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Understanding NMR Spectroscopy, 2nd Edition

ISBN: 978-0-470-74608-0
526 pages
May 2010
Understanding NMR Spectroscopy, 2nd Edition (0470746084) cover image
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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Preface to the first edition.

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

1.1 How this book is organized.

1.2 Scope and limitations.

1.3 Context and further reading.

1.4 On-line resources.

1.5 Abbreviations and acronyms.

2 Setting the scene.

2.1 NMR frequencies and chemical shifts.

2.2 Linewidths, lineshapes and integrals.

2.3 Scalar coupling.

2.4 The basic NMR experiment.

2.5 Frequency, oscillations and rotations.

2.6 Photons.

2.7 Further reading.

2.8 Exercises.

3 Energy levels and NMR spectra.

3.1 The problem with the energy level approach.

3.2 Introducing quantum mechanics.

3.3 The spectrum from one spin.

3.4 Writing the Hamiltonian in frequency units.

3.5 The energy levels for two coupled spins.

3.6 The spectrum from two coupled spins.

3.7 Three spins.

3.8 Summary. 

3.9 Further reading.

3.10 Exercises.

4 The vector model.

4.1 The bulk magnetization.

4.2 Larmor precession.

4.3 Detection.

4.4 Pulses.

4.5 On-resonance pulses.

4.6 Detection in the rotating frame.

4.7 The basic pulse–acquire experiment.

4.8 Pulse calibration.

4.9 The spin echo.

4.10 Pulses of different phases.

4.11 Off-resonance effects and soft pulses.

4.12 Further reading.

4.13 Exercises.

5 Fourier transformation and data processing.

5.1 How the Fourier transform works.

5.2 Representing the FID.

5.3 Lineshapes and phase.

5.4 Manipulating the FID and the spectrum.

5.5 Zero filling.

5.6 Truncation.

5.7 Further reading.

5.8 Exercises.

6 The quantum mechanics of one spin.

6.1 Introduction.

6.2 Superposition states.

6.3 Some quantum mechanical tools.

6.4 Computing the bulk magnetization.

6.5 Time evolution.

6.6 RF pulses.

6.7 Making faster progress: the density operator.

6.8 Coherence.

6.9 Further reading.

6.10 Exercises.

7 Product operators.

7.1 Operators for one spin.

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

7.3 Speeding things up.

7.4 Operators for two spins.

7.5 In-phase and anti-phase terms.

7.6 Hamiltonians for two spins.

7.7 Notation for heteronuclear spin systems.

7.8 Spin echoes and J-modulation.

7.9 Coherence transfer.

7.10 The INEPT experiment.

7.11 Selective COSY.

7.12 Coherence order and multiple-quantum coherences.

7.13 Summary. 

7.14 Further reading.

7.15 Exercises.

8 Two-dimensional NMR.

8.1 The general scheme for two-dimensional NMR.

8.2 Modulation and lineshapes.

8.3 COSY.


8.5 Double-quantum spectroscopy.

8.6 Heteronuclear correlation spectra.

8.7 HSQC.

8.8 HMQC.

8.9 Long-range correlation: HMBC.

8.10 HETCOR.

8.11 TOCSY.

8.12 Frequency discrimination and lineshapes.

8.13 Further reading.

8.14 Exercises.

9 Relaxation and the NOE.

9.1 The origin of relaxation.

9.2 Relaxation mechanisms.

9.3 Describing random motion – the correlation time.

9.4 Populations.

9.5 Longitudinal relaxation behaviour of isolated spins.

9.6 Longitudinal dipolar relaxation of two spins.

9.7 The NOE.

9.8 Transverse relaxation.

9.9 Homogeneous and inhomogeneous broadening.

9.10 Relaxation due to chemical shift anisotropy.

9.11 Cross correlation.

9.12 Further reading.

9.13 Exercises.

10 Advanced topics in two-dimensional NMR.

10.1 Product operators for three spins.

10.2 COSY for three spins.

10.3 Reduced multiplets in COSY spectra.

10.4 Polarization operators.

10.5 ZCOSY.

10.6 HMBC.

10.7 Sensitivity-enhanced experiments.

10.8 Constant time experiments.

10.9 TROSY.

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

10.11 Further reading.

10.12 Exercises.

11 Coherence selection: phase cycling and field gradient pulses.

11.1 Coherence order.

11.2 Coherence transfer pathways.

11.3 Frequency discrimination and lineshapes.

11.4 The receiver phase.

11.5 Introducing phase cycling.

11.6 Some phase cycling ‘tricks’.

11.7 Axial peak suppression.


11.9 Examples of practical phase cycles.

11.10 Concluding remarks about phase cycling.

11.11 Introducing field gradient pulses.

11.12 Features of selection using gradients.

11.13 Examples of using gradient pulses.

11.14 Advantages and disadvantages of coherence selection with gradients.

11.15 Suppression of zero-quantum coherence.

11.16 Selective excitation with the aid of gradients.

11.17 Further reading.

11.18 Exercises.

12 Equivalent spins and spin system analysis.

12.1 Strong coupling in a two-spin system.

12.2 Chemical and magnetic equivalence.

12.3 Product operators for AXn (InS) spin systems.

12.4 Spin echoes in InS spin systems.

12.5 INEPT in InS spin systems.

12.6 DEPT.

12.7 Spin system analysis.

12.8 Further reading.

12.9 Exercises.

13 How the spectrometer works.

13.1 The magnet.

13.2 The probe.

13.3 The transmitter.

13.4 The receiver.

13.5 Digitizing the signal.

13.6 Quadrature detection.

13.7 The pulse programmer.

13.8 Further reading.

13.9 Exercises.

A Some mathematical topics.

A.1 The exponential function and logarithms.

A.2 Complex numbers.

A.3 Trigonometric identities.

A.4 Further reading.


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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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  • 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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  • 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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