Determining the structure of molecules is a fundamental skill that all chemists must learn. Structural Methods in Molecular Inorganic Chemistry is designed to help readers interpret experimental data, understand the material published in modern journals of inorganic chemistry, and make decisions about what techniques will be the most useful in solving particular structural problems. Following a general introduction to the tools and concepts in structural chemistry, the following topics are covered in detail: computational chemistry nuclear magnetic resonance spectroscopy electron paramagnetic resonance spectroscopy Mössbauer spectroscopy rotational spectra and rotational structure vibrational spectroscopy electronic characterization techniques diffraction methods mass spectrometry The final chapter presents a series of case histories, illustrating how chemists have applied a broad range of structural techniques to interpret and understand chemical systems. Throughout the textbook a strong connection is made between theoretical topics and the real world of practicing chemists. Each chapter concludes with problems and discussion questions, and a supporting website contains additional advanced material.

Preface xiii

Acknowledgements xvii

1. Determining Structures – How and Why? 1

1.1 Structural Chemistry – Where did it Come From? 1

1.2 Asking Questions about Structure 4

1.3 Answering Questions about Structure 5

1.4 Plan of the Book 7

1.5 Supplementary Information 8

2. Tools and Concepts 9

2.1 Introduction 9

2.2 How Structural Chemistry Techniques Work 10

2.3 Symmetry 11

2.4 Electron Density 21

2.5 Potential-energy Surfaces 21

2.6 Timescales 24

2.7 Structural Definitions 26

2.8 Sample Preparation 27

2.9 Quantitative Measurements 30

2.10 Instrumentation 32

2.11 Data Analysis 36

Review Questions 41

Discussion Problems 43

References 43

3. Theoretical Methods 45

3.1 Introduction 45

3.2 Approximating the Multi-electron Schrodinger Equation 46

3.3 Exploring the Potential-energy Surface 52

3.4 Extending the Computational Model to the Solid State 56

3.5 Calculating Thermodynamic Properties 61

3.6 Calculating Properties of Chemical Bonding 63

3.7 Comparing Theory with Experiment: Geometry 65

3.8 Comparing Theory with Experiment: Molecular Properties 68

3.9 Combining Theory and Experiment 74

Review Questions 75

Discussion Problems 77

References 77

4. Nuclear Magnetic Resonance Spectroscopy 79

4.1 Introduction 79

4.2 The Nuclear Magnetic Resonance Phenomenon 79

4.3 Experimental Set-up 83

4.4 The Pulse Technique 86

4.5 Information from Chemical Shifts 92

4.6 Information from NMR Signal Intensities 100

4.7 Simple Splitting Patterns Due to Coupling Between Nuclear Spins 101

4.8 Information from Coupling Constants 112

4.9 Not-so-simple Spectra 116

4.10 The Multi-nuclear Approach 120

4.11 Multiple Resonance 121

4.12 Multi-pulse Methods 126

4.13 Two-dimensional NMR Spectroscopy 129

4.14 Gases 140

4.15 Liquid Crystals 140

4.16 Solids 141

4.17 Monitoring Dynamic Phenomena and Reactions 147

4.18 Paramagnetic Compounds 154

Review Questions 159

Discussion Problems 161

References 166

5. Electron Paramagnetic Spectroscopy 169

5.1 The Electron Paramagnetic Resonance Experiment 169

5.2 Hyperfine Coupling in Isotropic Systems 171

5.3 Anisotropic Systems 175

5.4 Transition-metal Complexes 179

5.5 Multiple Resonance 182

Review Questions 184

Discussion Problems 186

References 187

6. M€ossbauer Spectroscopy 189

6.1 Introduction 189

6.2 The M€ossbauer Effect 189

6.3 Experimental Arrangements 192

6.4 Information from M€ossbauer Spectroscopy 194

6.5 Compound Identification 204

6.6 Temperature- and Time-dependent Effects 208

6.7 Common Difficulties Encountered in M€ossbauer Spectroscopy 212

6.8 Further Possibilities in M€ossbauer Spectroscopy 213

Review Questions 213

Discussion Problems 214

