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 Electronic Density Functional Theory written by John F. Dobson and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an outcome of the International Workshop on Electronic Density Functional Theory, held at Griffith University in Brisbane, Australia, in July 1996. Density functional theory, standing as it does at the boundary between the disciplines of physics, chemistry, and materials science, is a great mixer. Invited experts from North America, Europe, and Australia mingled with students from several disciplines, rapidly taking up the informal style for which Australia is famous. A list of participants is given at the end of the book. Density functional theory (DFT) is a subtle approach to the very difficult problem of predicting the behavior of many interacting particles. A major application is the study of many-electron systems. This was the workshop theme, embracing inter alia computational chemistry and condensed matter physics. DFT circumvents the more conceptually straightforward (but more computationally intensive) approach in which one solves the many-body Schrodinger equation. It relies instead on rather delicate considerations involving the electron number density. For many years the pioneering work of Kohn and Sham (the Local Density Ap proximation of 1965 and immediate extensions) represented the state of the art in DFT. This approach was widely used for its appealing simplicity and computability, but gave rather modest accuracy. In the last few years there has been a renaissance of interest, quite largely due to the remarkable success of the new generation of gradient functionals whose initiators include invitees to the workshop (Perdew, Parr, Yang).

Download or read book Theoretical prediction of properties of atomistic systems written by Alexander Lindmaa and published by Linköping University Electronic Press. This book was released on 2017-08-15 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: The prediction of ground state properties of atomistic systems is of vital importance in technological advances as well as in the physical sciences. Fundamentally, these predictions are based on a quantum-mechanical description of many-electron systems. One of the hitherto most prominent theories for the treatment of such systems is density functional theory (DFT). The main reason for its success is due to its balance of acceptable accuracy with computational efficiency. By now, DFT is applied routinely to compute the properties of atomic, molecular, and solid state systems. The general approach to solve the DFT equations is to use a density-functional approximation (DFA). In Kohn-Sham (KS) DFT, DFAs are applied to the unknown exchangecorrelation (xc) energy. In orbital-free DFT on the other hand, where the total energy is minimized directly with respect to the electron density, a DFA applied to the noninteracting kinetic energy is also required. Unfortunately, central DFAs in DFT fail to qualitatively capture many important aspects of electronic systems. Two prime examples are the description of localized electrons, and the description of systems where electronic edges are present. In this thesis, I use a model system approach to construct a DFA for the electron localization function (ELF). The very same approach is also taken to study the non-interacting kinetic energy density (KED) in the slowly varying limit of inhomogeneous electron densities, where the effect of electronic edges are effectively included. Apart from the work on model systems, extensions of an exchange energy functional with an improved KS orbital description are presented: a scheme for improving its description of energetics of solids, and a comparison of its description of an essential exact exchange feature known as the derivative discontinuity with numerical data for exact exchange. An emerging alternative route towards the prediction of the properties of atomistic systems is machine learning (ML). I present a number of ML methods for the prediction of solid formation energies, with an accuracy that is on par with KS DFT calculations, and with orders-of-magnitude lower computational cost. Att kunna förutsäga egenskaper hos atomistiska system utgör en viktigdel av vår teknologiska utveckling, samt spelar en betydande roll i defysikaliska vetenskaperna. Sådana förutsägelser bygger på en kvantmekaniskbeskrivning av mångelektronsystem. En av de mest framståendeteorierna för att behandla den här typen av system är täthetsfunktionalteorin(DFT). Den främsta orsaken till dess framgång är attden lyckas kombinera skaplig noggrannhet med en bra beräkningseffektivitet.DFT används numera rutinmässigt för att beräkna storheterhos atomer, molekyler, och fasta kroppar. Generellt sett löses ekvationerna inom DFT genom att man inför entäthetsfunktionalapproximation (DFA). I Kohn-Sham (KS) DFT, användsDFAer för att approximera utbytes-korrelationsenergin. Inom orbitalfriDFT, där målet är att direkt minimera den totala energin med avseendepå elektrontätheten, så approximerar man också den icke-interageranderörelseenergin hos elektronerna. Dessvärre så fallerar många centralaDFAer att kvalitativt beskriva många viktiga aspekter hos elektronsystem.Två viktiga exempel är beskrivningen av lokaliserade elektroner,samt beskrivningen av system där det förekommer elektronytor. I denna avhandling använder jag modellsystem för att konstruera enDFAför elektronlokaliseringsfunktionen (ELF). Samma tillvägagångssättappliceras sedan för att studera den kinetiska energitätheten i gränsen avlångsamt varierande elektrontätheter, där effekten av elektronytor effektivtinkluderas. Förutom arbetet som berör modellsystem, så presenterasen utökad variant av en utbytes-energifunktional med en förbättrad KSorbitalbeskrivning: ett schema för att förbättra dess energiegenskaperför solida material, samt en jämförelse av dess beskrivning av en viktigegenskap hos den exakta utbytesenergin, vilket utgörs av diskontinuiteteri dess derivata. Ett mera nyligen uppkommet samt alternativt sätt att kunna förutsägaegenskaper hos atomistiska system utgörs av maskinlärning (ML).Jag presenterar ett antal ML-modeller för att kunna förutsäga formeringsenergierhos fasta material med en noggrannhet som är i linje medresultat som uppnås av beräkningar med hjälp av KS DFT, och med enberäkningseffektivitet som är flera storleksordningar snabbare.

