|
|
ix | |
Introduction: Crystal Structure Prediction, a Formidable Problem |
|
xi | |
|
1 Periodic-Graph Approaches in Crystal Structure Prediction |
|
|
1 | (28) |
|
|
|
|
1 | (1) |
|
|
2 | (3) |
|
1.3 The Types of Periodic Nets Important for Crystal Structure Prediction |
|
|
5 | (2) |
|
1.4 The Concept of Topological Crystal Structure Representation |
|
|
7 | (3) |
|
1.5 Computer Tools and Databases |
|
|
10 | (2) |
|
1.6 Current Results on Nets Abundance |
|
|
12 | (2) |
|
1.7 Some Properties of Nets Influencing the Crystal Structure |
|
|
14 | (11) |
|
1.7.1 Symmetry of Nets and Embeddings |
|
|
14 | (3) |
|
1.7.2 Relations Between Nets |
|
|
17 | (1) |
|
1.7.3 Role of Geometrical and Coordination Parameters |
|
|
18 | (7) |
|
|
25 | (4) |
|
|
26 | (3) |
|
2 Energy Landscapes and Structure Prediction Using Basin-Hopping |
|
|
29 | (26) |
|
|
|
29 | (1) |
|
2.2 Visualizing the Landscape |
|
|
30 | (6) |
|
2.3 Basin-Hopping Global Optimization |
|
|
36 | (6) |
|
2.4 Energy Landscapes for Crystals and Glasses |
|
|
42 | (13) |
|
|
46 | (9) |
|
|
55 | (12) |
|
|
|
|
55 | (2) |
|
|
57 | (1) |
|
|
58 | (3) |
|
3.4 Applications and Results |
|
|
61 | (3) |
|
3.5 Summary and Conclusions |
|
|
64 | (3) |
|
|
65 | (2) |
|
4 Predicting Solid Compounds Using Simulated Annealing |
|
|
67 | (40) |
|
|
|
|
67 | (1) |
|
4.2 Locally Ergodic Regions on the Energy Landscape of Chemical Systems |
|
|
68 | (3) |
|
4.3 Simulated Annealing and Related Stochastic Walker-Based Algorithms |
|
|
71 | (8) |
|
4.3.1 Basic Simulated Annealing |
|
|
71 | (3) |
|
4.3.2 Adjustable Features in Simulated Annealing |
|
|
74 | (1) |
|
4.3.2.1 Choice of Moveclass |
|
|
74 | (2) |
|
4.3.2.2 Temperature Schedule and Acceptance Criterion |
|
|
76 | (1) |
|
4.3.2.3 Extensions and Generalizations of Simulated Annealing |
|
|
77 | (2) |
|
|
79 | (17) |
|
4.4.1 Structure Prediction |
|
|
80 | (1) |
|
4.4.1.1 Alkali Metal Halides |
|
|
80 | (1) |
|
|
81 | (1) |
|
|
82 | (1) |
|
4.4.1.4 Elusive Alkali Metal Orthocarbonates Balancing M4(CO4) and M2O + M2(CO3), with M = Li, Na, K, Rb, Cs |
|
|
83 | (1) |
|
4.4.1.5 Alkali Metal Sulfides M2S (M = Li, Na, K, Rb, Cs) |
|
|
83 | (1) |
|
|
84 | (1) |
|
4.4.1.7 Structure Prediction of SrO as Function of Temperature and Pressure |
|
|
84 | (2) |
|
4.4.1.8 Phase Diagrams of the Quasi-Binary Mixed Alkali Halides |
|
|
86 | (1) |
|
4.4.2 Structure Prediction Employing Structural Restrictions |
|
|
87 | (1) |
|
4.4.2.1 Complex Ions as Primary Building Units |
|
|
87 | (1) |
|
4.4.2.2 Molecular Crystals |
|
|
88 | (3) |
|
|
91 | (1) |
|
4.4.2.4 Phase Diagrams Restricted to Prescribed Sublattices |
|
|
92 | (2) |
|
4.4.3 Structure Determination |
|
|
94 | (1) |
|
4.4.3.1 Structure Determination using Experimental Cell Information |
|
|
94 | (1) |
|
4.4.3.2 Reverse Monte Carlo Method and Pareto Optimization |
|
|
94 | (2) |
|
4.5 Evaluation and Outlook |
|
|
96 | (11) |
|
|
96 | (1) |
|
|
97 | (1) |
|
|
98 | (9) |
|
5 Simulation of Structural Phase Transitions in Crystals: The Metadynamics Approach |
|
|
107 | (24) |
|
|
|
107 | (1) |
|
5.2 Simulation of Structural Transformations |
|
|
108 | (2) |
|
5.3 The Metadynamics-Based Algorithm |
|
|
110 | (3) |
|
|
113 | (2) |
|
5.5 Examples of Applications |
|
|
115 | (10) |
|
5.6 Conclusions and Outlook |
|
|
125 | (6) |
|
|
126 | (1) |
|
|
127 | (4) |
|
