Atomic Structure Prediction of Nanostructures, Clusters and Surfaces

This work fills the gap for a comprehensive reference conveying the developments in global optimization of atomic structures using genetic algorithms. Over the last few decades, such algorithms based on mimicking the processes of natural evolution have made their way from computer science disciplines to solid states physics and chemistry, where they have demonstrated their versatility and predictive power for many materials. Following an introduction and historical perspective, the text moves on to provide an in-depth description of the algorithm before describing its applications to crystal structure prediction, atomic clusters, surface and interface reconstructions, and quasi one-dimensional nanostructures. The final chapters provide a brief account of other methods for atomic structure optimization and perspectives on the future of the field.

Preface IX

1 The Challenge of Predicting Atomic Structure 1

1.1 Evolution: Reality and Algorithms 2

1.2 Brief Historical Perspective 4

1.3 Scope and Organization of This Book 6

References 7

2 The Genetic Algorithm in Real-Space Representation 11

2.1 Structure Determination Problems 12

2.1.1 Cluster Structure 12

2.1.2 Crystal Structure Prediction 16

2.1.3 Surface Reconstructions 19

2.1.4 Range of Applications 21

2.2 General Procedure 23

2.3 Selection of Parent Structures 24

2.4 Crossover Operations 26

2.4.1 Cut-and-Splice Crossover in Real Space 27

2.4.2 Crossovers and Periodic Boundary Conditions 28

2.5 Mutations 30

2.5.1 Zero-Penalty Mutations 31

2.5.2 Regular Mutations 31

2.6 Updating the Genetic Pool: Survival of the Fittest 33

2.7 Stopping Criteria and Subsequent Analysis 34

References 35

3 Crystal Structure Prediction 37

3.1 Complexity of the Energy Landscape 38

3.2 Improving the Efficiency of GA 40

3.3 Interaction Models 41

3.3.1 Classical Potentials 41

3.3.2 Ab Initio Methods 42

3.3.3 Adaptive Classical Potentials 42

3.4 Creating the Generation-Zero Structures 44

3.5 Assessing Structural Diversity of the Pool 45

3.5.1 Fingerprint Functions 45

3.5.2 General Features of the PES 47

3.6 Variable Composition 48

3.7 Examples 51

3.7.1 Identification of Post-Pyrite Phase Transitions 51

3.7.1.1 Computational Details 52

3.7.1.2 Results and Discussion 52

3.7.2 Ultrahigh-Pressure Phases of Ice 57

3.7.2.1 Computational Details 58

3.7.2.2 Results and Discussion 59

3.7.3 Structure and Magnetic Properties of Fe–Co Alloys 63

3.7.3.1 Computational Details 63

3.7.3.2 Results and Discussion 64

References 67

4 Optimization of Atomic Clusters 71

4.1 Alloys, Oxides, and Other Cluster Materials 71

4.2 Optimization of Substrate-Supported Clusters via GA 73

4.3 GA Solution to the Thomson Problem 81

References 85

5 Atomic Structure of Surfaces, Interfaces, and Nanowires 87

5.1 Reconstruction of Semiconductor Surfaces as a Problem of Global Optimization 88

5.1.1 The Genetic Algorithm for Surface Reconstructions: the Case of Si(105) 89

5.1.1.1 Computational Details for Si(105) 89

5.1.1.2 Results for Si(105) 91

5.1.2 New Reconstructions for a Related Surface, Si(103) 95

5.1.3 Model Reconstructions for Si(337), an Unstable Surface: GA Followed by DFT Relaxations 99

5.1.3.1 Results for Si(337) Models 101

5.1.3.2 Discussion 106

5.1.4 Atomic Structure of Steps on High-Index Surfaces 107

5.1.4.1 Supercell Geometry and Algorithm Details 107

5.1.4.2 Results for Step Structures on Si(114) 110

5.2 Genetic Algorithm for Interface Structures 114

5.2.1 GA for Grain Boundary Structure Optimization 115

5.2.2 Structures Generated by GA 116

5.2.3 Grain Boundary Energy Calculations 121

5.3 Nanowire and Nanotube Structures via GA Optimization 123

5.3.1 Passivated Silicon Nanowires 123

5.3.2 One-Dimensional Nanostructures under Radial Confinement 130

5.3.2.1 Introduction 131

5.3.2.2 Description of the Algorithm 132

5.3.2.3 Results for Prototype Nanotubes 135

5.3.2.4 Discussion 139

5.3.2.5 Concluding Remarks 144

References 144

6 Other Methodologies for Investigating Atomic Structure 149

6.1 Parallel Tempering Monte Carlo Annealing 151

6.1.1 General Considerations 151

6.1.2 Advantages of the Parallel Tempering Algorithm as a Global Optimizer 153

6.1.3 Description of the Algorithm 154

6.2 Basin Hopping Monte Carlo 158

6.3 Optimization via Minima Hopping 160

6.4 The Metadynamics Approach 163

6.5 Comparative Studies between GA and Other Structural Optimization Techniques 165

6.5.1 Reconstructions of Si(114): Comparison between GA and PTMC 165

6.5.1.1 PTMC Results 166

6.5.1.2 GA Results 167

6.5.1.3 DFT Calculations 167

6.5.1.4 Structural Models for Si(114) 169

6.5.1.5 Discussion 174

6.5.1.6 Concluding Remarks 175

6.5.2 Crystal Structure Prediction: Comparison between GA and MH 175

6.5.2.1 GA Applied to AlxSc1x Alloys 176

6.5.2.2 Boron 180

6.5.2.3 Minima Hopping 182

References 185

7 Perspectives and Outlook 187

7.1 Expansion through the Community 187

7.2 Future Algorithm Developments 187

7.3 Problems to Tackle – Discovery versus Design 188

Index 191