Density Functional Theory of Two-dimensional Electronic Structures in a Magnetic Field PDF Download
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Author: Maurizio Ferconi
Publisher:
ISBN:
Category : Electronic structure
Languages : en
Pages : 280
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Book Description
Most of the work done in the physics of two-dimensional structures is either limited by the size of the systems that are studied due to the use of exact diagonalization techniques which do not allow to go beyond structures with only few electrons, or by other methods which do not include exchange-correlation effects, or correlation effects only. There are instances in which these effects cannot be neglected. In order to fill this gap we decided to use a density functional approach, which proved to be reliable in other problems. In Chapter 3 I shall present original results on the study of the ground-state properties of quantum dots in the presence of a magnetic field of arbitrary strength obtained within a current-density functional approach. The results obtained agree very well with those obtained by means of exact diagonalization approaches. In the regime not accessible by the latter methods we show how important are exchange-correlation effects, and we also make an analysis of correlation effects, by comparison with Hartree-Fock results. In Chapter 4 we address and study the density profile at the edge of a confined two-dimensional electron gas in the fractional quantum Hall regime. The strong correlation effects are accounted for in a density functional approach. I show that there exists a transition between two regimes as a function of the smoothness of the confining potential. In Chapter 5, we study the magnetophonon dispersion relations of a two-dimensional Wigner crystal in the presence of a strong magnetic field, and of its shear modulus, that we derived within a density functional scheme, that therefore includes correlation effects, and has the advantage of being analytical. In Chapter 6 I present a theory for the calculation of the pinning gap and magnetophonon spectrum of a disordered Wigner crystal. Its main feature resides in the inclusion in the pinning energy of the contribution arising from distortions of the crystal on all length scales.
Author: Maurizio Ferconi
Publisher:
ISBN:
Category : Electronic structure
Languages : en
Pages : 280
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Book Description
Most of the work done in the physics of two-dimensional structures is either limited by the size of the systems that are studied due to the use of exact diagonalization techniques which do not allow to go beyond structures with only few electrons, or by other methods which do not include exchange-correlation effects, or correlation effects only. There are instances in which these effects cannot be neglected. In order to fill this gap we decided to use a density functional approach, which proved to be reliable in other problems. In Chapter 3 I shall present original results on the study of the ground-state properties of quantum dots in the presence of a magnetic field of arbitrary strength obtained within a current-density functional approach. The results obtained agree very well with those obtained by means of exact diagonalization approaches. In the regime not accessible by the latter methods we show how important are exchange-correlation effects, and we also make an analysis of correlation effects, by comparison with Hartree-Fock results. In Chapter 4 we address and study the density profile at the edge of a confined two-dimensional electron gas in the fractional quantum Hall regime. The strong correlation effects are accounted for in a density functional approach. I show that there exists a transition between two regimes as a function of the smoothness of the confining potential. In Chapter 5, we study the magnetophonon dispersion relations of a two-dimensional Wigner crystal in the presence of a strong magnetic field, and of its shear modulus, that we derived within a density functional scheme, that therefore includes correlation effects, and has the advantage of being analytical. In Chapter 6 I present a theory for the calculation of the pinning gap and magnetophonon spectrum of a disordered Wigner crystal. Its main feature resides in the inclusion in the pinning energy of the contribution arising from distortions of the crystal on all length scales.
Author: Sidney Yip
Publisher: Springer Science & Business Media
ISBN: 1402032862
Category : Science
Languages : en
Pages : 2903
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Book Description
The first reference of its kind in the rapidly emerging field of computational approachs to materials research, this is a compendium of perspective-providing and topical articles written to inform students and non-specialists of the current status and capabilities of modelling and simulation. From the standpoint of methodology, the development follows a multiscale approach with emphasis on electronic-structure, atomistic, and mesoscale methods, as well as mathematical analysis and rate processes. Basic models are treated across traditional disciplines, not only in the discussion of methods but also in chapters on crystal defects, microstructure, fluids, polymers and soft matter. Written by authors who are actively participating in the current development, this collection of 150 articles has the breadth and depth to be a major contributor toward defining the field of computational materials. In addition, there are 40 commentaries by highly respected researchers, presenting various views that should interest the future generations of the community. Subject Editors: Martin Bazant, MIT; Bruce Boghosian, Tufts University; Richard Catlow, Royal Institution; Long-Qing Chen, Pennsylvania State University; William Curtin, Brown University; Tomas Diaz de la Rubia, Lawrence Livermore National Laboratory; Nicolas Hadjiconstantinou, MIT; Mark F. Horstemeyer, Mississippi State University; Efthimios Kaxiras, Harvard University; L. Mahadevan, Harvard University; Dimitrios Maroudas, University of Massachusetts; Nicola Marzari, MIT; Horia Metiu, University of California Santa Barbara; Gregory C. Rutledge, MIT; David J. Srolovitz, Princeton University; Bernhardt L. Trout, MIT; Dieter Wolf, Argonne National Laboratory.
