Understanding NMR Spectroscopy

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

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