【分享】Spin Dynamics-Basics of NMR Second ed.(2008) 有下载地址

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Contents
Part 1 Nuclear Magnetism 3
1 Matter 5
1.1 Atoms and Nuclei 5
1.2 Spin 5
1.2.1 Classical angular momentum 6
1.2.2 Quantum angular momentum 6
1.2.3 Spin angular momentum 7
1.2.4 Combining angular momenta 8
1.2.5 The Pauli Principle 9
1.3 Nuclei 9
1.3.1 The fundamental particles 9
1.3.2 Neutrons and protons 10
1.3.3 Isotopes 11
1.4 Nuclear Spin 12
1.4.1 Nuclear spin states 12
1.4.2 Nuclear Zeeman splitting 14
1.4.3 Zero-spin nuclei 14
1.4.4 Spin-1/2 nuclei 15
1.4.5 Quadrupolar nuclei with integer spin 15
1.4.6 Quadrupolar nuclei with half-integer spin 15
1.5 Atomic and Molecular Structure 15
1.5.1 Atoms 15
1.5.2 Molecules 16
1.6 States of Matter 17
1.6.1 Gases 17
1.6.2 Liquids 17
1.6.3 Solids 19
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
4.2.1 The synthesizer: radio-frequency phase shifts 67
4.2.2 The pulse gate: radio-frequency pulses 68
4.2.3 Radio-frequency amplifier 69
4.3 The Duplexer 69
4.4 The Probe 70
4.5 The Receiver Section 72
4.5.1 Signal preamplifier 73
4.5.2 The quadrature receiver 73
4.5.3 Analogue–digital conversion 74
4.5.4 Signal phase shifting 76
4.6 Overview of the Radio-Frequency Section 76
4.7 Pulsed Field Gradients 77
4.7.1 Magnetic field gradients 78
4.7.2 Field gradient coils 79
4.7.3 Field gradient control
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
5.8.1 Fourier transformation 96
5.8.2 Lorentzians 96
5.8.3 Explanation of Fourier transformation 100
5.8.4 Spectral phase shifts 102
5.8.5 Frequency-dependent phase correction 103
5.9 Two-Dimensional Spectroscopy 105
5.9.1 Two-dimensional signal surface 105
5.9.2 Two-dimensional Fourier transformation 105
5.9.3 Phase twist peaks 107
5.9.4 Pure absorption two-dimensional spectra 109
5.10 Three-Dimensional Spectroscopy

Part 3 Quantum Mechanics 119
6 Mathematical Techniques 121
6.1 Functions 121
6.1.1 Continuous functions 121
6.1.2 Normalization 122
6.1.3 Orthogonal and orthonormal functions 122
6.1.4 Dirac notation 122
6.1.5 Vector representation of functions 123
6.2 Operators 125
6.2.1 Commutation 126
6.2.2 Matrix representations 126
6.2.3 Diagonal matrices 129
6.2.4 Block diagonal matrices 129
6.2.5 Inverse 130
6.2.6 Adjoint 130
6.2.7 Hermitian operators 131
6.2.8 Unitary operators 131
6.3 Eigenfunctions, Eigenvalues and Eigenvectors 131
6.3.1 Eigenequations 131
6.3.2 Degeneracy 131
6.3.3 Eigenfunctions and eigenvalues of Hermitian operators 132
6.3.4 Eigenfunctions of commuting operators: non-degenerate case 132
6.3.5 Eigenfunctions of commuting operators: degenerate case 132
6.3.6 Eigenfunctions of commuting operators: summary 133
6.3.7 Eigenvectors 134
6.4 Diagonalization 134
6.4.1 Diagonalization of Hermitian or unitary matrices 135
6.5 Exponential Operators 135
6.5.1 Powers of operators 135
6.5.2 Exponentials of operators 136
6.5.3 Exponentials of unity and null operators 136
6.5.4 Products of exponential operators 137
6.5.5 Inverses of exponential operators 137
6.5.6 Complex exponentials of operators 137
6.5.7 Exponentials of small operators 137
6.5.8 Matrix representations of exponential operators 138
6.6 Cyclic Commutation 138
6.6.1 Definition of cyclic commutation 138
6.6.2 Sandwich formula

Review of Quantum Mechanics 143
7.1 Spinless Quantum Mechanics 143
7.1.1 The state of the particle 143
7.1.2 The equation of motion 144
7.1.3 Experimental observations 144
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
7.6.1 Angular momentum operators 149
7.6.2 Rotation operators 149
7.6.3 Rotation sandwiches 151
7.6.4 Angular momentum eigenstates and eigenvalues 152
7.6.5 The angular momentum eigenstates 154
7.6.6 Shift operators 154
7.6.7 Matrix representations of the angular momentum operators 156
7.7 Spin 157
7.7.1 Spin angular momentum operators 157
7.7.2 Spin rotation operators 158
7.7.3 Spin Zeeman basis 158
7.7.4 Trace 159
7.8 Spin-1/2 160
7.8.1 Zeeman eigenstates 160
7.8.2 Angular momentum operators 160
7.8.3 Spin-1/2 rotation operators 160
7.8.4 Unity operator 161
7.8.5 Shift operators 161
7.8.6 Projection operators 161
7.8.7 Ket-bra notation 162
7.9 Higher Spin 162
7.9.1 Spin I = 1 163
7.9.2 Spin I = 3/2 164
7.9.3 Higher spins 165

