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Atomistic Computer Simulations: A Practical Guide

ISBN: 978-3-527-41069-9
361 pages
April 2013
Atomistic Computer Simulations: A Practical Guide (3527410694) cover image

Many books explain the theory of atomistic computer simulations; this book teaches you how to run them


This introductory "how to" title enables readers to understand, plan, run, and analyze their own independent atomistic simulations, and decide which method to use and which questions to ask in their research project. It is written in a clear and precise language, focusing on a thorough understanding of the concepts behind the equations and how these are used in the simulations. As a result, readers will learn how to design the computational model and which parameters of the simulations are essential, as well as being able to assess whether the results are correct, find and correct errors, and extract the relevant information from the results. Finally, they will know which information needs to be included in their publications.

This book includes checklists for planning projects, analyzing output files, and for troubleshooting, as well as pseudo keywords and case studies.

The authors provide an accompanying blog for the book with worked examples, and additional material and references: http://www.atomisticsimulations.org/.

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Preface XV

References XVI

Color Plates XVII

Part One The World at the Atomic Scale 1

1 Atoms, Molecules and Crystals 3

1.1 Length- and Timescales 3

1.2 Electrons in an Atom 5

1.3 Local Environment of an Atom 8

1.3.1 Electrons 8

1.3.2 Local Arrangement of Atoms 11

1.4 Most Favorable Arrangement of Atoms 12

1.4.1 The Concept of Total Energy 12

1.4.2 Beyond the Total Energy 13

1.4.3 The Most Stable Configuration 15

References 16

2 Bonding 17

2.1 Electronic Ground State 18

2.2 Types of Bonds 18

2.2.1 Covalent Bonding 21

2.2.2 Ionic Bonding 22

2.2.3 Metallic Bonding 24

2.2.4 Hydrogen Bonding 25

2.2.5 Dispersion Bonding 25

2.3 Bond Breaking and Creation 26

2.4 Distortion of Bonds 27

References 29

3 Chemical Reactions 31

3.1 Chemical Equations 31

3.2 Reaction Mechanisms 32

3.3 Energetics of Chemical Reactions 33

3.4 Every (Valence) Electron Counts 37

3.5 The Energy Zoo 38

References 39

4 What Exactly is Calculated? 41

4.1 What Can Be Calculated? 41

4.2 What Actually Happens? 43

4.3 Models and Simulation Cells 44

4.4 Energies 47

4.5 Terms 48

4.6 Liquid Iron: An Example 50

References 53

Part Two Introducing Equations to Describe the System 55

5 Total Energy Minimization 57

5.1 The Essential Nature of Minimization 58

5.2 Minimization Algorithms 59

5.2.1 Steepest Descents 61

5.2.2 Conjugate Gradients 62

5.2.3 Quasi-Newton Methods 62

5.2.4 Alternatives 63

5.2.5 Exploring Landscapes 64

5.2.6 Scaling and Computational Cost 66

5.3 Optimize with Success 67

5.3.1 Initial Configuration 67

5.3.2 Initial Forces, Choice of Algorithm and Parameters 68

5.3.3 Fixing Atoms 69

5.3.4 Scaling with System Size 70

5.4 Transition States 71

5.5 Pseudokeywords 72

References 73

6 Molecular Dynamics and Monte Carlo 75

6.1 Equations of Motion 76

6.2 Time and Timescales 77

6.3 System Preparation and Equilibration 79

6.4 Conserving Temperature, Pressure, Volume or Other Variables 81

6.5 Free Energies 83

6.6 Monte Carlo Approaches 84

6.7 Pseudokeywords for an MD Simulation 86

References 87

Part Three Describing Interactions Between Atoms 89

7 Calculating Energies and Forces 91

7.1 Forcefields 92

7.1.1 Reliability and Transferability 95

7.2 Electrostatics 97

7.3 Electronic and Atomic Motion 98

7.3.1 The Born–Oppenheimer Approximation 99

7.3.2 Approximating the Electronic Many-Body Problem 100

7.4 Electronic Excitations 100

References 103

