Planewaves, Pseudopotentials, and the LAPW Method / Edition 2

Planewaves, Pseudopotentials, and the LAPW Method / Edition 2

by David J. Singh, Lars Nordstrom
     
 

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ISBN-10: 0387287809

ISBN-13: 9780387287805

Pub. Date: 11/29/2005

Publisher: Springer US

With its extreme accuracy and reasonable computational efficiency, the linearized augmented plane wave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. The second edition of Planewaves, Pseudopotentials and the LAPW Method presents an updated, thorough and

Overview

With its extreme accuracy and reasonable computational efficiency, the linearized augmented plane wave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. The second edition of Planewaves, Pseudopotentials and the LAPW Method presents an updated, thorough and self-contained exposition of the first principles methods for calculating properties of solids, in particular the "LAPW" method and will make connections between this method and planewave pseudopotential approaches. Theory is discussed, but the emphasis is on how practical implementation proceeds. In addition, the author suggests future directions for adapting the LAPW method to simulations of complex materials requiring large unit cells. He does this by elucidating the connections between the LAPW method and planewave pseudopotential approaches and by showing how Car-Parrinello type algorithms can be adapted to the LAPW method. The new edition contains new sections on developments over the last 10 years, including for example the LDA+U method, non-collinear magnetism and the APW+LO method.

Product Details

ISBN-13:
9780387287805
Publisher:
Springer US
Publication date:
11/29/2005
Edition description:
2nd ed. 2006
Pages:
134
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

Related Subjects

Table of Contents

Dedication v

List of Figures ix

Preface xi

1 Introduction 1

2 Density Functional Theory and Methods 5

2.1 Density Functional Theory 6

2.2 Solution of the Single Particle Kohn-Sham Equations 10

2.3 Self-Consistency in Density Functional Calculations 13

2.4 Spin-Polarized Systems 16

2.5 Non-Collinear Magnetism 18

2.6 The LDA+U Method 20

3 Planewave Pseudopotential Methods 23

3.1 Why Planewaves 24

3.2 Pseudopotentials 26

3.3 Introduction to the Car-Parrinello Method 36

4 Introduction to the LAPW Method 43

4.1 The Augmented Planewave Method 43

4.2 The LAPW Basis and its Properties 46

4.3 Role of the Linearization Energies 49

5 Nitty-Gritties 53

5.1 Representations of the Charge Density and Potential 53

5.2 Solution of Poisson's Equation 57

5.3 The Exchange Correlation Potential 60

5.4 Synthesis of the LAPW Basis Functions 62

5.5 Synthesis of the Hamiltonian and Overlap Matrices 67

5.6 Brillouin Zone Integration and the Fermi Energy 73

5.7 Computation of the Valence Charge Density 78

5.8 Core State Relaxation and Atomic Charge Densities 81

5.9 Multiple Windows and Local Orbital Extensions 83

5.10 The APW+LO Basis Set 88

5.11 Charge Density Mixing for Self-Consistency 90

5.12 Fixed Spin Moment Calculations 92

5.13 The Total Energy 94

5.14 Atomic Forces 95

5.15 Density Functional Perturbation Theory and Linear Response 99

5.16 Second Variational Treatment of Spin-Orbit Effects 102

5.17 Spin-Orbit with p[subscript 1/2] Local Orbitals 105

5.18 Iterative Diagonalization 106

6 Car-Parrinello and the LAPW Method 107

6.1 Preliminaries 107

6.2 The Transformation of Goedecker and Maschke 109

6.3 The Transformation of Singhet al. 113

6.4 Status and Outlook 121

References 123

Index 133

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