Preface xxi
Preface to the First Edition xxiii
Introduction 1
Part 1 Nuclear Magnetism 3
1 Matter 5
1.1 Atoms and Nuclei 5
1.2 Spin 5
1.3 Nuclei 9
1.4 Nuclear Spin 12
1.5 Atomic and Molecular Structure 15
2 Magnetism 23
2.1 The Electromagnetic Field 23
2.2 Macroscopic Magnetism 23
2.3 Microscopic Magnetism 25
2.4 Spin Precession 26
2.5 Larmor Frequency 29
2.6 Spin–Lattice Relaxation: Nuclear Paramagnetism 30
2.7 Transverse Magnetization and Transverse Relaxation 33
2.8 NMR Signal 36
2.9 Electronic Magnetism 36
3 NMR Spectroscopy 39
3.1 A Simple Pulse Sequence 39
3.2 A Simple Spectrum 39
3.3 Isotopomeric Spectra 42
3.4 Relative Spectral Frequencies: Case of Positive Gyromagnetic Ratio 44
3.5 Relative Spectral Frequencies: Case of Negative Gyromagnetic Ratio 46
3.6 Inhomogeneous Broadening 48
3.7 Chemical Shifts 50
3.8 J-Coupling Multiplets 56
3.9 Heteronuclear Decoupling 59
Part 2 The NMR Experiment 63
4 The NMR Spectrometer 65
4.1 The Magnet 65
4.2 The Transmitter Section 66
4.3 The Duplexer 69
4.4 The Probe 70
4.5 The Receiver Section 72
4.6 Overview of the Radio-Frequency Section 76
4.7 Pulsed Field Gradients 77
5 Fourier Transform NMR 85
5.1 A Single-Pulse Experiment 85
5.2 Signal Averaging 86
5.3 Multiple-Pulse Experiments: Phase Cycling 89
5.4 Heteronuclear Experiments 90
5.5 Pulsed Field Gradient Sequences 91
5.6 Arrayed Experiments 91
5.7 NMR Signal 93
5.8 NMR Spectrum 96
5.9 Two-Dimensional Spectroscopy 105
5.10 Three-Dimensional Spectroscopy 114
Part 3 Quantum Mechanics 119
6 Mathematical Techniques 121
6.1 Functions 121
6.2 Operators 125
6.3 Eigenfunctions, Eigenvalues and Eigenvectors 131
6.4 Diagonalization 134
6.5 Exponential Operators 135
6.6 Cyclic Commutation 138
7 Review of Quantum Mechanics 143
7.1 Spinless Quantum Mechanics 143
7.2 Energy Levels 145
7.3 Natural Units 146
7.4 Superposition States and Stationary States 147
7.5 Conservation Laws 148
7.6 Angular Momentum 148
7.7 Spin 157
7.8 Spin-1/ 2 160
7.9 Higher Spin 162
Part 4 Nuclear Spin Interactions 169
8 Nuclear Spin Hamiltonian 171
8.1 Spin Hamiltonian Hypothesis 171
8.2 Electromagnetic Interactions 172
8.3 External and Internal Spin Interactions 177
8.4 External Magnetic Fields 177
8.5 Internal Spin Hamiltonian 182
8.6 Motional Averaging 186
9 Internal Spin Interactions 195
9.1 Chemical Shift 195
9.2 Electric Quadrupole Coupling 206
9.3 Direct Dipole–Dipole Coupling 211
9.4 J-Coupling 217
9.5 Spin–Rotation Interaction 223
9.6 Summary of the Spin Hamiltonian Terms 224
Part 5 Uncoupled Spins 229
10 Single Spin-1/2 231
10.1 Zeeman Eigenstates 231
10.2 Measurement of Angular Momentum: Quantum Indeterminacy 232
10.3 Energy Levels 233
10.4 Superposition States 234
10.5 Spin Precession 238
10.6 Rotating Frame 241
10.7 Precession in the Rotating Frame 245
10.8 Radio-frequency Pulse 247
11 Ensemble of Spins-1/2 259
11.1 Spin Density Operator 259
11.2 Populations and Coherences 261
11.3 Thermal Equilibrium 266
11.4 Rotating-Frame Density Operator 268
11.5 Magnetization Vector 269
11.6 Strong Radio-Frequency Pulse 270
11.7 Free Precession Without Relaxation 276
11.8 Operator Transformations 279
11.9 Free Evolution with Relaxation 281
11.10 Magnetization Vector Trajectories 285
11.11 NMR Signal and NMR Spectrum 287
