List of Contributors ........................................ IX
Introduction: Crystal Structure Prediction, a Formidable
Problem ..................................................... XI
1 Periodic-Graph Approaches in Crystal Structure Prediction .... 1
Vladislav A. Blatov and Davide M. Proserpio
1.1 Introduction ............................................ 1
1.2 Terminology ............................................. 2
1.3 The Types of Periodic Nets Important for Crystal
Structure Prediction .................................... 5
1.4 The Concept of Topological Crystal Structure
Representation .......................................... 7
1.5 Computer Tools and Databases ........................... 10
1.6 Current Results on Nets Abundance ...................... 12
1.7 Some Properties of Nets Influencing the Crystal
Structure .............................................. 14
1.7.1 Symmetry of Nets and Embeddings ................. 14
1.7.2 Relations Between Nets .......................... 17
1.7.3 Role of Geometrical and Coordination
Parameters ...................................... 18
1.8 Outlook ................................................. 25
References .................................................. 26
2 Energy Landscapes and Structure Prediction Using Basin-
Hopping ..................................................... 29
David J. Wales
2.1 Introduction ........................................... 29
2.2 Visualizing the Landscape .............................. 30
2.3 Basin-Hopping Global Optimization ...................... 36
2.4 Energy Landscapes for Crystals and Glasses ............. 42
References .................................................. 46
3 Random Search Methods ....................................... 55
William W. Tipton and Richard G. Hennig
3.1 Introduction ........................................... 55
3.2 History and Overview ................................... 57
3.3 Methods ................................................ 58
3.4 Applications and Results ............................... 61
3.5 Summary and Conclusions ................................ 64
References .................................................. 65
4 Predicting Solid Compounds Using Simulated Annealing ........ 67
J. Christian Schön and Martin Jansen
4.1 Introduction ........................................... 67
4.2 Locally Ergodic Regions on the Energy Landscape of
Chemical Systems ....................................... 68
4.3 Simulated Annealing and Related Stochastic Walker-
Based Algorithms ....................................... 71
4.3.1 Basic Simulated Annealing ....................... 71
4.3.2 Adjustable Features in Simulated Annealing ...... 74
4.3.2.1 Choice of Moveclass .................... 74
4.3.2.2 Temperature Schedule and Acceptance
Criterion .............................. 76
4.3.2.3 Extensions and Generalizations of
Simulated Annealing .................... 77
4.4 Examples ............................................... 79
4.4.1 Structure Prediction ............................ 80
4.4.1.1 Alkali Metal Halides ................... 80
4.4.1.2 Na3N ................................... 81
4.4.1.3 Mg(BH4)2 ............................... 82
4.4.1.4 Elusive Alkali Metal Orthocarbonates
Balancing M4(CO4) and M2O + M2(CO3),
with M = Li, Na, K, Rb, Cs ............. 83
4.4.1.5 Alkali Metal Sulfides M2S (M = Li,
Na, K, Rb, Cs) ......................... 83
4.4.1.6 Boron Nitride .......................... 84
4.4.1.7 Structure Prediction of SrO as
Function of Temperature and Pressure ... 84
4.4.1.8 Phase Diagrams of the Quasi-Binary
Mixed Alkali Halides ................... 86
4.4.2 Structure Prediction Employing Structural
Restrictions .................................... 87
4.4.2.1 Complex Ions as Primary Building
Units .................................. 87
4.4.2.2 Molecular Crystals ..................... 88
4.4.2.3 Zeolites ............................... 91
4.4.2.4 Phase Diagrams Restricted to
Prescribed Sublattices ................. 92
4.4.3 Structure Determination ........................ 94
4.4.3.1 Structure Determination using
Experimental Cell Information .......... 94
4.4.3.2 Reverse Monte Carlo Method and Pareto
Optimization ........................... 94
4.5 Evaluation and Outlook ................................. 96
4.5.1 State-of-the-Art ................................ 96
4.5.2 Future .......................................... 97
References .................................................. 98
5 Simulation of Structural Phase Transitions in Crystals:
The Metadynamics Approach .................................. 107
Roman Martoñák
5.1 Introduction .......................................... 107
5.2 Simulation of Structural Transformations .............. 108
5.3 The Metadynamics-Based Algorithm ...................... 110
5.4 Practical Aspects ..................................... 113
