Full-Potential Electronic Structure Method (eBook)

John Wills is a Technical Staff Member in the Theoretical Division at Los Alamos National Laboratory, current serving as Group Leader of the Physics and Chemistry of Materials Group. He has worked on electronic structure theory and application for the past 27 years, and is an author on 170 publications in this area, 61 of which are on the electronic structure of f-electron elements and compounds. Olle Eriksson has been active in the theory of electronic structure of materials for 25 years, and has published some 400 articles in this field. He is currently chair professor at the Department of Physics and Materials Science, Uppsala University. Per Andersson is currently Senior Scientist at the Swedish Defence Research Agency and has been active in the field for 15 years. Anna Delin has been active in the theory of electronic structure of materials for 15 years, and has published some 100 articles in this field. She is currently associate professor at the Department of Physics and Materials Science, Uppsala University. Oleksiy Grechnyev is has been active in the theory of electronic structure of materials and magnetism for 10 years, and has published 16 articles in this field (using name spelling A. Grechnev). He has graduated from Kharkiv National University (Ukraine) and obtained a PhD degree in Uppsala University (Sweden). He is currently researcher at Department of Theoretical Physics, B. Verkin Institute for Low Temperature Physics and Engineering (Kharkov, Ukraine). Mebarek Alouani has been working on theory of electronic structure and spectroscopy for 26 years, and has published more than 100 articles and books in this field. He is currently full professor at the Institute of Physics and Chemistry of Materials of Strasbourg (IPCMS) of the University of Strasbourg, France.

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