References 217

7. Rotational Spectra and Rotational Structure 219

7.1 Introduction 219

7.2 The Rotation of Molecules 219

7.3 Rotational Selection Rules 224

7.4 Instrumentation 228

7.5 Using the Information in a Spectrum 229

7.6 Using Rotation Constants to Define Molecular Structures 232

Review Questions 234

Discussion Problems 235

References 236

8. Vibrational Spectroscopy 237

8.1 Introduction 237

8.2 The Physical Basis; Molecular Vibrations 237

8.3 Observing Molecular Vibrations 239

8.4 Effects of Phase on Spectra 245

8.5 Vibrational Spectra and Symmetry 248

8.6 Assignment of Bands to Vibrations 254

8.7 Complete Empirical Assignment of Vibrational Spectra 262

8.8 Information from Vibrational Spectra 263

8.9 Normal Coordinate Analysis 272

Review Questions 273

Discussion Problems 274

References 276

9. Electronic Characterization Techniques 277

9.1 Introduction 277

9.2 Electron Energy Levels in Molecules 278

9.3 Symmetry and Molecular Orbitals 279

9.4 Photoelectron Spectroscopy 281

9.5 Valence Excitation Spectroscopy 286

9.6 Electronic Energy Levels and Transitions in Transition-metal Complexes 289

9.7 Circular Dichroism 298

Review Questions 299

Discussion Problems 300

References 302

10. Diffraction Methods 303

10.1 Introduction 303

10.2 Diffraction of Electrons, Neutrons and X-rays 304

10.3 Diffraction by gases 308

10.4 Diffraction by liquids 321

10.5 Diffraction by Single Crystals; Symmetry 323

10.6 Diffraction by Single Crystals; the Theoretical Basis 329

10.7 Diffraction by Single Crystals; the Experiment 333

10.8 Diffraction by Single Crystals; Interpretation of Results 341

10.9 Diffraction by Single Crystals; Electron Density Determination 349

10.10 Topological Features of the Electron Density 352

10.11 Phase Dependence of Molecular Structures 363

10.12 Diffraction of Neutrons by Crystals 365

10.13 Diffraction by Powders 368

10.14 High-pressure Crystallography 368

10.15 Extended X-ray Absorption Fine Structure 370

Review Questions 375

Discussion Problems 377

References 381

11. Mass Spectrometry 383

11.1 Introduction 383

11.2 Experimental Arrangements 383

11.3 Data Analysis 387

11.4 Combined Mass Spectrometry Methods 392

Review Questions 396

Discussion Problems 397

References 397

12. Case Histories 399

12.1 Introduction 399

12.2 Xenon Compounds 400

Discussion problem 404

Discussion Problem 407

12.3 The Structure of N2O3 407

Discussion Problem 409

12.4 Bismuthine 409

Discussion Problem 410

12.5 Tetrahydroborates 410

Discussion Problem 415

12.6 Is Beryllocene a Sandwich Compound? 415

Discussion Problem 418

12.7 Silylium Cations – Free at Last 418

12.8 True Phosphinous Acids 422

Discussion Problem 425

12.9 Dihydrogen and Dihydride Complexes 425

Discussion Problem 428

12.10 Agostic Interactions: Alkyl Hydrogen Atoms Binding to Metal Atoms 428

Discussion Problem 430

12.11 Lower Symmetry than Expected in some Phosphines and Phosphoranes 430

Discussion Problem 432

12.12 Three-membered Rings with Dative Bonds? 432

Discussion Problem 436

12.13 Stable Radicals 436

Discussion Problem 438

Discussion Problem 441

12.14 Induced Proton Transfer in an Adduct of Squaric Acid and Bipyridine 441

Discussion Problem 442

12.15 High-pressure Studies of Metal Organic Framework Materials 443

Discussion Problem 445

12.16 Mistaken Identity: Mono-coordinate Copper(I) and Silver(I) Complexes 446

Discussion Problem 447

12.17 Oxidation States in a Palladium–tin Complex 447

Discussion Problem 450

12.18 Structural and Spectroscopic Consequences of a Chemical Change in an Iron

Complex 450

Discussion Problem 454

12.19 Some Metalloproteins 454

Discussion Problem 457

Discussion Problem 459

12.20 Atoms Inside Fullerene Cages 459

Discussion Problem 462

12.21 Structural Chemistry – Where is it Going? 463

Discussion Problem 463

References 463

Index 00