5.5 Examples of Applications .............................. 115
5.6 Conclusions and Outlook ............................... 125
Acknowledgments ............................................ 126
References ................................................. 127
6 Global Optimization with the Minima Hopping Method ......... 131
Stefan Goedecker
6.1 Posing the Problem .................................... 131
6.2 The Minima Hopping Algorithm .......................... 134
6.3 Applications of the Minima Hopping Method ............. 142
6.4 Conclusions ........................................... 143
References ................................................. 144
7 Crystal Structure Prediction Using Evolutionary Approach ... 147
Andriy O. Lyakhov, Artem R. Oganov, and Mario Valle
7.1 Theory ................................................ 148
7.1.1 Search Space, Population, and Fitness
Function ....................................... 150
7.1.2 Representation ................................. 150
7.1.3 Local Optimization and Constrains .............. 151
7.1.4 Initialization of the First Generation ......... 152
7.1.5 Variation Operators ............................ 155
7.1.6 Survival of the Fittest and Selection of
Parents ........................................ 157
7.1.7 Halting Criteria ............................... 158
7.1.8 Premature Convergence and How to Prevent It:
Fingerprint Function ........................... 159
7.1.9 Improved Selection Rules and Heredity
Operator ....................................... 161
7.1.10 Extension to Molecular Crystals ................ 162
7.1.11 Adaptation to Clusters ......................... 162
7.1.12 Extension to Variable Compositions: Toward
Simultaneous Prediction of Stoichiometry and
Structure ...................................... 163
7.2 A Few Illustrations of the Method ..................... 164
7.2.1 Elements ....................................... 165
7.2.1.1 Boron: Novel Phase with a Partially
Ionic Character ...................... 165
7.2.1.2 Sodium: A Metal that Goes
Transparent under Pressure ........... 167
7.2.1.3 Superconducting ξ-Oxygen ............. 170
7.2.1.4 Briefly on Some of the (Many)
Interesting Carbon Structures ........ 171
7.2.2 Compounds and Minerals ......................... 172
7.2.2.1 Insulators by Metal Alloying? ........ 172
7.2.2.2 MgB2: Analogy with Carbon and Loss
of Superconductivity under
Pressure ............................. 172
7.2.2.3 Hydrogen-Rich Hydrides under
Pressure, and Their
Superconductivity .................... 173
7.2.2 A High-Pressure Polymorphs of СаСО3 .... 175
7.3 Conclusions ........................................... 176
Acknowledgments ............................................ 177
References ................................................. 277
8 Pathways of Structural Transformations in Reconstructive
Phase Transitions: Insights from Transition Path Sampling
Molecular Dynamics ......................................... 181
Stefano Leoni and Salah Eddine Boulfelfel
8.1 Introduction .......................................... 181
8.1.1 Shape of the Nuclei ............................ 182
8.2 Transition Path Sampling Molecular Dynamics ........... 183
8.2.1 First Trajectory ............................... 183
8.2.2 Trajectory Shooting and Shifting ............... 184
8.3 The Lesson of Sodium Chloride ......................... 186
8.3.1 Simulation Strategy ............................ 187
8.3.2 Topological Models ............................. 187
8.3.3 Combining Modeling and Molecular Dynamics
Simulations .................................... 190
8.3.4 The Mechanism of the B1-B2 Phase Transition .... 191
8.3.5 Crossing the Line: NaBr ........................ 193
8.4 The Formation of Domains .............................. 194
8.5 Structure of the B2-B1 Interfaces ..................... 197
8.5.1 Domain Formation in RbCl ....................... 199
8.5.2 Liquid Interfaces in CaF2 ...................... 201
8.6 Domain Fragmentation in CdSe Under Pressure ........... 204
8.6.1 B4-B1-B4 Transformation ........................ 206
8.6.2 Defects ........................................ 209
8.6.3 The Lesson of CdSe ............................. 209
8.7 Intermediate Structures During Phase Transitions ...... 210
8.7.1 Intermediates Along the Pressure-Induced
Transformation of GaN .......................... 211
8.7.2 Polymorphism and Transformations of ZnO:
Tetragonal or Hexagonal Intermediate? .......... 214
8.8 Conclusions ........................................... 217
References ................................................. 218
Appendix: First Blind Test of Inorganic Crystal Structure
Prediction Methods .................................... 223
Color Plates ............................................... 233
Index ...................................................... 245
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