8 Electronic Structure Methods 105

8.1 Hartree–Fock 106

8.2 Going Beyond Hartree–Fock 109

8.3 Density Functional Theory 111

8.4 Beyond DFT 114

8.5 Basis Sets 116

8.6 Semiempirical Methods 119

8.7 Comparing Methods 121

References 124

9 Density Functional Theory in Detail 127

9.1 Independent Electrons 127

9.2 Exchange-Correlation Functionals 128

9.3 Representing the Electrons: Basis Sets 130

9.3.1 Plane Waves 131

9.3.2 Atomic-Like Orbitals 132

9.4 Electron–Nuclear Interaction 133

9.4.1 Pseudopotentials 133

9.4.2 PAW 136

9.4.3 Using All Electrons 136

9.5 Solving the Electronic Ground State 136

9.5.1 Charge Mixing and Electrostatics 137

9.5.2 Metals and Occupancy 139

9.6 Boundary Conditions and Reciprocal Space 139

9.7 Difficult Problems 141

9.8 Pseudokeywords 142

References 143

Part Four Setting Up and Running the Calculation 145

10 Planning a Project 147

10.1 Questions to Consider 147

10.1.1 Research Questions 148

10.1.2 Simulation Questions 149

10.2 Planning Simulations 151

10.2.1 Making it Simple 151

10.2.2 Planning and Adapting the Sequence of Calculations 151

10.3 Being Realistic: Available Resources for the Project 153

10.4 Creating Models 155

10.5 Choosing a Method 156

10.5.1 Molecular Mechanics and Forcefields 156

10.5.2 Semiempirical Methods 158

10.5.3 DFT 159

10.5.4 Post-HF 160

10.5.5 Post-DFT 161

10.6 Writing About the Simulation 162

10.7 Checklists 163

References 164

11 Coordinates and Simulation Cell 165

11.1 Isolated Molecules 166

11.1.1 Cartesian Coordinates 166

11.1.2 Molecular Symmetry 167

11.1.3 Internal Coordinates 169

11.2 Periodic Systems 170

11.2.1 Fractional Coordinates 171

11.2.2 Crystallography and Symmetry in Periodic Systems 172

11.2.3 Supercells 175

11.2.4 Understanding Crystallographic Notation: Space Groups 175

11.2.5 Understanding Crystallographic Notation: Atomic Coordinates 176

11.3 Systems with Lower Periodicity 180

11.3.1 Surfaces in Crystallography 180

11.3.2 Grain Boundaries and Dislocations 182

11.3.3 Modeling Surfaces, Wires and Isolated Molecules 182

11.4 Quality of Crystallographic Data 186

11.5 Structure of Proteins 187

11.6 Pseudokeywords 188

11.7 Checklist 189

References 190

12 The Nuts and Bolts 193

12.1 A Single-Point Simulation 193

12.2 Structure Optimization 194

12.3 Transition State Search 195

12.4 Simulation Cell Optimization 197

12.5 Molecular Dynamics 199

12.6 Vibrational Analysis 200

12.6.1 Simulation of Anharmonic Vibrational Spectra 201

12.6.2 Normal Mode Analysis 202

12.6.3 Harmonic or Anharmonic? 204

12.7 The Atomistic Model 205

12.7.1 Small Beginnings 205

12.7.2 Periodic Images and Duplicate Atoms 205

12.7.3 Crossing (Periodic) Boundaries 206

12.7.4 Hydrogen Atoms in Proteins 207

12.7.5 Solvating a Protein 209

12.8 How Converged is Converged? 209

12.9 Checklists 210

References 211

13 Tests 213

13.1 What is the Correct Number? 213

13.2 Test Systems 214

13.3 Cluster Models and Isolated Systems 215

13.4 Simulation Cells and Supercells of Periodic Systems 216

13.5 Slab Models of Surfaces 216

13.6 Molecular Dynamics Simulations 217

13.7 Vibrational Analysis by Finite Differences 218

13.8 Electronic-Structure Simulations 219

13.8.1 Basis Sets 219

13.8.2 Pseudopotentials and Projector-Augmented Waves 220

13.8.3 K-Points in Periodic Systems 220

13.9 Integration and FFT Grids 221

13.10 Checklists 222

References 223

Part Five Analyzing Results 225

14 Looking at Output Files 227

14.1 DeterminingWhat Happened 227

14.1.1 Has it Crashed? 227

14.2 Why Did it Stop? 229

14.2.1 Why it Did Not Converge? 230

14.3 Do the Results Make Sense? 233

14.4 Is the Result Correct? 234

14.5 Checklist 234

References 234

15 What to do with All the Numbers 235

15.1 Energies 236

15.1.1 Stability 236

15.1.2 Relative Energies: Adsorption, Binding etc. 239