6 Global Optimization with the Minima Hopping Method |
|
|
131 | (16) |
|
|
|
131 | (3) |
|
6.2 The Minima Hopping Algorithm |
|
|
134 | (8) |
|
6.3 Applications of the Minima Hopping Method |
|
|
142 | (1) |
|
|
143 | (4) |
|
|
144 | (3) |
|
7 Crystal Structure Prediction Using Evolutionary Approach |
|
|
147 | (34) |
|
|
|
|
|
148 | (16) |
|
7.1.1 Search Space, Population, and Fitness Function |
|
|
150 | (1) |
|
|
150 | (1) |
|
7.1.3 Local Optimization and Constrains |
|
|
151 | (1) |
|
7.1.4 Initialization of the First Generation |
|
|
152 | (3) |
|
7.1.5 Variation Operators |
|
|
155 | (2) |
|
7.1.6 Survival of the Fittest and Selection of Parents |
|
|
157 | (1) |
|
|
158 | (1) |
|
7.1.8 Premature Convergence and How to Prevent It: Fingerprint Function |
|
|
159 | (2) |
|
7.1.9 Improved Selection Rules and Heredity Operator |
|
|
161 | (1) |
|
7.1.10 Extension to Molecular Crystals |
|
|
162 | (1) |
|
7.1.11 Adaptation to Clusters |
|
|
162 | (1) |
|
7.1.12 Extension to Variable Compositions: Toward Simultaneous Prediction of Stoichiometry and Structure |
|
|
163 | (1) |
|
7.2 A Few Illustrations of the Method |
|
|
164 | (12) |
|
|
165 | (1) |
|
7.2.1.1 Boron: Novel Phase with a Partially Ionic Character |
|
|
165 | (2) |
|
7.2.1.2 Sodium: A Metal that Goes Transparent under Pressure |
|
|
167 | (3) |
|
7.2.1.3 Superconducting ξ-Oxygen |
|
|
170 | (1) |
|
7.2.1.4 Briefly on Some of the (Many) Interesting Carbon Structures |
|
|
171 | (1) |
|
7.2.2 Compounds and Minerals |
|
|
172 | (1) |
|
7.2.2.1 Insulators by Metal Alloying? |
|
|
172 | (1) |
|
7.2.2.2 MgB2: Analogy with Carbon and Loss of Superconductivity under Pressure |
|
|
172 | (1) |
|
7.2.2.3 Hydrogen-Rich Hydrides under Pressure, and Their Superconductivity |
|
|
173 | (2) |
|
7.2.2.4 High-Pressure Polymorphs of CaCO3 |
|
|
175 | (1) |
|
|
176 | (5) |
Acknowledgments |
|
177 | (1) |
References |
|
177 | (46) |
|
8 Pathways of Structural Transformations in Reconstructive Phase Transitions: Insights from Transition Path Sampling Molecular Dynamics |
|
|
181 | (42) |
|
|
|
|
181 | (2) |
|
8.1.1 Shape of the Nuclei |
|
|
182 | (1) |
|
8.2 Transition Path Sampling Molecular Dynamics |
|
|
183 | (3) |
|
|
183 | (1) |
|
8.2.2 Trajectory Shooting and Shifting |
|
|
184 | (2) |
|
8.3 The Lesson of Sodium Chloride |
|
|
186 | (8) |
|
8.3.1 Simulation Strategy |
|
|
187 | (1) |
|
|
187 | (3) |
|
8.3.3 Combining Modeling and Molecular Dynamics Simulations |
|
|
190 | (1) |
|
8.3.4 The Mechanism of the B1-B2 Phase Transition |
|
|
191 | (2) |
|
8.3.5 Crossing the Line: NaBr |
|
|
193 | (1) |
|
8.4 The Formation of Domains |
|
|
194 | (3) |
|
8.5 Structure of the B2-B1 Interfaces |
|
|
197 | (7) |
|
8.5.1 Domain Formation in RbCI |
|
|
199 | (2) |
|
8.5.2 Liquid Interfaces in CaF2 |
|
|
201 | (3) |
|
8.6 Domain Fragmentation in CdSe Under Pressure |
|
|
204 | (6) |
|
8.6.1 B4-B1-B4 Transformation |
|
|
206 | (3) |
|
|
209 | (1) |
|
|
209 | (1) |
|
8.7 Intermediate Structures During Phase Transitions |
|
|
210 | (7) |
|
8.7.1 Intermediates Along the Pressure-Induced Transformation of GaN |
|
|
211 | (3) |
|
8.7.2 Polymorphism and Transformations of ZnO: Tetragonal or Hexagonal Intermediate? |
|
|
214 | (3) |
|
|
217 | (6) |
|
|
218 | (5) |
Appendix: First Blind Test of Inorganic Crystal Structure Prediction Methods |
|
223 | (10) |
Color Plates |
|
233 | (12) |
Index |
|
245 | |