Atomistic Computer Simulations: A Practical Guide

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/.

Table of Contents:
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

About the Author :
Dr. Veronika Brazdova 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.

Review :
“What a gem! This is a truly outstandingly useful book for anyone working in (or supervising students in) projects based around atomistic computer simulations . . . This book is a joy to read and will be of interest to specialists but also to anyone with a general interest in physics and indeed the history of science.”  (Contemporary Physics, 11 April 2014)