1 Historical Introduction ...................................... 1
1.1 Introduction ............................................ 1
1.2 Chemical Bonds .......................................... 2
1.3 The Ionic Model ......................................... 3
1.4 Quantum Mechanics ....................................... 4
1.5 The Symmetry Model ...................................... 4
1.6 Topological Models ...................................... 5
1.7 Pauling's Electrostatic Valence Model ................... 6
2 The Flux Theory of the Chemical Bond ......................... 9
2.1 Introduction ............................................ 9
2.2 Theoretical Foundation ................................. 11
2.2.1 The Structure of the Atom ....................... 11
2.2.2 Electrostatic Theory ............................ 14
2.2.3 The Role of Symmetry ............................ 15
2.2.4 The Core-and-Valence-Shell Picture of tiie
Atom ............................................ 16
2.3 The Chemical Bond ...................................... 17
2.3.1 The Neutral Atom Model .......................... 17
2.3.2 Coordination Numbers ............................ 19
2.3.3 Bond Networks ................................... 19
2.3.4 The Ionic Model ................................. 23
2.3.5 Some Theorems ................................... 25
2.3.6 The Covalent Model .............................. 33
2.3.7 Bond Angles ..................................... 35
2.3.8 The Bond Valence Model .......................... 35
3 The Bond Valence Model ...................................... 36
3.1 Introduction ........................................... 36
3.2 Bond Lengths ........................................... 37
3.3 Coordination Number .................................... 40
3.4 Theorems of the Bond Valence Model ..................... 41
3.4.1 Valence Sum Rule ................................ 41
3.4.2 The Distortion Theorem .......................... 42
3.4.3 Lewis Acid and Base Strength .................... 45
3.4.4 Network Equations ............................... 48
3.4.5 Networks with Non-Bipartite Graphs .............. 50
3.4.6 Valence Maps .................................... 55
3.4.7 Bond Angles and Valence Vectors ................. 58
3.5 Hard and Soft Acids and Bases .......................... 61
4 Cation Coordination Number .................................. 64
4.1 Introduction ........................................... 64
4.2 Anion-Anion Repulsion .................................. 65
4.3 The Bonding Strength of the Anions ..................... 70
4.4 Availability of Counterions ............................ 72
4.5 Electronic Effects ..................................... 73
4.6 Steric Constraints ..................................... 73
4.7 Symmetry ............................................... 74
4.8 Conclusion ............................................. 75
5 Hydrogen Bonds .............................................. 76
5.1 Introduction ........................................... 76
5.2 The Role of Anion-Anion Repulsion ...................... 79
5.3 The Normal Hydrogen Bond ............................... 81
5.4 Short Hydrogen Bonds ................................... 82
5.5 Long Hydrogen Bonds .................................... 84
5.6 The Structural Chemistry of the Hydrogen Ion ........... 85
5.7 Other Types of Hydrogen Bond ........................... 87
5.8 Assigning Experimental Bond Valences to Hydrogen
Bonds .................................................. 88
6 Liquids ..................................................... 92
6.1 Introduction ........................................... 92
6.2 Aqueous Solubility ..................................... 92
6.3 Hydration of Cations ................................... 97
6.4 Protonation of Anions .................................. 99
6.5 Acidity and Alkalinity ................................ 102
6.6 Non-Aqueous Solutions and Melts ....................... 105
7 Electronically Distorted Structures ........................ 107
7.1 The Origins of Electronic Distortions ................. 107
7.2 Modelling Electronically Distorted Structures ......... 108
7.2.1 Multipoles ..................................... 108
7.2.2 Иих Methods .................................... 110
7.2.3 Bond Valence Vectors ........................... 111
7.3 Main Group Atoms with Lone Pairs ...................... 112
7.3.1 Behaviour of Lone Pairs on Cations ............. 117
7.3.2 Behaviour of Lone Pairs on Anions .............. 121
7.4 Transition Metals ..................................... 125
7.4.1 Early Transition Metal Cations with d0
or d1 Configurations ........................... 127
7.4.2 Jahn-Teller Distorted Cations .................. 131
7.4.3 Late Transition Metals ......................... 132
7.5 Conclusions ........................................... 134
8 Physical Properties of Bonds ............................... 136
8.1 Introduction .......................................... 136
8.2 Bond Energy ........................................... 137
8.3 Atomic Radii .......................................... 139
8.4 Bond Lengths and Bond Angles .......................... 140