Part 4 Nuclear Spin Interactions 169
8 Nuclear Spin Hamiltonian 171
8.1 Spin Hamiltonian Hypothesis 171
8.2 Electromagnetic Interactions 172
8.2.1 Electric spin Hamiltonian 173
8.2.2 Magnetic spin interactions 176
8.3 External and Internal Spin Interactions 177
8.3.1 Spin interactions: summary 177
8.4 External Magnetic Fields 177
8.4.1 Static field 179
8.4.2 Radio-frequency field 179
8.4.3 Gradient field 181
8.4.4 External spin interactions: summary 181
8.5 Internal Spin Hamiltonian 182
8.5.1 The internal spin interactions 182
8.5.2 Simplification of the internal Hamiltonian 185
8.6 Motional Averaging 186
8.6.1 Modes of molecular motion 186
8.6.2 Molecular rotations 186
8.6.3 Molecular translations 187
8.6.4 Intramolecular and intermolecular spin interactions 189
8.6.5 Summary of motional averaging
9 Internal Spin Interactions 195
9.1 Chemical Shift 195
9.1.1 Chemical shift tensor 196
9.1.2 Principal axes 197
9.1.3 Principal values 198
9.1.4 Isotropic chemical shift 198
9.1.5 Chemical shift anisotropy (CSA) 198
9.1.6 Chemical shift for an arbitrary molecular orientation 200
9.1.7 Chemical shift frequency 201
9.1.8 Chemical shift interaction in isotropic liquids 201
9.1.9 Chemical shift interaction in anisotropic liquids 203
9.1.10 Chemical shift interaction in solids 204
9.1.11 Chemical shift interaction: summary 206
9.2 Electric Quadrupole Coupling 206
9.2.1 Electric field gradient tensor 207
9.2.2 Nuclear quadrupole Hamiltonian 208
9.2.3 Isotropic liquids 209
9.2.4 Anisotropic liquids 209
9.2.5 Solids 210
9.2.6 Quadrupole interaction: summary 210
9.3 Direct Dipole–Dipole Coupling 211
9.3.1 Secular dipole–dipole coupling 213
9.3.2 Dipole–dipole coupling in isotropic liquids

9.3.3 Dipole–dipole coupling in liquid crystals 216
9.3.4 Dipole–dipole coupling in solids 216
9.3.5 Dipole–dipole interaction: summary 217
9.4 J-Coupling 217
9.4.1 Isotropic J-coupling 219
9.4.2 Liquid crystals and solids 221
9.4.3 Mechanism of the J-coupling 222
9.4.4 J-coupling: summary 223
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
10.4.1 General spin states 234
10.4.2 Vector notation 234
10.4.3 Some particular states 235
10.4.4 Phase factors 237
10.5 Spin Precession 238
10.5.1 Dynamics of the eigenstates 239
10.5.2 Dynamics of the superposition states 240
10.6 Rotating Frame 241
10.7 Precession in the Rotating Frame 245
10.8 Radio-frequency Pulse 247
10.8.1 Rotating-frame Hamiltonian 247
10.8.2 x-pulse 248
10.8.3 Nutation 251
10.8.4 Pulse of general phase 252
10.8.5 Off-resonance effects 253

11 Ensemble of Spins-1/2 259
11.1 Spin Density Operator 259
11.2 Populations and Coherences 261
11.2.1 Density matrix 261
11.2.2 Box notation 261
11.2.3 Balls and arrows 262
11.2.4 Orders of coherence 263
11.2.5 Relationships between populations and coherences 263
11.2.6 Physical interpretation of the populations 264
11.2.7 Physical interpretation of the coherences 265
11.3 Thermal Equilibrium 266
11.4 Rotating-Frame Density Operator 268
Contents •xiii
11.5 Magnetization Vector 269
11.6 Strong Radio-Frequency Pulse 270
11.6.1 Excitation of coherence 271
11.6.2 Population inversion 273
11.6.3 Cycle of states 274
11.6.4 Stimulated absorption and emission 275
11.7 Free PrecessionWithout Relaxation 276
11.8 Operator Transformations 279
11.8.1 Pulse of phase φp = 0 279
11.8.2 Pulse of phase φp = π/2 279
11.8.3 Pulse of phase φp = π 279
11.8.4 Pulse of phase φp = 3π/2 279
11.8.5 Pulse of general phase φp 280
11.8.6 Free precession for an interval τ 280
11.9 Free Evolution with Relaxation 281
11.9.1 Transverse relaxation 281
11.9.2 Longitudinal relaxation 283
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 T1 295
12.2 Spin Echoes: Measurement of T2 298
12.2.1 Homogenous and inhomogenenous broadening 298
12.2.2 Inhomogenenous broadening in the time domain 299
12.2.3 Spin echo pulse sequence 299
12.2.4 Refocusing 302
12.2.5 Coherence interpretation 303
12.2.6 Coherence transfer pathway 305
12.3 Spin Locking: Measurement of T1ρ 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
13.1.1 Spin-1 states 319
13.1.2 Spin-1 energy levels 320
13.1.3 Spin-1 density matrix 321
13.1.4 Coherence evolution 323
13.1.5 Observable coherences and NMR spectrum 325
13.1.6 Thermal equilibrium 326
13.1.7 Strong radio-frequency pulse 326
13.1.8 Excitation of coherence 328
13.1.9 NMR spectrum 328
13.1.10 Quadrupolar echo 331