Science of Crystal Structures (eBook)

Istvan Hargittai, PhD, DSc, is Professor Emeritus (Active) of the Budapest University of Technology and Economics. He is a member of the Hungarian Academy of Sciences and the Academia Europaea (London) and foreign member of the Norwegian Academy of Science and Letters. He is Dr.h.c. of Moscow State University, the University of North Carolina and the Russian Academy of Sciences. He is the Editor-in-Chief of Structural Chemistry, an international research journal by Springer-Verlag.Balazs Hargittai, PhD (University of Minnesota), is Professor of Chemistry of Saint Francis University, Loretto, Pennsylvania. He is also Associate Dean, School of Sciences and Director of the Office of Student Research of Saint Francis University. He was co-author of Candid Science V (Imperial College Press, London) and of Great Minds--Reflections of 111 Top Scientists (OUP, New York). He has been active in publishing and editorial activities in addition to his research and teaching. 

Also by the Editors 8
Preface 10
Contents 12
Part I: Direct Methods 15
X-Ray Crystallography: The Past and Present of the Phase Problem 16
Introduction 16
Part I: Crystals and Bragg Spots 17
Fourier Refinement (Early 1930s) 17
The Patterson Map (1934), Heavy Atoms (Mid- and Later 1930s) 17
Three Brief Digressions 18
The State of Affairs at the Start of the Postwar Period (1946) 18
A Bit of Personal History 18
The Beginnings of Digital Computation (Late 1940s, Early 1950s) 19
Direct Methods (Late 1940s–Present) 19
Macromolecules: DNA (1953), Isomorphous Replacement (1953–Present) 20
Macromolecules: Anomalous Dispersion (1949–Present) 21
Macromolecules: Additional Methods 21
One More Method: Three-Beam Diffraction (1977–Present) 22
The Sparse or “Dream” Crystal 22
Part II: Finer Sampling (1980–Present) 23
Overview and Brief History 23
The Two Probable Experimental Regimes 24
The Free-Electron Laser-Flash Technique for Molecules 24
A Synchrotron/Cryoprotection Technique for Supramolecular Specimens 24
Phasing the Pattern 26
Summary 28
References 30
History of X-Ray Crystallographya 32
References 35
Gas Electron Diffraction and Its Influence on the Solution of the Phase Problem in Crystal Structure Determinationa 36
Introduction to Gas Electron Diffraction 36
Getting Started at NRL 37
Problems to Be Overcome 38
Early Studies 39
Implications 39
Non-negativity 40
The Period Between the 1940s and 1963 40
Introduction 40
Historical Background 41
Titles of Additional Topics 42
The Remaining Problem 43
Some Later Structure Analyses 45
References 46
Part II: Beyond the Classical System 48
Generalized Crystallography 49
Introduction 49
The Reality of Spatial Structure 50
Generalised Microscopy 50
Generalized Geometric Algebra (Clifford Algebra) 51
The Description of Structure 51
Crystal Chemistry and Informatics 52
Recognition of Higher Level Structure 52
Hierarchic Structures 52
Synthesis on Growth and Form 52
References 53
Mackay, Anti-Mackay, Double-Mackay, Pseudo-Mackay, and Related Icosahedral Shell Clustersa,b 55
Introduction 55
Icosahedron and Related Polyhedra 56
Icosahedral Shell Structures 57
Hierarchic Icosahedral Structures 59
I13(I) Cluster 60
I13(V) Cluster 61
I13(P) Cluster 61
References 63
Crystallography Without a Latticea,b 65
Prologue 65
Introduction 66
Experimental 67
Theory 68
Results 68
Partial Radial Distribution Functions 68
Spatial Distribution Functions 72
Orientational Distribution Functions 74
Structural Basis of the Hydrophobic Interaction 77
Conclusions 79
References 80
Polygrammal Symmetries in Biomacromolecules: Heptagonal Poly d (As4T) · poly d (As4T) and Heptameric ?-Hemolysina,b 81
Introduction 81
Crystallography of Star Heptagons 83
?-Hemolysin 87
Poly d(As4T) · poly d(As4T) 88
References 91
Helical Structures: The Geometry of Protein Helices and Nanotubesa,b 92
Introduction 92
Nomenclature 92
Metrical Parameters of a CHL 93
Metrical Parameters of a THP 93
The Boerdijk–Coxeter Structure 95
Sphere Packings 95
Extension of the Helical Sphere Packing 96
Nanotubes 97
Collagen and the Polytope {3, 3, 5} 97
Defects in THPS and Nanotubes 98
Miscellany 99
Conclusions 101
References 101
From Waxes to Polymers—Crystallography of Polydisperse Chain Assembliesa,b 102
Introduction 102
Why Electron Diffraction? 102
