Preface ...................................................... xiii
Companion Website .............................................. xv
Acknowledgements .............................................. xvn
Biographies ................................................... xix
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
2.3.1 Symmetry operations and elements ................ 13
2.3.2 Point groups .................................... 15
2.3.3 Characters, character tables and symmetry
species ......................................... 17
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
2.8.1 Unstable species ................................ 27
2.8.2 Solutions in supercritical fluids ............... 28
2.8.3 Involatile species .............................. 28
2.8.4 Variable temperature and pressure measurements .. 29
2.9 Quantitative measurements .............................. 30
2.10 Instrumentation ........................................ 32
2.10.1 Radiation sources ............................... 32
2.10.2 Detectors ....................................... 35
2.11 Data analysis .......................................... 36
2.11.1 Fourier transformation .......................... 36
2.11.2 Experimental errors and uncertainties ........... 37
2.11.3 Least-squares refinement ........................ 39
2.11.4 Database mining ................................. 39
Review questions ............................................ 41
Discussion problems ......................................... 43
References .................................................. 43
3 Theoretical Methods ......................................... 45
3.1 Introduction ........................................... 45
3.2 Approximating the multi-electron Schrфdinger equation .. 46
3.2.1 The Hamiltonian operator, H ..................... 46
3.2.2 The molecular wavefunction ...................... 49
3.3 Exploring the potential-energy surface ................. 52
3.4 Extending the computational model to the solid state ... 56
3.4.1 Modeling a delocalized wavefunction, Ф;
periodic boundary conditions .................... 58
3.4.2 Approximating Я for solid-state structures ...... 60
3.4.3 Exploring the potential-energy surface for
solid-state structures .......................... 60
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
3.8.1 Vibrational spectra ............................. 69
3.8.2 NMR, EPR and Mossbauer spectra .................. 69
3.8.3 Molecular orbitals .............................. 70
3.8.4 Electronic spectra .............................. 71
3.8.5 Modeling solvent effects ........................ 73
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
4.3.1 NMR spectrometers ............................... 83
4.3.2 Sample preparation .............................. 85
4.3.3 Continuous wave and Fourier transform spectra ... 85
4.4 The pulse technique .................................... 86
4.4.1 Inducing magnetization by a pulse ............... 86
4.4.2 Relaxation of magnetization after a pulse ....... 87
4.4.3 Free induction decay and Fourier
transformation .................................. 90
4.5 Information from chemical shifts ....................... 92
4.5.1 General principles .............................. 92
4.5.2 Proton chemical shifts .......................... 94
4.5.3 Chemical shifts of other elements ............... 96
4.6 Information from NMR signal intensities ............... 100
4.7 Simple splitting patterns due to coupling between
nuclear spins ......................................... 101
4.7.1 First-order spectra of spin-1/2 isotopes of
100% abundance ................................. 101
4.7.2 Nuclear spin systems ........................... 102
4.7.3 Coupling to spin-1/2 isotopes of low
abundance ...................................... 106
4.7.4 Spectra of spin-1/2 isotopes of low abundance .. 107
4.7.5 Coupling to quadrupolar nuclei ................. 110
4.8 Information from coupling constants ................... 112
4.8.1 General principles ............................. 112
4.8.2 One-bond coupling .............................. 112
4.8.3 Two-bond coupling .............................. 114
4.8.4 Coupling over three bonds ...................... 114
4.8.5 Coupling over more than three bonds ............ 115
4.8.6 Coupling through space ......................... 116
4.9 Not-so-simple spectra ................................. 116
4.9.1 Second-order spectra ........................... 116
4.9.2 Chiral and prochiral non-equivalence ........... 119
4.9.3 Coincidences ................................... 119
4.10 The multi-nuclear approach ............................ 120
4.11 Multiple resonance .................................... 121
4.11.1 Selective spin decoupling ...................... 122
4.11.2 Spin decoupling ................................ 123
4.11.3 Triple resonance ............................... 124
4.11.4 The Nuclear Оverhauser Effect .................. 125
4.11.5 Gated decoupling ............................... 126
4.12 Multi-pulse methods ................................... 126
4.12.1 Introduction ................................... 126
4.12.2 Sensitivity enhancement by polarization
transfer ....................................... 127
4.12.3 Spectrum editing ............................... 129
4.13 Two-dimensional NMR spectroscopy ...................... 129
4.13.1 General principles and homonuclear
correlation experiments ........................ 129
4.13.2 Heteronuclear correlation experiments .......... 134
4.13.3 Two-dimensional nuclear Overhauser effect
spectra ........................................ 136
4.13.4 Diffusion ordered spectroscopy (DOSY) .......... 138
4.14 Gases ................................................. 140
4.15 Liquid crystals ....................................... 140
4.16 Solids ................................................ 141
