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 1 (10)
Structure
1.1 Evolution: Reality and Algorithms 2 (2)
1.2 Brief Historical Perspective 4 (2)
1.3 Scope and Organization of This Book 6 (5)
References 7 (4)
2 The Genetic Algorithm in Real-Space 11 (26)
Representation
2.1 Structure Determination Problems 12 (11)
2.1.1 Cluster Structure 12 (4)
2.1.2 Crystal Structure Prediction 16 (3)
2.1.3 Surface Reconstructions 19 (2)
2.1.4 Range of Applications 21 (2)
2.2 General Procedure 23 (1)
2.3 Selection of Parent Structures 24 (2)
2.4 Crossover Operations 26 (4)
2.4.1 Cut-and-Splice Crossover in Real 27 (1)
Space
2.4.2 Crossovers and Periodic Boundary 28 (2)
Conditions
2.5 Mutations 30 (3)
2.5.1 Zero-Penalty Mutations 31 (1)
2.5.2 Regular Mutations 31 (2)
2.6 Updating the Genetic Pool: Survival 33 (1)
of the Fittest
2.7 Stopping Criteria and Subsequent 34 (3)
Analysis
References 35 (2)
3 Crystal Structure Prediction 37 (34)
3.1 Complexity of the Energy Landscape 38 (2)
3.2 Improving the Efficiency of GA 40 (1)
3.3 Interaction Models 41 (3)
3.3.1 Classical Potentials 41 (1)
3.3.2 Ab Initio Methods 42 (1)
3.3.3 Adaptive Classical Potentials 42 (2)
3.4 Creating the Generation-Zero 44 (1)
Structures
3.5 Assessing Structural Diversity of the 45 (3)
Pool
3.5.1 Fingerprint Functions 45 (2)
3.5.2 General Features of the PES 47 (1)
3.6 Variable Composition 48 (3)
3.7 Examples 51 (20)
3.7.1 Identification of Post-Pyrite 51 (1)
Phase Transitions
3.7.1.1 Computational Details 52 (1)
3.7.1.2 Results and Discussion 52 (5)
3.7.2 Ultrahigh-Pressure Phases of Ice 57 (1)
3.7.2.1 Computational Details 58 (1)
3.7.2.2 Results and Discussion 59 (4)
3.7.3 Structure and Magnetic Properties 63 (1)
of Fe--Co Alloys
3.7.3.1 Computational Details 63 (1)
3.7.3.2 Results and Discussion 64 (3)
References 67 (4)
4 Optimization of Atomic Clusters 71 (16)
4.1 Alloys, Oxides, and Other Cluster 71 (2)
Materials
4.2 Optimization of Substrate-Supported 73 (8)
Clusters via GA
4.3 GA Solution to the Thomson Problem 81 (6)
References 85 (2)
5 Atomic Structure of Surfaces, Interfaces, 87 (62)
and Nanowires
5.1 Reconstruction of Semiconductor 88 (26)
Surfaces as a Problem of Global
Optimization
5.1.1 The Genetic Algorithm for Surface 89 (1)
Reconstructions: the Case of Si(105)
5.1.1.1 Computational Details for 89 (2)
Si(105)
5.1.1.2 Results for Si(105) 91 (4)
5.1.2 New Reconstructions for a Related 95 (4)
Surface, Si(103)
5.1.3 Model Reconstructions for 99 (2)
Si(337), an Unstable Surface: GA
Followed by DFT Relaxations
5.1.3.1 Results for Si(337) Models 101(5)
5.1.3.2 Discussion 106(1)
5.1.4 Atomic Structure of Steps on 107(1)
High-Index Surfaces
5.1.4.1 Supercell Geometry and 107(3)
Algorithm Details
5.1.4.2 Results for Step Structures on 110(4)
Si(114)
5.2 Genetic Algorithm for Interface 114(9)
Structures
5.2.1 GA for Grain Boundary Structure 115(1)
Optimization
5.2.2 Structures Generated by GA 116(5)
5.2.3 Grain Boundary Energy Calculations 121(2)
5.3 Nanowire and Nanotube Structures via 123(26)
GA Optimization
5.3.1 Passivated Silicon Nanowires 123(7)
5.3.2 One-Dimensional Nanostructures 130(1)
under Radial Confinement
5.3.2.1 Introduction 131(1)
5.3.2.2 Description of the Algorithm 132(3)
5.3.2.3 Results for Prototype Nanotubes 135(4)
5.3.2.4 Discussion 139(5)
5.3.2.5 Concluding Remarks 144(1)
References 144(5)
6 Other Methodologies for Investigating 149(38)
Atomic Structure
6.1 Parallel Tempering Monte Carlo 151(7)
Annealing
6.1.1 General Considerations 151(2)
6.1.2 Advantages of the Parallel 153(1)
Tempering Algorithm as a Global
Optimizer
6.1.3 Description of the Algorithm 154(4)
6.2 Basin Hopping Monte Carlo 158(2)
6.3 Optimization via Minima Hopping 160(3)
6.4 The Metadynamics Approach 163(2)
6.5 Comparative Studies between GA and 165(22)
Other Structural Optimization Techniques
6.5.1 Reconstructions of Si(114): 165(1)
Comparison between GA and PTMC
6.5.1.1 PTMC Results 166(1)
6.5.1.2 GA Results 167(1)
6.5.1.3 DFT Calculations 167(2)
6.5.1.4 Structural Models for Si(114) 169(5)
6.5.1.5 Discussion 174(1)
6.5.1.6 Concluding Remarks 175(1)
6.5.2 Crystal Structure Prediction: 175(1)
Comparison between GA and MH
6.5.2.1 GA Applied to AlxSc1-x Alloys 176(4)
6.5.2.2 Boron 180(2)
6.5.2.3 Minima Hopping 182(3)
References 185(2)
7 Perspectives and Outlook 187(104)
7.1 Expansion through the Community 187(100)
7.2 Future Algorithm Developments 287(1)
7.3 Problems to Tackle - Discovery versus 288(3)
Design
Index 291
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