Malcolm H. Levitt0470511184, 9780470511183, 9780470517123
The book assumes only a basic knowledge of complex numbers and matrices, and provides the reader with numerous worked examples and exercises to encourage understanding. With the explicit aim of carefully developing the subject from the beginning, the text starts with coverage of quarks and nucleons and progresses through to a detailed explanation of several important NMR experiments, including NMR imaging, COSY, NOESY and TROSY.
Completely revised and updated, the Second Edition features new material on the properties and distributions of isotopes, chemical shift anisotropy and quadrupolar interactions, Pake patterns, spin echoes, slice selection in NMR imaging, and a complete new chapter on the NMR spectroscopy of quadrupolar nuclei. New appendices have been included on Euler angles, and coherence selection by field gradients. As in the first edition, all material is heavily supported by graphics, much of which is new to this edition.
Written for undergraduates and postgraduate students taking a first course in NMR spectroscopy and for those needing an up-to-date account of the subject, this multi-disciplinary book will appeal to chemical, physical, material, life, medical, earth and environmental scientists. The detailed physical insights will also make the book of interest for experienced spectroscopists and NMR researchers.
• An accessible and carefully written introduction, designed to help students to fully understand this complex and dynamic subject
• Takes a multi-disciplinary approach, focusing on basic principles and concepts rather than the more practical aspects
• Presents a strong pedagogical approach throughout, with emphasis placed on individual spins to aid understanding
• Includes numerous worked examples, problems, further reading and additional notes
Praise from the reviews of the First Edition:
“This is an excellent book… that many teachers of NMR spectroscopy will cherish… It deserves to be a ‘classic’ among NMR spectroscopy texts .” NMR IN BIOMEDICINE
“I strongly recommend this book to everyone…it is probably the best modern comprehensive description of the subject.” ANGEWANDTE CHEMIE, INTERNATIONAL EDITION
Table of contents :
Spin Dynamics Basics of Nuclear Magnetic Resonance……Page 1
Contents……Page 9
Preface……Page 23
Preface to the First Edition……Page 25
Introduction……Page 29
Part 1 Nuclear Magnetism……Page 31
1.2 Spin……Page 33
1.2.2 Quantum angular momentum……Page 34
1.2.3 Spin angular momentum……Page 35
1.2.4 Combining angular momenta……Page 36
1.3.1 The fundamental particles……Page 37
1.3.2 Neutrons and protons……Page 38
1.3.3 Isotopes……Page 39
1.4.1 Nuclear spin states……Page 40
1.4.3 Zero-spin nuclei……Page 42
1.5.1 Atoms……Page 43
1.5.2 Molecules……Page 44
1.6.2 Liquids……Page 45
1.6.3 Solids……Page 47
2.2 Macroscopic Magnetism……Page 51
2.3 Microscopic Magnetism……Page 53
2.4 Spin Precession……Page 54
2.5 Larmor Frequency……Page 57
2.6 SpinLattice Relaxation: Nuclear Paramagnetism……Page 58
2.7 Transverse Magnetization and Transverse Relaxation……Page 61
2.9 Electronic Magnetism……Page 64
3.2 A Simple Spectrum……Page 67
3.3 Isotopomeric Spectra……Page 70
3.4 Relative Spectral Frequencies: Case of Positive Gyromagnetic Ratio……Page 72
3.5 Relative Spectral Frequencies: Case of Negative Gyromagnetic Ratio……Page 74
3.6 Inhomogeneous Broadening……Page 76
3.7 Chemical Shifts……Page 78
3.8 J-Coupling Multiplets……Page 84
3.9 Heteronuclear Decoupling……Page 87
