Download or read book Complex energy Approach to Sum Rules Within Nuclear Density Functional Theory written by and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.
Download or read book Nuclear Density Functional Theory written by I. Zh Petkov and published by . This book was released on 1991 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the enormous amount of material accumulated in the field of nuclear density functional theory over the last few decades. The goal of the theory is to provide a complete quantum mechanical description and explanation of nuclear phenomena in terms of the local density distribution as a basic ingredient rather than the many particle wavefunction. This leads to a considerable reduction in the mathematical complexity of nuclear many-body problems and to a great conceptual simplicity and visual clarity in its theoretical treatment. The authors develop the mathematical framework on which the theory is based and consider the associated approaches used to analyze experimental data in a variety of nuclei and nuclear processes with widely differing properties.
Download or read book Extended Density Functionals in Nuclear Structure Physics written by G. A. Lalazissis and published by Springer Science & Business Media. This book was released on 2004-03-25 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The experimental and theoretical investigation of nuclei far from the valley of beta-stability is the main subject of modern nuclear structure research. Although the most successful nuclear structure models are purely phenomenological, they nevertheless exploit basic properties of QCD at low energies. This book focuses on the current efforts to bridge the gap between phenomenology and the principles derived from QCD using the extended density functional approach which is based on the successful DFT methods to tackle similarly complex interacting systems in molecular and condensed matter physics. Conceived as a series of pedagogical lectures, this volume addresses researchers in the field as well as postgraduate students and non-specialized scientists from related areas who seek a high-level but accessible introduction to the subject.
Download or read book Exploring the Energy Density Functional with High performance Computing written by Erik Michael Olsen and published by . This book was released on 2014 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: For theoretical nuclear physics to make predictions on nuclei far from stability it is necessary to develop a framework where meaningful calculations can be made throughout the nuclear chart. Such a framework has been established; using nuclear Density Functional Theory (DFT) along with massively parallel computing, it is now possible to make large-scale mass table calculations in a short period of time. For this work, large-scale mass tables were made using Skyrme Energy Density Functionals (EDFs). In order to determine the statistical and systematic uncertainties of these calculations, six different EDFs were used. Using ground state binding energy, pairing gap, radius, and deformation data from these tables, the following global properties were analyzed: the two-proton and two-neutron driplines, two-proton radioactivity, ground state reflection-asymmetric shapes, and neutron-skin thicknesses. These data were also used in the development of a new EDF. Lastly, in an effort to better understand nuclear collective modes, massively parallel computational techinques were used in the development of a method to calculate the sum rules for giant resonances.
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 Energy Density Functional Methods for Atomic Nuclei written by Nicolas Schunck and published by Iph001. This book was released on 2019-01-28 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy density functional (EDF) approaches have become over the past twenty years a powerful framework to study the structure and reactions of atomic nuclei. This book gives an updated presentation of non-relativistic and covariant energy functionals, single- and multi-reference methods, and techniques to describe small- and large-amplitude collective motion or nuclei at high excitation energy. Edited by an expert in energy density functional theory, Dr Nicolas Schunck, alongside several experts within the field, this book provides a comprehensive and informative exploration of EDF methods. Detailed derivations, practical approaches, examples and figures are used throughout the book to give a coherent narrative of topics that have hitherto rarely been covered together.
Download or read book Density Functional Theory written by David S. Sholl and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Demonstrates how anyone in math, science, and engineering can master DFT calculations Density functional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. Density Functional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to students from a variety of backgrounds. The book therefore offers several features that have proven to be helpful in enabling students to master the subject, including: Problem sets in each chapter that give readers the opportunity to test their knowledge by performing their own calculations Worked examples that demonstrate how DFT calculations are used to solve real-world problems Further readings listed in each chapter enabling readers to investigate specific topics in greater depth This text is written at a level suitable for individuals from a variety of scientific, mathematical, and engineering backgrounds. No previous experience working with DFT calculations is needed.