4.17 Monitoring dynamic phenomena and reactions ............ 147
4.17.1 Intramolecular dynamic phenomena ............... 147
4.17.2 Exchange reactions and equilibria .............. 149
4.17.3 Monitoring reactions: identification of
intermediates .................................. 151
4.18 Paramagnetic compounds ................................ 154
Review questions ........................................... 159
Discussion problems ........................................ 161
References ................................................. 166
5 Electron Paramagnetic Resonance Spectroscopy ............... 169
5.1 The electron paramagnetic resonance experiment ......... 169
5.2 Hyperfine coupling in isotropic systems ................ 171
5.3 Anisotropic systems .................................... 175
5.3.1 Hyperfine splittings and g factors .............. 175
5.3.2 Electron-electron interactions .................. 176
5.4 Transition-metal complexes ............................. 179
5.5 Multiple resonance ..................................... 182
Review questions ........................................... 184
Discussion problems ........................................ 186
References ................................................. 187
6 Mуssbauer Spectroscopy ..................................... 189
6.1 Introduction .......................................... 189
6.2 The Mуssbauer effect .................................. 189
6.3 Experimental arrangements ............................. 192
6.4 Information from Mуssbauer spectroscopy ............... 194
6.4.1 The isomer shift ............................... 194
6.4.2 Quadrupole splitting ........................... 198
6.4.3 Magnetic splitting ............................. 202
6.5 Compound identification ............................... 204
6.5.1 The interhalogen compound I2Br2Cl2 ............. 205
6.5.2 Iron in very high oxidation states - Fe(V)
and Fe(VI) nitride complexes ................... 206
6.6 Temperature-and time-dependent effects ................ 208
6.6.1 Basic iron acetates ............................ 209
6.6.2 Spin crossover in the complex
[Fe(phen)2(NCS)2] .............................. 210
6.6.3 Valence fluctuation ............................ 211
6.7 Common difficulties encountered in Mуssbauer
spectroscopy .......................................... 212
6.8 Further possibilities in Mуssbauer 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
7.2.1 Classical rotation ............................. 219
7.2.2 Quantized rotation, moments of inertia and
rotation constants ............................. 220
7.2.3 Centrifugal distortion; the semi-rigid rotor ... 223
7.3 Rotational selection rules ............................ 224
7.3.1 Pure rotation spectra .......................... 224
7.3.2 Vibration-rotation spectra ..................... 225
7.4 Instrumentation ....................................... 228
7.5 Using the information in a spectrum ................... 229
7.5.1 Fingerprinting ................................. 229
7.5.2 Determination of rotation constants ............ 230
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
8.2.1 Vibrational motions and energies ............... 237
8.2.2 Non-ideal restoring forces; anharmonicity ...... 238
8.3 Observing molecular vibrations ........................ 239
8.3.1 Absorption in the infrared ..................... 239
8.3.2 Raman scattering ............................... 242
8.3.3 Resonance Raman spectroscopy ................... 242
8.3.4 Inelastic scattering of neutrons and
electrons ...................................... 244
8.4 Effects of phase on spectra ........................... 245
8.5 Vibrational spectra and symmetry ...................... 248
8.5.1 Fundamental vibrational selection rule ......... 248
8.5.2 Symmetry selection rules ....................... 248
8.5.3 Symmetry of an entire set of normal
vibrations ..................................... 249
8.5.4 Symmetry of vibrational modes .................. 251
8.6 Assignment of bands to vibrations ..................... 254
8.6.1 Raman polarization ............................. 255
8.6.2 Band contours in gases ......................... 256
8.6.3 Intensities of allowed fundamentals ............ 259
8.6.4 Mode numbering ................................. 260
8.6.5 Non-fundamental transitions .................... 260
8.7 Complete empirical assignment of vibrational spectra .. 262
8.8 Information from vibrational spectra .................. 263
8.8.1 Quantitative information ....................... 263
8.8.2 Qualitative information ........................ 264
8.8.3 Transition-metal carbonyl complexes ............ 267
8.8.4 Use of isotopes in interpreting and assigning
vibrational spectra ............................ 269
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
9.4.1 Observing valence-shell electrons .............. 281
9.4.2 Vibrational structure of PE bands .............. 281
9.4.3 Structural information from valence-shell PE
spectroscopy: making assignments ............... 285
9.4.4 Observing core-shell electrons ................. 286
9.5 Valence excitation spectroscopy ....................... 286
9.5.1 Experimental methods ........................... 286
9.5.2 The information in an electronic spectrum ...... 288
9.6 Electronic energy levels and transitions in
transition-metal complexes ............................ 289
9.6.1 Metal, ligand and metal-ligand bonding levels .. 289
9.6.2 Selection rules ................................ 290
9.6.3 Ligand-ligand and metal-metal transitions ...... 292
9.6.4 Metal-ligand and ligand-metal (charge-
transfer) bands ................................ 295
9.6.5 Inter-valence transitions ...................... 295
9.6.6 Assigning bands of transition-metal complexes .. 296
9.6.7 Spectra of compounds of elements with partly-
filled f sub-shells (lanthanides and
actinides) ..................................... 297