Part 2 The NMR Experiment……Page 91
4.1 The Magnet……Page 93
4.2 The Transmitter Section……Page 94
4.2.1 The synthesizer: radio-frequency phase shifts……Page 95
4.2.2 The pulse gate: radio-frequency pulses……Page 96
4.3 The Duplexer……Page 97
4.4 The Probe……Page 98
4.5 The Receiver Section……Page 100
4.5.2 The quadrature receiver……Page 101
4.5.3 Analoguedigital conversion……Page 102
4.6 Overview of the Radio-Frequency Section……Page 104
4.7 Pulsed Field Gradients……Page 105
4.7.1 Magnetic field gradients……Page 106
4.7.2 Field gradient coils……Page 107
4.7.3 Field gradient control……Page 108
5.1 A Single-Pulse Experiment……Page 113
5.2 Signal Averaging……Page 114
5.3 Multiple-Pulse Experiments: Phase Cycling……Page 117
5.4 Heteronuclear Experiments……Page 118
5.6 Arrayed Experiments……Page 119
5.7 NMR Signal……Page 121
5.8.2 Lorentzians……Page 124
5.8.3 Explanation of Fourier transformation……Page 128
5.8.4 Spectral phase shifts……Page 130
5.8.5 Frequency-dependent phase correction……Page 131
5.9.2 Two-dimensional Fourier transformation……Page 133
5.9.3 Phase twist peaks……Page 135
5.9.4 Pure absorption two-dimensional spectra……Page 137
5.10 Three-Dimensional Spectroscopy……Page 142
Part 3 Quantum Mechanics……Page 147
6.1.1 Continuous functions……Page 149
6.1.4 Dirac notation……Page 150
6.1.5 Vector representation of functions……Page 151
6.2 Operators……Page 153
6.2.2 Matrix representations……Page 154
6.2.4 Block diagonal matrices……Page 157
6.2.6 Adjoint……Page 158
6.3.2 Degeneracy……Page 159
6.3.5 Eigenfunctions of commuting operators: degenerate case……Page 160
6.3.6 Eigenfunctions of commuting operators: summary……Page 161
6.4 Diagonalization……Page 162
6.5.1 Powers of operators……Page 163
6.5.3 Exponentials of unity and null operators……Page 164
6.5.7 Exponentials of small operators……Page 165
6.6.1 Definition of cyclic commutation……Page 166
6.6.2 Sandwich formula……Page 167
7.1.1 The state of the particle……Page 171
7.1.3 Experimental observations……Page 172
7.2 Energy Levels……Page 173
7.3 Natural Units……Page 174
7.4 Superposition States and Stationary States……Page 175
7.6 Angular Momentum……Page 176
7.6.2 Rotation operators……Page 177
7.6.3 Rotation sandwiches……Page 179
7.6.4 Angular momentum eigenstates and eigenvalues……Page 180
7.6.6 Shift operators……Page 182
7.6.7 Matrix representations of the angular momentum operators……Page 184
7.7.1 Spin angular momentum operators……Page 185
7.7.3 Spin Zeeman basis……Page 186
7.7.4 Trace……Page 187
7.8.3 Spin-1/2 rotation operators……Page 188
7.8.6 Projection operators……Page 189
7.9 Higher Spin……Page 190
7.9.1 SpinI= 1……Page 191
7.9.2 SpinI= 3/2……Page 192
7.9.3 Higher spins……Page 193
Part 4 Nuclear Spin Interactions……Page 197
8.1 Spin Hamiltonian Hypothesis……Page 199
8.2 Electromagnetic Interactions……Page 200
8.2.1 Electric spin Hamiltonian……Page 201
8.2.2 Magnetic spin interactions……Page 204
8.4 External Magnetic Fields……Page 205
8.4.2 Radio-frequency field……Page 207
8.4.4 External spin interactions: summary……Page 209
8.5.1 The internal spin interactions……Page 210
8.5.2 Simplification of the internal Hamiltonian……Page 213
8.6.2 Molecular rotations……Page 214
8.6.3 Molecular translations……Page 215
8.6.4 Intramolecular and intermolecular spin interactions……Page 217
8.6.5 Summary of motional averaging……Page 218
9.1 Chemical Shift……Page 223
9.1.1 Chemical shift tensor……Page 224
9.1.2 Principal axes……Page 225
9.1.5 Chemical shift anisotropy (CSA)……Page 226
9.1.6 Chemical shift for an arbitrary molecular orientation……Page 228