Download or read book Theory of the Inhomogeneous Electron Gas written by Stig Lundqvist and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the inhomogeneous electron gas had its origin in the Thomas Fermi statistical theory, which is discussed in the first chapter of this book. This already leads to significant physical results for the binding energies of atomic ions, though because it leaves out shell structure the results of such a theory cannot reflect the richness of the Periodic Table. Therefore, for a long time, the earlier method proposed by Hartree, in which each electron is assigned its own personal wave function and energy, dominated atomic theory. The extension of the Hartree theory by Fock, to include exchange, had its parallel in the density description when Dirac showed how to incorporate exchange in the Thomas-Fermi theory. Considerably later, in 1951, Slater, in an important paper, showed how a result similar to but not identical with that of Dirac followed as a simplification of the Hartree-Fock method. It was Gombas and other workers who recognized that one could also incorporate electron correlation consistently into the Thomas-Fermi-Dirac theory by using uniform electron gas relations locally, and progress had been made along all these avenues by the 1950s.
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 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 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 344 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 Part II expands on the methodology and applications of DFT. Some of the chapters report on the latest developments (since the publication of Part I in 1995), while others extend the applications to wider range of molecules and their environments. Together, this and other recent review volumes on DFT show that DFT provides an efficient and accurate alternative to traditional quantum chemical methods. Such demonstration should hopefully stimulate frutiful developments in formal theory, better exchange-correlation functionals, and linear scaling methodology.
Download or read book Construction of First principles Density Functional Approximations and Their Applications to Materials written by Aaron Kaplan and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kohn-Sham density functional theory is a rigorous formulation of many-electron quantum mechanics which, for practical purposes, requires approximation of one term in its total energy expression: the exchange-correlation energy. This work elucidates systematic methods for constructing approximations to the exchange-correlation energy solely from first-principles physics. We review the constraints that can be built into approximate density functionals, and use thermochemical data to argue that satisfaction of these constraints permits a more general description of electronic matter. Contact with semiclassical physics is made by studying the turning surfaces of Kohn-Sham potentials in solids. Perfect metals and covalently-bound, narrow-gap insulators do not have turning surfaces at equilibrium, but do under expansive strain. Wide-gap insulators, ionic crystals, and layered solids tend to have turning surfaces at equilibrium. Chemical bonds in solids are classified using the turning surface radii of its constituent atoms. Depletion of the charge density, such as near a monovacancy in platinum, is shown to produce a turning surface. Further, this work demonstrates why generalized gradient approximations (GGAs) are often able to describe some properties of sp-bonded narrow-gap insulators well. A Laplacian-level pure-density functional is developed with the goal of describing metallic condensed matter. This functional is derived from the r2SCAN orbital-dependent meta-GGA, and reduces its tendency to over-magnetize ferromagnets; improves its description of the equation of state properties of alkali metals; and improves its description of intermetallic thermodynamics. It is constructed to enforce the fourth-order exchange gradient expansion constraint (not satisfied by r2SCAN), and a few free parameters are fitted to paradigmatic metallic systems: jellium surfaces and closed-shell jellium clusters. Last, we modify an exchange-correlation kernel that describes the density-density response of jellium to better satisfy known frequency sum rules. We also constrain the kernel to reproduce the correlation energies of jellium, and compare it to a wide variety of common kernels in use for linear response, time-dependent density functional theory calculations.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976-03 with total page 938 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Density Functional Theory of Atoms and Molecules written by Robert G. Parr and published by Oxford University Press. This book was released on 1994-05-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a rigorous, unified account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. Containing a detailed discussion of the chemical potential and its derivatives, it provides an understanding of the concepts of electronegativity, hardness and softness, and chemical reactivity. Both the Hohenberg-Kohn-Sham and the Levy-Lieb derivations of the basic theorems are presented, and extensive references to the literature are included. Two introductory chapters and several appendices provide all the background material necessary beyond a knowledge of elementary quantum theory. The book is intended for physicists, chemists, and advanced students in chemistry.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