15.1.3 Free Energies 242

15.2 Structural Data 242

15.2.1 Bond Lengths and Angles 243

15.2.2 Distributions 243

15.2.3 Atomic Transport 244

15.2.4 Elastic Constants 246

15.3 Normal Mode Analysis 246

15.3.1 Irreducible Representations 246

15.3.2 Selection Rules from Irreducible Representations 250

15.3.3 Fundamentals, Overtones, and Combination Bands 250

15.4 Other Numbers 251

References 252

16 Visualization 253

16.1 The Importance Of Visualizing Data 253

16.2 Sanity Checks 253

16.3 Is There a Bond? 254

16.4 Atom Representations 254

16.5 Plotting Properties 256

16.5.1 Looking at Charge Density 256

16.5.2 Density of States 256

16.6 Looking at Vibrations 257

16.7 Conveying Information 258

16.7.1 Selecting the Important Bits 258

16.7.2 From Three to Two Dimensions 258

16.7.3 How to Make Things Look Different 260

16.8 Technical Pitfalls Of Image Preparation 264

16.8.1 JPEG, GIF, PNG, TIFF: Raster Graphics Images 264

16.8.2 Manipulating Raster Graphics Images 265

16.8.3 How to Get a 3D Scene into a 2D Image that Can Be Saved 266

16.9 Ways and Means 266

References 268

17 Electronic Structure Analysis 269

17.1 Energy Levels and Band Structure 269

17.2 Wavefunctions and Atoms 271

17.3 Localized Functions 273

17.4 Density of States, Projected DOS 274

17.5 STM and CITS 276

17.5.1 Tersoff–Hamann 277

17.5.2 Bardeen 278

17.6 Other Spectroscopies: Optical, X-Ray, NMR, EPR 278

References 280

18 Comparison to Experiment 283

18.1 Why It Is Important 284

18.2 What Can and Cannot Be Directly Compared 285

18.2.1 Energies 285

18.2.2 Structural Data 286

18.2.3 Spectroscopy 288

18.2.4 Vibrational Spectroscopy 290

18.2.5 Scanning Probes 291

18.2.6 Barriers 292

18.3 How to Determine Whether There is Agreement with Experiment 293

18.4 Case Studies 295

18.4.1 Proton Pumping in Cytochrome c Oxidase 295

18.4.2 Bismuth Nanolines on Silicon 300

References 304

Appendix A UNIX 307

A.1 What’s in a Name 307

A.2 On the Command Line 308

A.3 Getting Around 309

A.4 Working with Data 309

A.5 Running Programs 311

A.6 Remote Work 312

A.7 Managing Data 313

A.8 Making Life Easier by Storing Preferences 314

A.9 Be Careful What You Wish For 315

Appendix B Scientific Computing 317

B.1 Compiling 317

B.2 High Performance Computing 319

B.3 MPI and mpirun 320

B.3.1 How to Run an MPI Job 321

B.3.2 Scaling 321

B.3.3 How to Kill a Parallel Job 321

B.4 Job Schedulers and Batch Jobs 322

B.4.1 How to Queue 322

B.4.2 Submitting and Monitoring 323

B.5 File Systems and File Storage 324

B.6 Getting Help 324

Index 325

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Dr. Veronika Brázdová obtained her PhD from Humboldt University Berlin in 2005 with Professor J. Sauer. She is currently a Postdoctoral Research Fellow at the London Centre for Nanotechnology, University College London. Her research is focused on computational simulations of solid state surfaces and interfaces, using mainly density functional theory. She has been collaborating closely with experimental groups. She is also an experienced programmer, particularly in Fortran 90 and the Message Passing Interface. She has supervised many undergraduate students taking their first steps in computational physics.

Dr. David R. Bowler received his D.Phil. from Oxford University in 1997. He has been a Reader in Physics at UCL since 2005, and held a Royal Society University Research Fellowship from 2002-2010. He is a PI in the London Centre for Nanotechnology and the London-wide Thomas Young Centre. He has driven the development of the massively-parallel linear scaling density functional theory code, Conquest, and collaborates extensively with experimental groups on the growth and properties of nanostructures on semiconductor surfaces.

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