9.1.8 Chemical shift interaction in isotropic liquids……Page 229
9.1.9 Chemical shift interaction in anisotropic liquids……Page 231
9.1.10 Chemical shift interaction in solids……Page 232
9.2 Electric Quadrupole Coupling……Page 234
9.2.1 Electric field gradient tensor……Page 235
9.2.2 Nuclear quadrupole Hamiltonian……Page 236
9.2.4 Anisotropic liquids……Page 237
9.2.6 Quadrupole interaction: summary……Page 238
9.3 Direct DipoleDipole Coupling……Page 239
9.3.1 Secular dipoledipole coupling……Page 241
9.3.2 Dipoledipole coupling in isotropic liquids……Page 243
9.3.4 Dipoledipole coupling in solids……Page 244
9.4 J-Coupling……Page 245
9.4.1 IsotropicJ-coupling……Page 247
9.4.2 Liquid crystals and solids……Page 249
9.4.3 Mechanism of theJ-coupling……Page 250
9.5 SpinRotation Interaction……Page 251
9.6 Summary of the Spin Hamiltonian Terms……Page 252
Part 5 Uncoupled Spins……Page 257
10.1 Zeeman Eigenstates……Page 259
10.2 Measurement of Angular Momentum: Quantum Indeterminacy……Page 260
10.3 Energy Levels……Page 261
10.4.2 Vector notation……Page 262
10.4.3 Some particular states……Page 263
10.4.4 Phase factors……Page 265
10.5 Spin Precession……Page 266
10.5.1 Dynamics of the eigenstates……Page 267
10.5.2 Dynamics of the superposition states……Page 268
10.6 Rotating Frame……Page 269
10.7 Precession in the Rotating Frame……Page 273
10.8.1 Rotating-frame Hamiltonian……Page 275
10.8.2 x-pulse……Page 276
10.8.3 Nutation……Page 279
10.8.4 Pulse of general phase……Page 280
10.8.5 Off-resonance effects……Page 281
11.1 Spin Density Operator……Page 287
11.2.2 Box notation……Page 289
11.2.3 Balls and arrows……Page 290
11.2.5 Relationships between populations and coherences……Page 291
11.2.6 Physical interpretation of the populations……Page 292
11.2.7 Physical interpretation of the coherences……Page 293
11.3 Thermal Equilibrium……Page 294
11.4 Rotating-Frame Density Operator……Page 296
11.5 Magnetization Vector……Page 297
11.6 Strong Radio-Frequency Pulse……Page 298
11.6.1 Excitation of coherence……Page 299
11.6.2 Population inversion……Page 301
11.6.3 Cycle of states……Page 302
11.6.4 Stimulated absorption and emission……Page 303
11.7 Free Precession Without Relaxation……Page 304
11.8.4 Pulse of phasep = 3/2……Page 307
11.8.6 Free precession for an interval……Page 308
11.9.1 Transverse relaxation……Page 309
11.9.2 Longitudinal relaxation……Page 311
11.10 Magnetization Vector Trajectories……Page 313
11.11 NMR Signal and NMR Spectrum……Page 315
11.12 Single-Pulse Spectra……Page 317
12.1 Inversion Recovery: Measurement ofT1……Page 323
12.2.1 Homogenous and inhomogenenous broadening……Page 326
12.2.3 Spin echo pulse sequence……Page 327
12.2.4 Refocusing……Page 330
12.2.5 Coherence interpretation……Page 331
12.3 Spin Locking: Measurement ofT1……Page 333
12.4 Gradient Echoes……Page 334
12.5 Slice Selection……Page 335
12.6 NMR Imaging……Page 337
13.1.1 Spin-1 states……Page 347
13.1.2 Spin-1 energy levels……Page 348
13.1.3 Spin-1 density matrix……Page 349
13.1.4 Coherence evolution……Page 351
13.1.5 Observable coherences and NMR spectrum……Page 353
13.1.7 Strong radio-frequency pulse……Page 354
13.1.9 NMR spectrum……Page 356
13.1.10 Quadrupolar echo……Page 359
13.2 SpinI= 3/2……Page 362
13.2.1 Spin-3/2 energy levels……Page 363
13.2.2 Populations and coherences……Page 364
13.2.3 NMR signal……Page 366
13.2.4 Single pulse spectrum……Page 367
13.2.5 Spin-3/2 spectra for small quadrupole couplings……Page 369
13.2.6 Second-order quadrupole couplings……Page 370
13.2.7 Central transition excitation……Page 371
13.3 SpinI= 5/2……Page 373
