Density Functional Theory

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.

Autorentext

David S. Sholl is a Professor of Chemical & Biomolecular
Engineering at the Georgia Institute of Technology, where he holds
the Michael Tennenbaum Family Chair and is a GRA Eminent Scholar in
Energy Sustainability.

Janice A. Steckel is a Physical Scientist at the U.S.
Department of Energy, National Energy Technology Laboratory in
Pittsburgh, Pennsylvania.

Zusammenfassung
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.

Inhalt

Preface xi

1 What Is Density Functional Theory? 1

1.1 How to Approach This Book 1

1.2 Examples of DFT in Action 2

1.2.1 Ammonia Synthesis by Heterogeneous Catalysis 2

1.2.2 Embrittlement of Metals by Trace Impurities 4

1.2.3 Materials Properties for Modeling Planetary Formation 6

1.3 The Schrodinger Equation 7

1.4 Density Functional Theory—From Wave Functions to Electron Density 10

1.5 Exchange–Correlation Functional 14

1.6 The Quantum Chemistry Tourist 16

1.6.1 Localized and Spatially Extended Functions 16

1.6.2 Wave-Function-Based Methods 18

1.6.3 Hartree–Fock Method 19

1.6.4 Beyond Hartree–Fock 23

1.7 What Can DFT Not Do? 28

1.8 Density Functional Theory in Other Fields 30

1.9 How to Approach This Book (Revisited) 30

References 31

Further Reading 32

2 DFT Calculations for Simple Solids 35

2.1 Periodic Structures Supercells and Lattice Parameters 35

2.2 Face-Centered Cubic Materials 39

2.3 Hexagonal Close-Packed Materials 41

2.4 Crystal Structure Prediction 43

2.5 Phase Transformations 44

Exercises 46

Further Reading 47

Appendix Calculation Details 47

3 Nuts and Bolts of DFT Calculations 49

3.1 Reciprocal Space and k Points 50

3.1.1 Plane Waves and the Brillouin Zone 50

3.1.2 Integrals in k Space 53

3.1.3 Choosing k Points in the Brillouin Zone 55

3.1.4 Metals—Special Cases in k Space 59

3.1.5 Summary of k Space 60

3.2 Energy Cutoffs 61

3.2.1 Pseudopotentials 63

3.3 Numerical Optimization 65

3.3.1 Optimization in One Dimension 65

3.3.2 Optimization in More than One Dimension 69

3.3.3 What Do I Really Need to Know about Optimization? 73

3.4 DFT Total Energies—An Iterative Optimization Problem 73

3.5 Geometry Optimization 75

3.5.1 Internal Degrees of Freedom 75

3.5.2 Geometry Optimization with Constrained Atoms 78

3.5.3 Optimizing Supercell Volume and Shape 78

Exercises 79

References 80

Further Reading 80

Appendix Calculation Details 81

4 DFT Calculations for Surfaces of Solids 83

4.1 Importance of Surfaces 83

4.2 Periodic Boundary Conditions and Slab Models 84

4.3 Choosing k Points for Surface Calculations 87

4.4 Classification of Surfaces by Miller Indices 88

4.5 Surface Relaxation 94

4.6 Calculation of Surface Energies 96

4.7 Symmetric and Asymmetric Slab Models 98

4.8 Surface Reconstruction 100

4.9 Adsorbates on Surfaces 103

4.9.1 Accuracy of Adsorption Energies 106

4.10 Effects of Surface Coverage 107

Exercises 110

References 111

Further Reading 111

Appendix Calculation Details 112

5 DFT Calculations of Vibrational Frequencies 113

5.1 Isolated Molecules 114

5.2 Vibrations of a Collection of Atoms 117

5.3 Molecules on Surfaces 120

5.4 Zero-Point Energies 122

5.5 Phonons and Delocalized Modes 127

Exercises 128

Reference 128

Further Reading 128 Appendix Calculation Details 129</...