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
10.3.1 Experimental set-up ............................ 308
10.3.2 Theoretical basis of gas-phase diffraction ..... 309
10.3.3 Interpretation of results ...................... 314
10.3.4 Problems with underdetermined structures ....... 315
10.3.5 Experimental limitations ....................... 320
10.4 Diffraction by liquids ................................ 321
10.5 Diffraction by single crystals; symmetry .............. 323
10.5.1 The unit cell .................................. 324
10.5.2 Symmetry elements within the unit cell ......... 324
10.5.3 The seven crystal systems ...................... 326
10.5.4 Three-dimensional periodic symmetry; space
groups ......................................... 329
10.6 Diffraction by single crystals; the theoretical
basis ................................................. 329
10.7 Diffraction by single crystals; the experiment ........ 333
10.7.1 Crystal growth ................................. 333
10.7.2 Experimental set-up ............................ 334
10.7.3 Indexing and determining unit cell dimensions .. 336
10.7.4 Data collection ................................ 337
10.7.5 Experimental problems: X-ray absorption and
extinction ..................................... 338
10.7.6 Data analysis .................................. 338
10.8 Diffraction by single crystals; interpretation of
results ............................................... 341
10.8.1 How good is a structure? ....................... 341
10.8.2 Common problems: incorrect atom assignment ..... 343
10.8.3 Common problems: disorder ...................... 344
10.8.4 Recognizing chemical bonds ..................... 347
10.8.5 Absolute structure determination ............... 348
10.8.6 How big can we go? ............................. 348
10.9 Diffraction by single crystals; electron density
determination ......................................... 349
10.10 Topological features of the electron density ......... 352
10.10.1 Displaying topological features of the
electron density ............................. 353
10.10.2 Definition of a topological atom and its
properties ................................... 354
10.10.3 Critical points .............................. 355
10.10.4 Bonding description .......................... 356
10.10.5 The Laplacian of the electron density ........ 358
10.10.6 Some examples of electron topology studies ... 360
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 ............. 371
Review questions ........................................... 375
Discussion problems ........................................ 377
References ................................................. 381
11 Mass Spectrometry .......................................... 383
11.1 Introduction .......................................... 383
11.2 Experimental arrangements ............................. 383
11.2.1 Ion sources .................................... 383
11.2.2 Mass analyzers and detectors ................... 384
11.3 Data analysis ......................................... 387
11.3.1 Molecular ions ................................. 387
11.3.2 Fragmentation .................................. 389
11.4 Combined mass spectrometry methods .................... 392
11.4.1 Tandem mass spectrometry (MS/MS) ............... 392
11.4.2 Chromatography-coupled mass spectrometry ....... 394
Review questions ........................................... 396
Discussion problems ........................................ 397
References ................................................. 397
12 Case Histories ............................................. 399
12.1 Introduction .......................................... 399
12.2 Xenon compounds ....................................... 400
12.2.1 Xenon hexafluoride ............................. 400
12.2.2 Xenon-xenon bonds - strange but true ........... 404
12.3 The structure of N2O3 ................................. 407
12.4 Bismuthine ............................................ 409
12.5 Tetrahydroborates ..................................... 410
12.6 Is beryllocene a sandwich compound? ................... 415
12.7 Silylium cations - free at last ....................... 418
12.8 True phosphinous acids ................................ 422
12.9 Dihydrogen and dihydride complexes .................... 425
12.10 Agostic interactions: alkyl hydrogen atoms binding
to metal atoms ....................................... 428
12.11 Lower symmetry than expected in some phosphines and
phosphoranes ......................................... 430
12.12 Three-membered rings with dative bonds? .............. 432
12.13 Stable radicals ...................................... 436
12.13.1 Nitrogen radicals ............................ 436
12.13.2 Jack-in-the-box compounds .................... 438
12.14 Induced proton transfer in an adduct of squaric
acid and bipyridine .................................. 441
12.15 High-pressure studies of metal organic framework
materials ............................................ 443
12.16 Mistaken identity: mono-coordinate copper(I) and
silver(I) complexes .................................. 446
12.17 Oxidation states in a palladium-tin complex .......... 447
12.18 Structural and spectroscopic consequences of a
chemical change in an iron complex ................... 450
12.19 Some metalloproteins ................................. 454
12.19.1 Fixing N2 from air ........................... 455
12.19.2 Making oxygen from water ..................... 457
12.20 Atoms inside fullerene cages ......................... 459
12.21 Structural chemistry - where is it going? ............ 463
Discussion problem ......................................... 464
References ................................................. 464
Index ......................................................... 467
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