13.4 SpinsI= 7/2……Page 377
13.5 SpinsI= 9/2……Page 378
Part 6 Coupled Spins……Page 381
14.1 Coupling Regimes……Page 383
14.2 Zeeman Product States and Superposition States……Page 384
14.3 Spin-Pair Hamiltonian……Page 385
14.4.1 Singlets and triplets……Page 387
14.4.2 Energy levels……Page 388
14.4.3 NMR spectra……Page 390
14.5.1 Weak coupling……Page 391
14.5.3 Energy levels……Page 392
14.5.4 AX spectrum……Page 393
14.5.5 Heteronuclear spin pairs……Page 394
15.1 Eigenstates and Energy Levels……Page 397
15.2 Density Operator……Page 398
15.3 Rotating Frame……Page 403
15.4.1 Evolution of a spin pair……Page 404
15.4.2 Evolution of the coherences……Page 405
15.5 Spectrum of the AX System: SpinSpin Splitting……Page 406
15.6 Product Operators……Page 409
15.6.1 Construction of product operators……Page 410
15.6.2 Populations and coherences……Page 411
15.6.3 Spin orientations……Page 414
15.7 Thermal Equilibrium……Page 417
15.8 Radio-Frequency Pulses……Page 419
15.8.1 Rotations of a single spin pair……Page 420
15.8.2 Rotations of the spin density operator……Page 421
15.8.3 Operator transformations……Page 423
15.9 Free Evolution of the Product Operators……Page 425
15.9.1 Chemical shift evolution……Page 427
15.9.2 J-coupling evolution……Page 428
15.10 Spin Echo Sandwich……Page 433
16.1.1 The assignment problem……Page 437
16.1.3 Theory of COSY: coherence interpretation……Page 439
16.1.4 Product operator interpretation……Page 443
16.2.1 13C isotopomers……Page 446
16.2.2 Pulse sequence……Page 451
16.2.3 Theory of INADEQUATE……Page 452
16.2.4 Coherence transfer pathways and phase cycling……Page 457
16.2.5 Two-dimensional INADEQUATE……Page 459
16.3.1 The sensitivity of nuclear isotopes……Page 464
16.3.2 INEPT pulse sequence……Page 465
16.3.3 Refocused INEPT……Page 468
16.4.2 Spin Hamiltonian……Page 471
16.4.3 Orienting media……Page 472
16.4.4 Doublet splittings……Page 474
17.1 Molecular Spin System……Page 481
17.3 Motionally SuppressedJ-Couplings……Page 482
17.4 Chemical Equivalence……Page 483
17.5 Magnetic Equivalence……Page 486
17.6 Weak Coupling……Page 489
17.7 Heteronuclear Spin Systems……Page 490
17.8 Alphabet Notation……Page 491
17.9 Spin Coupling Topologies……Page 492
18.1 Spin Hamiltonian……Page 495
18.2 Energy Eigenstates……Page 496
18.3 Superposition States……Page 497
18.4 Spin Density Operator……Page 498
18.5.2 Combination coherences and simple coherences……Page 499
18.5.3 Coherence frequencies……Page 500
18.5.5 Observable coherences……Page 501
18.6 NMR Spectra……Page 503
18.7.1 Construction of product operators……Page 505
18.7.2 Populations and coherences……Page 506
18.7.3 Physical interpretation of product operators……Page 508
18.9 Radio-Frequency Pulses……Page 509
18.10.1 Chemical shift evolution……Page 510
18.10.2 J-coupling evolution……Page 511
18.11 Spin Echo Sandwiches……Page 513
18.12 INEPT in anI2S System……Page 516
18.13 COSY in Multiple-Spin Systems……Page 519
18.13.1 AMX spectrum……Page 520
18.13.2 Active and passive spins……Page 521
18.13.3 Cross-peak multiplets……Page 522
18.13.4 Diagonal peaks……Page 524
18.14.1 The ambiguity of COSY spectra……Page 525
18.14.3 Theory of TOCSY……Page 527
Part 7 Motion and Relaxation……Page 535
19.1.1 Molecular vibrations……Page 537
19.1.4 Chemical exchange……Page 538
19.1.5 Molecular rotations……Page 539
19.1.6 Translational motion……Page 540
19.2 Motional Time-Scales……Page 541
19.3 Motional Effects……Page 542
19.4 Motional Averaging……Page 543
19.5 Motional Lineshapes and Two-Site Exchange……Page 544
19.5.1 Slow intermediate exchange and motional broadening……Page 546