11.12 Single-Pulse Spectra 289
12 Experiments on Non-Interacting Spins-1/2 295
12.1 Inversion Recovery: Measurement of T 1 295
12.2 Spin Echoes: Measurement of T 2 298
12.3 Spin Locking: Measurement of T 1ρ 305
12.4 Gradient Echoes 306
12.5 Slice Selection 307
12.6 NMR Imaging 309
13 Quadrupolar Nuclei 319
13.1 Spin I = 1 319
13.2 Spin I = 3/2 334
13.3 Spin I = 5/2 345
13.4 Spins I = 7/2 349
13.5 Spins I = 9/2 350
Part 6 Coupled Spins 353
14 Spin-1/2 Pairs 355
14.1 Coupling Regimes 355
14.2 Zeeman Product States and Superposition States 356
14.3 Spin-Pair Hamiltonian 357
14.4 Pairs of Magnetically Equivalent Spins 359
14.5 Weakly Coupled Spin Pairs 363
15 Homonuclear AX System 369
15.1 Eigenstates and Energy Levels 369
15.2 Density Operator 370
15.3 Rotating Frame 375
15.4 Free Evolution 376
15.5 Spectrum of the AX System: Spin–Spin Splitting 378
15.6 Product Operators 381
15.7 Thermal Equilibrium 389
15.8 Radio-Frequency Pulses 391
15.9 Free Evolution of the Product Operators 397
15.10 Spin Echo Sandwich 405
16 Experiments on AX Systems 409
16.1 Cosy 409
16.2 Inadequate 418
16.3 Inept 436
16.4 Residual Dipolar Couplings 443
17 Many-Spin Systems 453
17.1 Molecular Spin System 453
17.2 Spin Ensemble 454
17.3 Motionally Suppressed J-Couplings 454
17.4 Chemical Equivalence 455
17.5 Magnetic Equivalence 458
17.6 Weak Coupling 461
17.7 Heteronuclear Spin Systems 462
17.8 Alphabet Notation 463
17.9 Spin Coupling Topologies 464
18 Many-Spin Dynamics 467
18.1 Spin Hamiltonian 467
18.2 Energy Eigenstates 468
18.3 Superposition States 469
18.4 Spin Density Operator 470
18.5 Populations and Coherences 471
18.6 NMR Spectra 475
18.7 Many-Spin Product Operators 477
18.8 Thermal Equilibrium 481
18.9 Radio-Frequency Pulses 481
18.10 Free Precession 482
18.11 Spin Echo Sandwiches 485
18.12 INEPT in an I2 S System 488
18.13 COSY in Multiple-Spin Systems 491
18.14 Tocsy 497
Part 7 Motion and Relaxation 507
19 Motion 509
19.1 Motional Processes 509
19.2 Motional Time-Scales 513
19.3 Motional Effects 514
19.4 Motional Averaging 515
19.5 Motional Lineshapes and Two-Site Exchange 516
19.6 Sample Spinning 527
19.7 Longitudinal Magnetization Exchange 529
19.8 Diffusion 539
20 Relaxation 543
20.1 Types of Relaxation 543
20.2 Relaxation Mechanisms 543
20.3 Random Field Relaxation 545
20.4 Dipole–Dipole Relaxation 556
20.5 Steady-State Nuclear Overhauser Effect 566
20.6 Noesy 570
20.7 Roesy 577
20.8 Cross-Correlated Relaxation 584
Part 8 Appendices 597
Appendix A: Supplementary Material 599
A. 1 Euler Angles and Frame Transformations 599
A. 1 Definition of the Euler angles 599
A. 2 Rotations and Cyclic Commutation 604
A. 3 Rotation Sandwiches 605
A. 4 Spin-1/2 Rotation Operators 606
A. 5 Quadrature Detection and Spin Coherences 608
A. 6 Secular Approximation 611
A. 7 Quadrupolar Interaction 614
A. 8 Strong Coupling 615
A. 9 J-Couplings and Magnetic Equivalence 621
A. 10 Spin Echo Sandwiches 623
A. 11 Phase Cycling 629
A.12 Coherence Selection by Pulsed Field Gradients 649
A. 13 Bloch Equations 653
A. 14 Chemical Exchange 654
A. 15 Solomon Equations 660
A. 16 Cross-Relaxation Dynamics 662
Appendix B: Symbols and Abbreviations 665
Answers to the Exercises 681
Index 693
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