8.5 Bond Force Constants and Thermal Vibrations ........... 141
8.6 Thermal Expansion ..................................... 144
8.7 The Effects of Pressure on the Lengths of Bonds ....... 148
8.8 The Variation of Rq with Temperature and Pressure ..... 150
9 Space and Space Groups ..................................... 152
9.1 Introduction .......................................... 152
9.2 The Crystal Lattice and Translational Symmetry ........ 153
9.3 Space Groups .......................................... 156
9.4 Special Positions ..................................... 158
9.5 Matching the Special Positions to the Chemistry ....... 160
9.6 The Symmetry of Bonded Neighbours ..................... 161
9.7 Conclusion ............................................ 164
10 Modelling Inorganic Structures ............................. 165
10.1 The Problem of A Priori Modelling ..................... 165
10.2 Determining the Topology .............................. 166
10.2.1 Space-Based Approaches ......................... 168
10.2.2 Chemistry-Based Approaches ..................... 173
10.2.3 Valence Maps ................................... 191
10.3 Refining the Geometry ................................. 191
10.4 Modelling Defect Structures ........................... 193
10.5 Modelling Glasses ..................................... 196
10.6 Example of an A Priori Modelling: Beryl ............... 197
10.7 Conclusion ............................................ 202
11 Steric Strain .............................................. 203
11.1 The Origins of Steric Strain .......................... 203
11.2 Measurement of Steric Strain .......................... 206
11.3 Relaxation of Steric Strain ........................... 208
11.3.1 Relaxation of die Geometry ..................... 209
11.3.2 Relaxation by Defects .......................... 209
11.3.3 Electronic Relaxation .......................... 210
11.3.4 Effects of Temperature and Displacive Phase
Transitions .................................... 211
11.3.5 Changing the Bond Graph—Reconstructive
Phase Transitions .............................. 212
11.3.6 Summary of Relaxations ......................... 213
11.4 Incommensurate Structures ................................ 213
12 Applications ............................................... 217
12.1 Introduction .......................................... 217
12.2 Crystallography ....................................... 218
12.2.1 Structure Determination ........................ 218
12.2.2 Analysis of Crystal Structures ................. 220
12.3 Physics ............................................... 222
12.3.1 Perovskite-Related SoUds ....................... 223
12.3.2 Electrical Properties .......................... 227
12.3.3 Magnetic Properties ............................ 232
12.3.4 Other Physical Properties ...................... 233
12.4 Chemistry ............................................. 233
12.4.1 Non-Diffraction Techniques ..................... 233
12.4.2 Heterogeneous Catalysis ........................ 234
12.4.3 Esterification and Hydrolysis .................. 236
12.4.4 Education ...................................... 237
12.5 Mineralogy ............................................ 238
12.5.1 Soil Chemistry ................................. 239
12.5.2 Zeolites ....................................... 242
12.5.3 Glasses ........................................ 242
12.6 Materials ............................................. 242
12.6.1 Crystal Growth ................................. 242
12.6.2 Surfaces and Interfaces ........................ 243
12.7 Biology ............................................... 245
12.7.1 Enzymes ........................................ 245
12.7.2 Calcium and Sodium Binding by Proteins ......... 247
12.8 Databases ............................................. 249
13 Chemical Implications of the Bond Valence Model ............ 250
13.1 Historical Development of the Bond Theory ............. 250
13.2 The Complementary Natures of the Flux and Quantum
Theories .............................................. 252
13.3 Properties of the Bond Flux ........................... 255
13.4 Relationship to Other Chemical Models ................. 258
13.5 Conclusion ............................................ 260
Appendix 1 Determining Bond Valence Parameters ................ 261
A1.1 Introduction .......................................... 261
Al.2 Determination of Bond Valence Parameters .............. 262
A1.2.1 Methods of Determining Bond Valences .......... 262
A1.2.2 Selection of the Target Set of Observed
Atomic Environments ........................... 263
A1.2.3 Refinement .................................... 264
A1.2.4 Special Cases ................................. 266
A1.3 Other Expressions ..................................... 267
Appendix 2 Space Group Spectra ................................ 269
Appendix 3 Refcodes for Crystal Structures .................... 278
Appendix 4 Glossary ........................................... 283
References .................................................... 291
Index ......................................................... 311
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