19.5.2 Fast intermediate exchange and motional narrowing……Page 548
19.5.3 Averaging ofJ-splittings……Page 551
19.5.4 Asymmetric two-site exchange……Page 552
19.5.5 Knight shift……Page 553
19.6 Sample Spinning……Page 555
19.7.1 Two-dimensional exchange spectroscopy……Page 557
19.7.2 Theory……Page 560
19.8 Diffusion……Page 567
20.2 Relaxation Mechanisms……Page 571
20.3.1 Autocorrelation functions and correlation times……Page 573
20.3.2 Spectral density……Page 576
20.3.3 Normalized spectral density……Page 577
20.3.4 Transition probabilities……Page 578
20.3.5 Thermally corrected transition probabilities……Page 579
20.3.6 Spinlattice relaxation……Page 580
20.4.1 Rotational correlation time……Page 584
20.4.2 Transition probabilities……Page 585
20.4.3 Solomon equations……Page 589
20.4.4 Longitudinal relaxation……Page 592
20.4.5 Transverse relaxation……Page 593
20.5 Steady-State Nuclear Overhauser Effect……Page 594
20.6.2 NOESY signal……Page 598
20.6.3 NOESY spectra……Page 601
20.6.4 NOESY and chemical exchange……Page 603
20.6.5 Molecular structure determination……Page 604
20.7.1 Transverse cross-relaxation……Page 605
20.7.3 Transverse Solomon equations……Page 606
20.7.4 ROESY spectra……Page 608
20.7.5 ROESY and chemical exchange……Page 610
20.7.6 ROESY and TOCSY……Page 611
20.8.1 Cross-correlation……Page 612
20.8.2 Cross-correlation of spin interactions……Page 613
20.8.3 Dipoledipole cross-correlation and angular estimations……Page 614
20.8.4 TROSY……Page 618
Part 8 Appendices……Page 625
A.1.2 Euler rotations: first scheme……Page 627
A.1.3 Euler rotations: second scheme……Page 628
A.1.5 Reference-frame orientations……Page 629
A.1.7 Passive rotations……Page 630
A.1.8 Tensor transformations……Page 631
A.2 Rotations and Cyclic Commutation……Page 632
A.3 Rotation Sandwiches……Page 633
A.4 Spin-1/2 Rotation Operators……Page 634
A.5 Quadrature Detection and Spin Coherences……Page 636
A.6 Secular Approximation……Page 639
A.7.2 First-order quadrupolar interaction……Page 642
A.8.1 Strongly-coupled Spin-1/2 pairs……Page 643
A.8.2 General strongly coupled systems……Page 648
A.9 J-Couplings and Magnetic Equivalence……Page 649
A.10 Spin Echo Sandwiches……Page 651
A.10.2 Long-duration limit……Page 653
A.10.3 Two spin echo sequences……Page 654
A.10.4 Heteronuclear spin echo sequences……Page 655
A.11.1 Coherence transfer pathways……Page 657
A.11.2 Coherence transfer amplitudes……Page 658
A.11.3 Coherence orders and phase shifts……Page 659
A.11.4 The pathway phase……Page 660
A.11.5 A sum theorem……Page 661
A.11.6 Pathway selection I……Page 662
A.11.7 Pathway selection II……Page 663
A.11.8 Pathway selection III……Page 665
A.11.9 Selection of a single pathway I……Page 666
A.11.10 Selection of a single pathway II……Page 667
A.11.11 Dual pathway selection……Page 668
A.11.12 Internal phases I……Page 669
A.11.13 Internal phases II……Page 670
A.11.14 Nested phase cycles I……Page 672
A.11.15 Nested phase cycles II……Page 673
A.11.16 Different ways of constructing phase cycles……Page 676
A.12.1 Field gradient dephasing……Page 677
A.12.2 Pathway phase……Page 679
A.12.5 Heteronuclear coherence transfer echoes……Page 680
A.13 Bloch Equations……Page 681
A.14 Chemical Exchange……Page 682
A.14.2 The coherent dynamics……Page 683
A.14.3 The spectrum……Page 684
A.14.4 Longitudinal magnetization exchange……Page 686
A.15 Solomon Equations……Page 688
A.16 Cross-Relaxation Dynamics……Page 690
Appendix B: Symbols and Abbreviations……Page 693
Answers to the Exercises……Page 709
Index……Page 721
Colour Plate……Page 743
Reviews
There are no reviews yet.