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Understanding NMR Spectroscopy, 2nd Edition

ISBN: 978-0-470-74609-7
526 pages
May 2010
Understanding NMR Spectroscopy, 2nd Edition (0470746092) cover image

Description

This text is aimed at people who have some familiarity with high-resolution NMR and who wish to deepen their understanding of how NMR experiments actually ‘work’. This revised and updated edition takes the same approach as the highly-acclaimed first edition. The text concentrates on the description of commonly-used experiments and explains in detail the theory behind how such experiments work. The quantum mechanical tools needed to analyse pulse sequences are introduced set by step, but the approach is relatively informal with the emphasis on obtaining a good understanding of how the experiments actually work. The use of two-colour printing and a new larger format improves the readability of the text. In addition, a number of new topics have been introduced:
  • How product operators can be extended to describe experiments in AX2 and AX3 spin systems, thus making it possible to discuss the important APT, INEPT and DEPT experiments often used in carbon-13 NMR.
  • Spin system analysis i.e. how shifts and couplings can be extracted from strongly-coupled (second-order) spectra.
  • How the presence of chemically equivalent spins leads to spectral features which are somewhat unusual and possibly misleading, even at high magnetic fields.
  • A discussion of chemical exchange effects has been introduced in order to help with the explanation of transverse relaxation.
  • The double-quantum spectroscopy of a three-spin system is now considered in more detail.

Reviews of the First Edition

“For anyone wishing to know what really goes on in their NMR experiments, I would highly recommend this book” – Chemistry World

“…I warmly recommend for budding NMR spectroscopists, or others who wish to deepen their understanding of elementary NMR theory or theoretical tools” – Magnetic Resonance in Chemistry

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Table of Contents

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

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Author Information

Dr James Keeler is a Senior Lecturer in Chemistry at the University of Cambridge, and a Fellow of Selwyn College. In addition to being actively involved in the development of new NMR techniques, he is also responsible for the undergraduate chemistry course, and is Editor-In-chief of Magnetic Resonance in Chemistry. Dr Keeler is well-known for his clear and accessible exposition of NMR spectroscopy.
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New to This Edition

  • Completely new page layout incorporating extensive use of a second colour
  • A discussion of how to analyse the behaviour of AX2 and AX3 spin systems. This is a relatively straightforward extension of the product operator scheme set out in Chapter 7. It is worthwhile including this as there are some commonly encountered experiments, such as DEPT and APT
  • An elementary discussion of chemical exchange. Although the first edition included material relating to relaxation (Chapter 9), it didn’t discuss the closely related topic of chemical exchange. The two phenomena have quite a lot in common, and for a didactic point of view it is helpful to be able to refer to the similarities (and differences) between the two processes
  • Addition of a short chapter on classic spin-system analysis. This topic has become rather unfashionable (having been the mainstay of classic NMR texts in the sixties and seventies), but nevertheless remains important.
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The Wiley Advantage

  • Remains the only book which sets out the theory of NMR in an accessible and comprehensible manner, avoiding excessive mathematics and taking the reader step by step though the argument.
  • Completely new page layout incorporating extensive use of a second colour
  • Inclusion of material on chemical exchange, spin-system analysis and the behavior of AX2 and AC3 spin systems
  • Addition of interactive web-based resources for the book which go beyond simply reproducing the figures.
  • Each chapter with tested exercises.
  • Incorporating feedback from course participants and internet users.
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