n-Paraffin Binary Solid Solutions 103
Fractionation of n-Paraffin Binaries—Miscibility Gap 105
Fractionation of n-Paraffin Binaries—Eutectic Interactions 106
“Typical” Lamellar Paraffin Wax Structures 106
From Wax to Polymer Crystal—Interlayer Bridges 107
What Is Wax and What Is Polyethylene? 109
References 109
Structure, Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onionsa,b 111
Introduction 111
Euler’s Law in Graphitic Structures 112
Stability of Giant Icosahedral Fullerenes and Geometrical Rules 113
Polyhedral Particles and Graphitic Onion Formation 116
Sphericity of Graphitic Onions 117
Conclusions 120
References 121
A Generalized Model for the Shell Structure of Icosahedral Virusesa 123
Introduction 123
Capsids of Non-Quasi-Equivalent Viruses 124
Concluding Remarks 125
References 126
Intermetallic Compounds of the NaCd2 Family Perceived as Assemblies of Nanoclustersa 127
Introduction 127
Principles and Methods of Analysis in Terms of Nanoclusters 128
The Nanocluster Model of the NaCd2 Crystal Structure 130
Conclusion 133
References 134
Linus Pauling’s Quest for the Structure of Proteinsa 135
References 141
“There Is No Such Animal (??? ??? ???)”—Lessons of a Discoverya,b 142
References 145
Quasicrystal Discovery—From NBS/NIST to Stockholma 146
References 151
Atomic Structure of Quasicrystalsa,b 152
Introduction 152
How Can the Atomic Structure of Quasicrystals Be Solved? 153
Tilings 153
Superspace Crystallography 154
Periodic Approximant, Clusters and Local Order 154
Analysing Diffraction Data: The CdYb Icosahedral Case 157
Superspace Crystallography Analysis and Modeling 157
Analysis of the Resulting Structure 157
Beyond the Average Structure: Diffuse Scattering and Phason Modes 160
Conclusion 162
References 162
Some Properties of Three-Periodic Sphere Packingsa,b 164
Introduction 164
Circle Packings 165
Low Density Sphere Packings in Three Dimensions 165
12-Coordination 166
11-Coordination 166
10-Coordination 166
9-Coordination 167
8-Coordination 167
7-Coordination 167
6-Coordination 168
5-Coordination 168
4-Coordination 168
3-Coordination 169
Some Properties of Sphere Packing Graphs 170
Symmetric (Vertex- and Edge-Transitive) Graphs 170
Triclinic Graphs 171
Ring Sizes for 4-Coordinated Sphere Packings 171
References 171
Cluster Packing from a Higher Dimensional Perspective 173
Introduction 173
(LS) Cluster and Fibonacci Sequence 174
Decagon Cluster and 2D Penrose Tiling 176
Triacontahedron Cluster and 3D Penrose (Ammann) Tiling 178
Conclusions 178
References 178
Part III: Structural and Materials Properties 179
Magnetic Properties of Quasicrystals: Effects of Disorder on Fe Magnetic Moment Formationa 180
Introduction 180
Appearance of Disorder in Quasi-Crystalline Structures 180
Fe Magnetic Moment Formation in Quasicrystals 181
References 183
Overlooked Opportunities in Stereochemistry. Part III: Alfred Werner’s Awareness of Spontaneous Resolutions and of the Meaning of Hemihedral Faces in Optically Active Crystalsa 185
Comments on Werner’s Seeding Experiments with Bosshart [5, 6] 188
Comments on Werner and Poupardin’s Spontaneous Resolution of K3[Rh(C2O4)] · H2O as a Conglomerate 189
References 191
The Geometry of Intermolecular Interactions in Some Crystalline Fluorine-Containing Organic Compounds 193
Introduction 193
Materials and Methods 194
Results 194
Compounds Containing C, H, and F Atoms 194
Comparison of C—H and C—F 196
Graph-Set Analysis of Packing 196
Compounds Containing C, H, F Together with O and/or N Atoms 199
Conclusions 204
References 209
Molecular and Crystal Structures of a Class of Push-Pull Quinonoid Compounds with Potential Nonlinear Optical Applicationsa 210
Introduction 210
Results and Discussion 211
Theoretical Studies of Hyperpolarizability 211
Molecular and Crystal Structures 212
Conclusion 214
Experimental 215
Synthesis 215
7,7?-Dipiperazino-8,8?-Dicyanoquinodimethane (3) 216
7,7?-Dimorpholino-8,8?-Dicyanoquinodimethane (4) 216
Crystal Structure Determination 216
References 216
X-ray Crystallographic Studies on the Noncovalent Syntheses of Supermoleculesa 217
Introduction 217
Discovery of a New Recognition Motif 218
Extending the Recognition Motif 219
Never Forget the Counterions! 222
Interwoven Supramolecular Bundles 227
Summary and Outlook to the Future 231
References 232
