Wills / Alouani / Andersson Full-Potential Electronic Structure Method

Energy and Force Calculations with Density Functional and Dynamical Mean Field Theory
1. Auflage 2010
ISBN: 978-3-642-15144-6
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 167, 200 Seiten

Reihe: Springer Series in Solid-State Sciences

This is a book describing electronic structure theory and application within the framework of a methodology implemented in the computer code RSPt. In 1986, when the code that was to become RSPt was developed enough to be useful, it was one of the ?rst full-potential, all-electron, relativistic implem- tations of DFT (density functional theory). While RSPt was documented p- asitically in many publications describing the results of its application, it was many years before a publication explicitly describing aspects of the method appeared. In the meantime, several excellent all-electron, full-potential me- ods had been developed, published, and become available. So why a book about RSPt now? The code that became RSPt was initially developed as a personal research tool, rather than a collaborative e?ort or as a product. As such it required some knowledge of its inner workings to use, and as it was meant to be m- imally ?exible, the code required experience to be used e?ectively. These - tributes inhibited, but did not prevent, the spread of RSPt as a research tool. While applicable across the periodic table, the method is particularly useful in describing a wide range of materials, including heavier elements and c- pounds, and its ?exibility provides targeted accuracy and a convenient and accurate framework for implementing and assessing the e?ect of new models.

Autoren/Hrsg.

Wills, John M.