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 Density Functional Theory written by Reiner M. Dreizler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density Functional Theory is a rapidly developing branch of many-particle physics that has found applications in atomic, molecular, solid-state and nuclear physics. This book describes the conceptual framework of density functional theory and discusses in detail the derivation of explicit functionals from first principles as well as their application to Coulomb systems. Both non-relativistic and relativistic systems are treated. The connection of density functional theory with other many-body methods is highlighted. The presentation is self-contained; the book is, thus, well suited for a graduate course on density functional theory.

Download or read book Quantal Density Functional Theory II written by Viraht Sahni and published by Springer Science & Business Media. This book was released on 2009-10-16 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In my original proposal to Springer for a book on Quantal Density Functional Theory, I had envisaged one that was as complete in its presentation as possible, describing the basic theory as well as the approximation methods and a host of applications. However,after workingon the bookforabout ?ve years, I realizedthat the goal was too ambitious, and that I would be writing for another ?ve years for it to be achieved. Fortunately,there was a natural breakin the material, and I proposed to my editor, Dr. Claus Ascheron, that we split the book into two components: the ?rst on the basic theoretical framework, and the second on approximation methods and applications. Dr. Ascheron consented, and I am thankful to him for agreeing to do so. Hence, we published Quantal Density Functional Theory in 2004, and are now publishing Quantal Density Functional Theory II: Approximation Methods and Applications. One signi?cant advantage of this, as it turns out, is that I have been able to incorporate in each volume the most recent understandings available. This volume, like the earlier one, is aimed at advanced undergraduates in physics and chemistry, graduate students and researchers in the ?eld. It is written in the same pedagogical style with details of all proofs and numerous ?gures provided to explain the physics. The book is independent of the ?rst volume and stands on its own. However, proofs given in the ?rst volume are not repeated here.

Download or read book Recent Progress in Orbital free Density Functional Theory written by Tomasz A. Wesolowski and published by World Scientific. This book was released on 2013 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive overview of state-of-the-art computational methods based on orbital-free formulation of density functional theory completed by the most recent developments concerning the exact properties, approximations, and interpretations of the relevant quantities in density functional theory.The book is a compilation of contributions stemming from a series of workshops which had been taking place since 2002. It not only chronicles many of the latest developments but also summarises some of the more significant ones. The chapters are mainly reviews of sub-domains but also include original research.

Download or read book Density Functional Theory of Many electron Systems in Strong Imposed Magnetic Fields written by Shiwei Li and published by . This book was released on 1990 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Primer in Density Functional Theory written by Carlos Fiolhais and published by Springer. This book was released on 2008-01-11 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional theory (DFT) is by now a well-established method for tackling the quantum mechanics of many-body systems. Originally applied to compute properties of atoms and simple molecules, DFT has quickly become a work horse for more complex applications in the chemical and materials sciences. The present set of lectures, spanning the whole range from basic principles to relativistic and time-dependent extensions of the theory, is the ideal introduction for graduate students or nonspecialist researchers wishing to familiarize themselves with both the basic and most advanced techniques in this field.