Asymmetry in the Multiprotein Systems of Molecular Biologya,b 234
Introduction 234
Abandoning Symmetry in Living Systems 235
The Symmetry and Asymmetry of Signaling and Regulatory Systems 235
Signaling Through Growth Factors and Receptor Tyrosyl Kinases 235
NGF Receptor and the Heterohexameric 7S NGF Storage Complex 235
Insulin, Insulinlike Growth Factor-1 (IGF-1), and Their Receptors 236
Hepatocyte Growth Factor/Scatter Factor, HGF/SF, and Its Met Receptor 237
Fibroblast Growth Factor 1 (FGF1) in Complex with Its Receptor (FGFR2) Ectodomain and Heparin 237
DNA Repair Signaling 238
Nonhomologous DNA End Joining: The Crystal Structure of an Xrcc4-DNA Ligase IV Complex 238
Homologous Recombination: Interactions of Tumor Suppressor Protein BRCA2 with RAD51 239
Conclusions 239
References 240
Molecular van der Waals Symmetry Affecting Bulk Properties of Condensed Phases: Melting and Boiling Pointsa,b 241
Introduction 241
Experimental 242
Results 242
Methane Analogues MX4 and MX4?nYn 242
Substituted Ethanes C2H6?nXn and Ethylenes C2H4?nXn 244
Substituted Benzenes C6H6?nXn 245
Substituted Cyclohexanes C6H12?nXn 246
Discussion 247
Molecular Mass as a Variable in Tm,b(M?) Plots 247
General Trends in Tm and Tb 248
Hypothesis of van der Waals Symmetry 249
Van der Waals Symmetry in Crystals and Liquids 251
Non-van der Waals Factors Influencing Tm and Tb 253
Electrostatic Forces 253
Secondary Bonding 253
Geometry-Dependent T?S Term 254
Conclusions 255
References 255
The Role of Symmetry in Building Up Zeolite Frameworks from Layered Zeolite Precursors Having Ferrierite and CAS Layersa,b 256
Introduction 256
Discussion 257
The Discovery of Layered Zeolite Precursor MCM-22P and Its Consequences 257
General Comments on the Formation of Precursors and Their Conversion to Frameworks 257
Layered Precursors with FER Sheets 257
Zeolites CAS and NSI 258
The Role of Symmetry in Building Up Layered Frameworks 260
References 260
Part IV: Data Mining and Management 262
The Correspondence Fedorov-­Schoenflies: The Groups Pm, Pc, Cm, Cca 263
Postscript 1 267
Postscript 2 267
References 267
Prediction of H-Bonding Motifs for Pyrazoles and Oximes Using the Cambridge Structural Databasea 268
Introduction 268
Methodology 269
Results and Discussion 270
Pyrazole Results 273
Oxime Results 274
E/Z Oximes 275
Comparison of Pyrazole/Oxime Structures 275
A Predictive Test 278
Energetic Considerations 278
Conclusions 278
References 279
Hierarchies of Intermolecular Potentials and Forces: Progress Towards a Quantitative Evaluationa 280
Introduction: Hierarchy and Significance of Intermolecular Bonds 280
Methods 282
The PIXEL Procedure 282
Analysis of Crystal Packing 282
Three Crystal Structures 283
Naphthalene 283
Naphthoquinone 284
2-Naphthoic Acid 286
Conclusion 287
References 288
Where Are Genes in Paulingite? Mathematical Principles of Formation of Inorganic Materials on the Atomic Levela 290
Introduction 290
Paulingite: Structural Architecture 292
Paulingite: Cellular Automata Modeling 293
ISC-1: A New Theoretical Zeolite Framework 296
Conclusions 296
References 296
Supramolecular Architectures of Metal–Organic Host–Guest Compoundsa 297
The “Wheel and Axle Metal–Organic” Diols 297
Building of the Metal–Organic Host 299
Ag(I) Complexes as WAMODs: 1D Coordination Polymers 299
Pd(II) Complexes as WAMODs 299
The Structure 299
Sorption/Desorption of Organic Guests 302
Validation of the WAMOD Concept 302
The Pt(II) Complexes: From WAMODs to Supramolecular Metallamacrocycles 304
Conclusions 304
References 306
What Is a Chemical Substance and How Is It Formed?a,b,c 307
Introduction 307
On the Definition of “Chemical Substance” 309
Space Dividing and Fundamental Configurations 310
Calculations of Chemical Composition 313
Structural Generality of the Objects of Nature in the Nanostate 314
On the “Silicon” Life Forms 317
How Does the Matter Think? 318
Summary 319
References 319
Investigation of Structural Relations Among the Compounds in the ICSD Using Geometry Based Comparison Techniquesa 320
Introduction 320
Methodology 321
The CMPZ Algorithm [24] 321
Procedure for the Analysis of the Database 322
Results 322
Preliminary Results 322
Families of Structures 323
Relations Between Families of Structures of Different AB_FORMs 326
Discussion 326
References 328
Index 329