Understanding NMR Spectroscopy

Preface v

Preface to the first edition vi

1 What this book is about and who should read it 1

1.1 How this book is organized 2

1.2 Scope and limitations 3

1.3 Context and further reading 3

1.4 On-line resources 4

1.5 Abbreviations and acronyms 4

2 Setting the scene 5

2.1 NMR frequencies and chemical shifts 5

2.2 Linewidths, lineshapes and integrals 9

2.3 Scalar coupling 10

2.4 The basic NMR experiment 13

2.5 Frequency, oscillations and rotations 15

2.6 Photons 20

2.7 Moving on 21

2.8 Further reading 21

2.9 Exercises 22

3 Energy levels and NMR spectra 23

3.1 The problem with the energy level approach 24

3.2 Introducing quantum mechanics 26

3.3 The spectrum from one spin 31

3.4 Writing the Hamiltonian in frequency units 34

3.5 The energy levels for two coupled spins 35

3.6 The spectrum from two coupled spins 38

3.7 Three spins 40

3.8 Summary 44

3.9 Further reading 44

3.10 Exercises 45

4 The vector model 47

4.1 The bulk magnetization 47

4.2 Larmor precession 50

4.3 Detection 51

4.4 Pulses 52

4.5 On-resonance pulses 57

4.6 Detection in the rotating frame 60

4.7 The basic pulse-acquire experiment 60

4.8 Pulse calibration 61

4.9 The spin echo 63

4.10 Pulses of different phases 66

4.11 Off-resonance effects and soft pulses 67

4.12 Moving on 71

4.13 Further reading 71

4.14 Exercises 72

5 Fourier transformation and data processing 77

5.1 How the Fourier transform works 78

5.2 Representing the FID 82

5.3 Lineshapes and phase 83

5.4 Manipulating the FID and the spectrum 90

5.5 Zero filling 99

5.6 Truncation 100

5.7 Further reading 101

5.8 Exercises 102

6 The quantum mechanics of one spin 105

6.1 Introduction 105

6.2 Superposition states 106

6.3 Some quantum mechanical tools 107

6.4 Computing the bulk magnetization 112

6.5 Summary 117

6.6 Time evolution 118

6.7 RF pulses 123

6.8 Making faster progress: the density operator 126

6.9 Coherence 134

6.10 Further reading 135

6.11 Exercises 136

7 Product operators 139

7.1 Operators for one spin 139

7.2 Analysis of pulse sequences for a one-spin system 143

7.3 Speeding things up 146

7.4 Operators for two spins 149

7.5 In-phase and anti-phase terms 152

7.6 Hamiltonians for two spins 157

7.7 Notation for heteronuclear spin systems 157

7.8 Spin echoes and J-modulation 158

7.9 Coherence transfer 166

7.10 The INEPT experiment 167

7.11 Selective COSY 171

7.12 Coherence order and multiple-quantum coherences 173

7.13 Summary 178

7.14 Further reading 179

7.15 Exercises 180

8 Two-dimensional NMR 183

8.1 The general scheme for two-dimensional NMR 184

8.2 Modulation and lineshapes 187

8.3 COSY 190

8.4 DQF COSY 200

8.5 Double-quantum spectroscopy 203

8.6 Heteronuclear correlation spectra 208

8.7 HSQC 209

8.8 HMQC 212

8.9 Long-range correlation: HMBC 215

8.10 HETCOR 220

8.11 TOCSY 221

8.12 Frequency discrimination and lineshapes 226

8.13 Further reading 236

8.14 Exercises 238

9 Relaxation and the NOE 241

9.1 The origin of relaxation 242

9.2 Relaxation mechanisms 249

9.3 Describing random motion - the correlation time 251

9.4 Populations 258

9.5 Longitudinal relaxation behaviour of isolated spins 263

9.6 Longitudinal dipolar relaxation of two spins 267

9.7 The NOE 274

9.8 Transverse relaxation 286

9.9 Homogeneous and inhomogeneous broadening 300

9.10 Relaxation due to chemical shift anisotropy 304

9.11 Cross correlation 306

9.12 Summary 311

9.13 Further reading 311

9.14 Exercises 313

10 Advanced topics in two-dimensional NMR 319

10.1 Product operators for three spins 320

10.2 COSY for three spins 325

10.3 Reduced multiplets in COSY spectra 330

10.4 Polarization operators 337

10.5 ZCOSY 345

10.6 HMBC 347

10.7 Sensitivity-enhanced experiments 349

10.8 Constant time experiments 353

10.9 TROSY 358

10.10 Double-quantum spectroscopy of a three-spin system 366

10.11 Further reading 374

10.12 Exercises 376

11 Coherence selection: phase cycling and field gradient pulses 381

11.1 Coherence order 382

11.2 Coherence transfer pathways 387

11.3 Frequency discrimination and lineshapes 389

11.4 The receiver phase 391

11.5 Introducing phase cycling 395

11.6 Some phase cycling 'tricks' 401

11.7 Axial peak suppression 403

11.8 CYCLOPS 403

11.9 Examples of practical phase cycles 404

11.10 Concluding remarks about phase cycling 408

11.11 Introducing field gradient pulses 409

11.12 Features of selection using gradients 416

11.13 Examples of using gradient pulses 421

11.14 Advantages and disadvantages of coherence selection with gradients 426

11.15 Suppression of zero-quantum coherence 426

11.16 Selective excitation with the aid of gradients 432

11.17 Further reading 435

11.18 Exercises 436

12 Equivalent spins and spin system analysis 441

12.1 Strong coupling in a two-spin system 442

12.2 Chemical and magnetic equivalence 446

12.3 Product operators for AXn (InS) spin systems 450

12.4 Spin echoes in InS spin systems 455

12.5 INEPT in InS spin systems 458

12.6 DEPT 462

12.7 Spin system analysis 468

12.8 Further reading 477

12.9 Exercises 478

13 How the spectrometer works 483

13.1 The magnet 483

13.2 The probe 485

13.3 The transmitter 486

13.4 The receiver 488

13.5 Digitizing the signal 489

13.6 Quadrature detection 491

13.7 The pulse programmer 493

13.8 Further reading 493

13.9 Exercises 494

A Some mathematical topics 495

A.1 The exponential function and logarithms 495

A.2 Complex numbers 497

A.3 Trigonometric identities 499

A.4 Further reading 500

Index 501