Download or read book The Fundamentals of Density Functional Theory written by and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density functional methods form the basis of a diversified and very active area of present days computational atomic, molecular, solid state and even nuclear physics. A large number of computational physicists use these meth ods merely as a recipe, not reflecting too much upon their logical basis. One also observes, despite of their tremendeous success, a certain reservation in their acceptance on the part of the more theoretically oriented researchers in the above mentioned fields. On the other hand, in the seventies (Thomas Fermi theory) and in the eighties (Hohenberg-Kohn theory), density func tional concepts became subjects of mathematical physics. In 1994 a number of activities took place to celebrate the thirtieth an niversary of Hohenberg-Kohn-Sham theory. I took this an occassion to give lectures on density functional theory to senior students and postgraduates in the winter term of 1994, particularly focusing on the logical basis of the the ory. Preparing these lectures, the impression grew that, although there is a wealth of monographs and reviews in the literature devoted to density func tional theory, the focus is nearly always placed upon extending the practical applications of the theory and on the development of improved approxima tions. The logical foundadion of the theory is found somewhat scattered in the existing literature, and is not always satisfactorily presented. This situation led to the idea to prepare a printed version of the lecture notes, which resulted in the present text.

Download or read book Density Functional Theory written by Eberhard Engel and published by Springer Science & Business Media. This book was released on 2011-02-14 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory.

Download or read book Modern Density Functional Theory A Tool For Chemistry written by P. Politzer and published by Elsevier. This book was released on 1995-01-27 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Density Functional Theory (DFT) is currently receiving a great deal of attention as chemists come to realize its important role as a tool for chemistry. This book covers the theoretical principles of DFT, and details its application to several contemporary problems. All current techniques are covered, many are critically assessed, and some proposals for the future are reviewed. The book demonstrates that DFT is a practical solution to the problems standard ab initio methods have with chemical accuracy.The book is aimed at both the theoretical chemist and the experimentalist who want to relate their experiments to the governing theory. It will prove a useful and enduring reference work.

Download or read book Energy Functionals for Inhomogeneous Many electron Systems written by and published by . This book was released on 1991 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary purpose of these lectures is to provide a pedagogical introduction Density Functional Theory (DF). We begin with the very early picture of Thomas and Fermi for the ground state energy of a neutral atom and proceed to the highly successful method of Kohn and Sham (KS) which focuses attention on the exchange-correlation contribution E{sub XC}(n) to the energy functional. We stress the importance of a systematic approach to the study of the subtle nonlocal structure of E{sub XC}(n) in inhomogeneous systems. The local and global convergence properties of gradient expansions are examined in some detail for detail for both density and low density systems. The structure of E{sub XC}(n) in the low density regime is described. Aspects of energy functionals which are determined by global symmetries and boundary conditions (in contrast to largely local energetics) are illustrated by the examples of the structure factor in bounded geometry and band gap discontinuities in semiconductors. An illustrative application of DFT is made to the problem of instabilities of the strongly correlated low density electron liquid with respect to charge modulated ground states.

Download or read book Recent Advances in Density Functional Methods written by Delano Pun Chong and published by World Scientific. This book was released on 1995 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of all the different areas in computational chemistry, density functional theory (DFT) enjoys the most rapid development. Even at the level of the local density approximation (LDA), which is computationally less demanding, DFT can usually provide better answers than Hartree-Fock formalism for large systems such as clusters and solids. For atoms and molecules, the results from DFT often rival those obtained by ab initio quantum chemistry, partly because larger basis sets can be used. Such encouraging results have in turn stimulated workers to further investigate the formal theory as well as the computational methodology of DFT.This volume contains ten contributions from active workers in DFT, covering topics from basic principles to methodology to applications. In the Foreword, Prof Walter Kohn gives his perspective on the recent advances in DFT. Because DFT is being developed in so many different directions, no single volume can provide a complete review of DFT. However, this volume will help both beginners and experimentalists to read the growing DFT literature more easily.

Download or read book Density Functional Methods In Physics written by Reiner M. Dreizler and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Density Functional Theory in Quantum Chemistry written by Takao Tsuneda and published by Springer Science & Business Media. This book was released on 2014-02-18 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, density functional theory (DFT) is introduced within the overall context of quantum chemistry. DFT has become the most frequently used theory in quantum chemistry calculations. However, thus far, there has been no book on the fundamentals of DFT that uses the terminology and methodology of quantum chemistry, which is familiar to many chemists, including experimentalists. This book first reviews the basic concepts and historical background of quantum chemistry and then explains those of DFT, showing how the latter fits into the bigger picture. Recent interesting topics of DFT in chemistry are also targeted. In particular, the physical meanings of state-of-the-art exchange-correlation functionals and their corrections are described in detail. Owing to its unconventionality, this book is certain to be of great interest not only to chemists but also to solid state physicists.

Download or read book Many Electron Approaches in Physics Chemistry and Mathematics written by Volker Bach and published by Springer. This book was released on 2014-07-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.