目錄 |
| 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. | Determining What 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 |