Author: Viraht Sahni
Publisher: Springer
ISBN: 3662498421
Category : Science
Languages : en
Pages : 417
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Book Description
This book is on quantal density functional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the ‘quantal Newtonian’ second and first laws for the individual electron. These laws are in terms of ‘classical’ fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schrödinger theory from the new perspective of the single electron in terms of the ‘quantal Newtonian’ laws. Hohenberg-Kohn density functional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.
Author: David S. Sholl
Publisher: John Wiley & Sons
ISBN: 1118211049
Category : Science
Languages : en
Pages : 252
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Book Description
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.
Author: Viraht Sahni
Publisher: Springer Science & Business Media
ISBN: 3540922296
Category : Science
Languages : en
Pages : 426
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Book Description
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.
Author: David S. Sholl
Publisher: John Wiley & Sons
ISBN: 1119840864
Category : Science
Languages : en
Pages : 228
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Book Description
Density Functional Theory A concise and rigorous introduction to the applications of DFT calculations In the newly revised second edition of Density Functional Theory: A Practical Introduction, the authors deliver a concise and easy-to-follow introduction to the key concepts and practical applications of density functional theory (DFT) with an emphasis on plane-wave DFT. The authors draw on decades of experience in the field, offering students from a variety of backgrounds a balanced approach between accessibility and rigor, creating a text that is highly digestible in its entirety. This new edition: Discusses in more detail the accuracy of DFT calculations and the choice of functionals Adds an overview of the wide range of available DFT codes Contains more examples on the use of DFT for high throughput materials calculations Puts more emphasis on computing phase diagrams and on open ensemble methods widely used in electrochemistry Is significantly extended to cover calculation beyond standard DFT, e.g., dispersion-corrected DFT, DFT+U, time-dependent DFT Perfect for graduate students and postdoctoral candidates in physics and engineering, Density Functional Theory: A Practical Introduction will also earn a place in the libraries of researchers and practitioners in chemistry, materials science, and mechanical engineering.
Author: P. Politzer
Publisher: Elsevier
ISBN: 0080536700
Category : Science
Languages : en
Pages : 419
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Book Description
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.
Author: D.E. Ellis
Publisher: Springer Science & Business Media
ISBN: 9401104875
Category : Science
Languages : en
Pages : 321
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Book Description
Rapid advances are taking place in the application of density functional theory (DFT) to describe complex electronic structures, to accurately treat large systems and to predict physical and chemical properties. Both theoretical content and computational methodology are developing at a pace which offers researchers new opportunities in areas such as quantum chemistry, cluster science, and solid state physics. This volume contains ten contributions by leading scientists in the field and provides an authoritative overview of the most important developments. The book focuses on the following themes: determining adequate approximations for the many-body problem of electronic correlations; how to transform these approximations into computational algorithms; applications to discover and predict properties of electronic systems; and developing the theory. For researchers in surface chemistry, catalysis, ceramics and inorganic chemistry.
Author: Carlos Fiolhais
Publisher: Springer Science & Business Media
ISBN: 3540030832
Category : Science
Languages : en
Pages : 290
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Book Description
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.
Author: Daniel Glossman-Mitnik
Publisher: BoD – Books on Demand
ISBN: 178985167X
Category : Science
Languages : en
Pages : 168
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Book Description
Density Functional Theory (or DFT for short) is a potent methodology useful for calculating and understanding the molecular and electronic structure of atoms, molecules, clusters, and solids. Its use relies not only in the ability to calculate the molecular properties of the species of interest but also provides interesting concepts that allow a better comprehension of the chemical reactivity of the studied systems. This book represents an attempt to present examples on the utility of DFT for the understanding of the chemical reactivity through descriptors that constitute the basis of the so called Conceptual DFT (sometimes also named as Chemical Reactivity Theory) as well as the application of the theory and its related computational procedures in the determination of the molecular properties of different systems of academic and industrial interest.
