tools at the disposal of chemists have emerged from recent studies in quantum chemistry. The acceptance and application of these tools in the interfacial disciplines of the life and physical sciences continue to grow. The new era of modern quantum chemistry throws up promising potentialities for further research.Reviews of Modern Quantum Chemistry is a joint endeavor, in which renowned scientists from leading universities and research laboratories spanning 22 countries present 59 in?depth reviews. Along with a personal introduction written by Professor Walter Kohn, Nobel laureate (Chemistry, 1998), the articles celebrate the scientific contributions of Professor Robert G Parr on the occasion of his 80th birthday.List of Contributors: W Kohn, M Levy, R Pariser, B R Judd, E Lo, B N Plakhutin, A Savin, P Politzer, P Lane, J S Murray, A J Thakkar, S R Gadre, R F Nalewajski, K Jug, M Randic, G Del Re, U Kaldor, E Eliav, A Landau, M Ehara, M Ishida, K Toyota, H Nakatsuji, G Maroulis, A M Mebel, S Mahapatra, R Carb¢?Dorca, ? Nagy, I A Howard, N H March, S?B Liu, R G Pearson, N Watanabe, S Ten?no, S Iwata, Y Udagawa, E Valderrama, X Fradera, I Silanes, J M Ugalde, R J Boyd, E V Lude¤a, V V Karasiev, L Massa, T Tsuneda, K Hirao, J-M Tao, J P Perdew, O V Gritsenko, M Grning, E J Baerends, F Aparicio, J Garza, A Cedillo, M Galv n, R Vargas, E Engel, A Hck, R N Schmid, R M Dreizler, J Poater, M Sol , M Duran, J Robles, X Fradera, P K Chattaraj, A Poddar, B Maiti, A Cedillo, S Gutirrez?Oliva, P Jaque, A Toro?Labb, H Chermette, P Boulet, S Portmann, P Fuentealba, R Contreras, P Geerlings, F De Proft, R Balawender, D P Chong, A Vela, G Merino, F Kootstra, P L de Boeij, R van Leeuwen, J G Snijders, N T Maitra, K Burke, H Appel, E K U Gross, M K Harbola, H F Hameka, C A Daul, I Ciofini, A Bencini, S K Ghosh, A Tachibana, J M Cabrera?Trujillo, F Tenorio, O Mayorga, M Cases, V Kumar, Y Kawazoe, A M Kster, P Calaminici, Z G¢mez, U Reveles, J A Alonso, L M Molina, M J L¢pez, F Dugue, A Ma¤anes, C A Fahlstrom, J A Nichols, D A Dixon, P A Derosa, A G Zacarias, J M Seminario, D G Kanhere, A Vichare, S A Blundell, Z?Y Lu, H?Y Liu, M Elstner, W?T Yang, J Mu¤oz, X Fradera, M Orozco, F J Luque, P Tarakeshwar, H M Lee, K S Kim, M Valiev, E J Bylaska, A Gramada, J H Weare, J Brickmann, M Keil, T E Exner, M Hoffmann & J Rychlewski.