Alouani, Mebarek

Andersson, Per

Delin, Anna

Eriksson, Olle

Grechnyev, Oleksiy

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Part I Formalisms;12
3.1;1 Introductory Information;13
3.1.1;1.1 Objectives and What You Will Learn from Reading This Book;13
3.1.2;1.2 On Units;14
3.1.3;1.3 Obtaining RSPt and the RSPt Web Site;14
3.1.4;1.4 A Short Comment on the History of Linear Muffin-Tin Orbitals and RSPt;14
3.2;2 Density Functional Theory and the Kohn--Sham Equation;17
3.2.1;2.1 The Many-Particle Problem;18
3.2.2;2.2 Early Attempts to Solve the Many-Particle Problem;20
3.2.2.1;2.2.1 Free Electron Model;20
3.2.2.2;2.2.2 The Hartree and Hartree--Fock Approaches;20
3.2.2.3;2.2.3 Thomas--Fermi Theory;21
3.2.3;2.3 Density Functional Theory;22
3.2.3.1;2.3.1 Hohenberg--Kohn Theory;22
3.2.3.2;2.3.2 The Kohn--Sham Equation;24
3.2.3.3;2.3.3 Approximations to Exc[n];26
3.3;3 Consequences of Infinite Crystals and Symmetries;30
3.4;4 Introduction to Electronic Structure Theory;34
3.4.1;4.1 Born--Oppenheimer Approximation and One-Electron Theory;34
3.4.2;4.2 Born--von Karman Boundary Condition and Bloch Waves;34
3.4.3;4.3 Energy Bands and the Fermi Level;35
3.4.4;4.4 Different Types of k-Space Integration;36
3.4.5;4.5 Self-Consistent Fields;40
3.4.6;4.6 Rayleigh--Ritz Variational Procedure;42
3.5;5 Linear Muffin-Tin Orbital Method in the Atomic Sphere Approximation;44
3.5.1;5.1 Muffin-Tin Methods;44
3.5.1.1;5.1.1 The Korringa, Kohn, and Rostoker (KKR) Method;45
3.5.1.2;5.1.2 The KKR-ASA Method;48
3.5.1.3;5.1.3 The LMTO-ASA Method;49
3.5.1.4;5.1.4 Matrix Elements of the Hamiltonian;51
3.5.1.5;5.1.5 Logarithmic Derivatives and Choice of the Linearization Energies;53
3.5.1.6;5.1.6 Advantages of LMTO-ASA Method;54
3.6;6 The Full-Potential Electronic Structure Problem and RSPt;56
3.6.1;6.1 General Aspects;56
3.6.1.1;6.1.1 Notation;56
3.6.1.2;6.1.2 Dividing Space: The Muffin-Tin Geometry;58
3.6.1.3;6.1.3 A Note on the Language of FPLMTO Methods;58
3.6.2;6.2 Symmetric Functions in RSPt;59
3.6.2.1;6.2.1 The Fourier Grid for Symmetric Functions in RSPt;61
3.6.3;6.3 Basis Functions;61
3.6.3.1;6.3.1 Muffin-Tin Orbitals;61
3.6.3.2;6.3.2 FP-LMTO Basis Functions;62
3.6.3.3;6.3.3 Choosing a Basis Set;67
3.6.3.4;6.3.4 Choosing Basis Parameters;67
3.6.4;6.4 Matrix Elements;71
3.6.4.1;6.4.1 Muffin-Tin Matrix Elements;71
3.6.4.2;6.4.2 Interstitial Matrix Elements;72
3.6.5;6.5 Charge Density;75
3.6.6;6.6 Core States;76
3.6.7;6.7 Potential;76
3.6.7.1;6.7.1 Coulomb Potential;76
3.6.7.2;6.7.2 Density Gradients;78
3.6.8;6.8 All-Electron Force Calculations;78
3.6.8.1;6.8.1 Symmetry;78
3.6.8.2;6.8.2 Helmann--Feynman and Incomplete Basis Set Contributions;79
3.7;7 Dynamical Mean Field Theory;83
3.7.1;7.1 Strong Correlations;83
3.7.2;7.2 LDA/GGA+DMFT Method;84
3.7.2.1;7.2.1 LDA/GGA+U Hamiltonian;85
3.7.2.2;7.2.2 LDA/GGA+DMFT Equations;86
3.7.3;7.3 Implementation;88
3.7.3.1;7.3.1 Using the LMTO Basis Set;89
3.7.3.2;7.3.2 Correlated Orbitals;90
3.7.3.3;7.3.3 Other Technical Details;90
3.7.4;7.4 Examples;91
3.7.4.1;7.4.1 Body-Centered Cubic Iron;91
3.7.4.2;7.4.2 Systems Close to Localization, the Hubbard-I Approximation;93
3.8;8 Implementation;96
3.8.1;8.1 Fortran-C Interface;96
3.8.2;8.2 Diagonalization;97
3.8.3;8.3 Fast Fourier Transforms;98
3.8.4;8.4 Parallelization;99
3.9;9 Obtaining RSPt from the Web;101
3.9.1;9.1 Installing RSPt;101
3.9.2;9.2 Running RSPt;102
4;Part II Applications;104
4.1;10 Total Energy and Forces: Some Numerical Examples;105
4.1.1;10.1 Equation of State;105
4.1.1.1;10.1.1 Convergence;109
4.1.2;10.2 Phonon Calculations;110
4.2;11 Chemical Bonding of Solids;114
4.2.1;11.1 Electron Densities;115
4.2.2;11.2 Crystal Orbital Overlap Population (COOP);115
4.2.3;11.3 Equilibrium Volumes of Materials;118
4.2.3.1;11.3.1 Transition Metals;119
4.2.3.2;11.3.2 Lanthanides and Actinides;120
4.2.3.3;11.3.3 Compounds;123
4.2.4;11.4 Cohesive Energy;124
4.2.5;11.5 Structural Stability and Pressure-Induced Phase Transitions;125
4.2.5.1;11.5.1 An sp-Bonded Material, Ca;125
4.2.5.2;11.5.2 Transition Metals;127
4.2.5.3;11.5.3 Systems with f-Electrons;128
4.2.6;11.6 Valence Configuration of f-Elements;129
4.2.7;11.7 Elastic Constants;131
4.3;12 Magnetism;135
4.3.1;12.1 Spin and Orbital Moments of Itinerant Electron Systems;136
4.3.1.1;12.1.1 Symmetry Aspects of Relativistic Spin-Polarized Calculations;138
4.3.1.2;12.1.2 Elements and Compounds;138
4.3.1.3;12.1.3 Surfaces;140
4.3.2;12.2 Magnetic Anisotropy Energy;141
4.3.2.1;12.2.1 k-Space Convergence;142
4.3.2.2;12.2.2 MAE of hcp Gd;143
4.3.3;12.3 Magnetism of Nano-objects;144
4.4;13 Excitated State Properties;146
4.4.1;13.1 Phenomenology;146
4.4.1.1;13.1.1 Index of Refraction and Attenuation Coefficient;149
4.4.1.2;13.1.2 Reflectivity;149
4.4.1.3;13.1.3 Absorption Coefficient;150
4.4.1.4;13.1.4 Energy Loss;150
4.4.1.5;13.1.5 Faraday Effect;150
4.4.1.6;13.1.6 Magneto-optical Kerr Effect;151
4.4.2;13.2 Excited States with DFT: A Contradiction in Terms?;152
4.4.3;13.3 Quasiparticle Theory versus the Local Density Approximation;153
4.4.4;13.4 Calculation of the Dielectric Function;155
4.4.4.1;13.4.1 Dynamical Dielectric Function;155
4.4.4.2;13.4.2 Momentum Matrix Elements;157
4.4.4.3;13.4.3 Velocity Operator and Sum Rules;159
4.4.5;13.5 Optical Properties of Semiconductors;160
4.4.6;13.6 Optical Properties of Metals;163
4.4.7;13.7 Magneto-optical Properties;165
4.4.8;13.8 X-Ray Absorption and X-Ray Magnetic Circular Dichroism;167
4.4.8.1;13.8.1 The XMCD Formalism;168
4.4.8.2;13.8.2 The XMCD Sum Rules;171
4.5;14 A Database of Electronic Structures;180
4.5.1;14.1 Database Generation;180
4.5.2;14.2 Data-Mining: An Example from Scintillating Materials;181
4.6;15 Future Developments and Outlook;183
5;References;186
6;Index;194