Spin dynamics: basics of nuclear magnetic resonance
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| Format: | Book |
| Language: | English |
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Chichester
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2008
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Table of contents only Inhaltsverzeichnis |
| Physical Description: | XXV, 714 S., [5] Bl. Ill., graph. Darst. |
| ISBN: | 9780470511176 9780470511183 0470511176 |
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| 100 | 1 | |a Levitt, Malcolm H. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spin dynamics |b basics of nuclear magnetic resonance |c Malcolm H. Levitt |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2008 | |
| 300 | |a XXV, 714 S., [5] Bl. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Nuclear magnetic resonance | |
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| 650 | 0 | 7 | |a Spindynamik |0 (DE-588)4417075-0 |2 gnd |9 rswk-swf |
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| adam_text | Preface xxi
Preface to the First Edition xxiii
Introduction i
Parti Nuclear Magnet ism 3
i 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
2 Magnetism 23
2.1 The Electromagnetic Field ^
2.2 Macroscopic Magnetism
2.3 Microscopic Magnetism
2.4 Spin Precession
2.5 Larmor Frequency
2.6 Spin-Lattice Relaxation: Nuclear Paramagnetism M
2.7 Transverse Magnetization and Transverse Relaxation 33
2.8 NMR Signal ^
2.9 Electronic Magnetism
3 NMRSpectroscopy 39
3.1 A Simple Pulse Sequence
3.2 A Simple Spectrum
3.3 Isotopomeric Spectra
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
3.7 Chemical Shifts ^°
3.8 /-Coupling Multiplets 56
3.9 Heteronuclear Decoupling
Part 2 The NMR Experiment 63
4 The NMR Spectrometer 65
4.1 The Magnet 65
4.2 The Transmitter Section
4.2.1 The Synthesizer: radio-frequency phase shifts
4.2.2 The pulse gate: radio-frequency pulses
4.2.3 Radio-frequency amplifier
4.3 The Duplexer ^
4.4 The Probe 70
4.5 The Receiver Section
4.5.1 Signal preamplifier
4.5.2 The quadrature receiver
4.5.3 Analogue-digital conversion
4.5.4 Signal phase shifting
4.6 Overview of the Radio-Frequency Section L?
4.7 Pulsed Field Gradients
4.7.1 Magnetic field gradients „g
4.7.2 Field gradient coils l!
4.7.3 Field gradient control :
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
5.8.1 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 114
Part 3 Quantum Mechanics 119
6 Mathematical Techniques 121
6.1 Functions 121
6.1.1 Continuous functions 121
6.1.2 Norrnalization 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 Herrnitian 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 Eigeflfunctions of commuting Operators: non-degenerate case 132
i 6.3.5 Eigeflfunctions of commuting Operators: degenerate case 132
t 6.3.6 Eigenfunctions of commuting Operators: summary 133
I 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 13°
6.6.1 Definition of cyclic commutation 138
6.6.2 Sandwich formula 139
7 Review of Quantum Mechanics *43
7.1 Spinless Quantum Mechanics 143
7.1.1 The State of the particle I43
7.1.2 The equation of motion 144
7.1.3 Experimental observations 144
7.2 Energy Levels 145
7.3 Natural Units I46
7.4 Superposition States and Stationary States 14^
7.5 Conservation Laws 14^
7.6 Angular Momentum 148
7.6.1 Angular momentum Operators 14
7.6.2 Rotation Operators U9
7.6.3 Rotation Sandwiches
7.6.4 Angular momentum eigenstates and eigenvalues 1^
7.6.5 The angular momentum eigenstates 1^
7.6.6 Shift Operators I54
7.6.7 Matrix representations of the angular momentum Operators 156
7.7 Spin I57
7.7.1 Spin angular momentum Operators i0
7.7.2 Spin rotation Operators
7.7.3 Spin Zeeman basis ^
7.7A Trace 159
7.8 Spin-1/2 l60
7.8.1 Zeeman eigenstates 1^
7.8.2 Angular momentum Operators
7.8.3 Spin-1/2 rotation Operators 160
7.8.4 Unity Operator l61
7.8.5 Shift Operators 161
7.8.6 Projection Operators
7.8.7 Ket-bra notation 162
7.9 Higher Spin 162
7.9.1 Spin/ = 1 163 !
7.9.2 Spin 7 = 3/2 164 i
7.9.3 Higher spins 165 i
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 Statte 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 190
9 Internal Spin Interactions 195
9.1 Chemical Shirt 195
9.1.1 Chemical shift tensor 196
9.1.2 Principal axes 197
9.1.3 Principal values 198
9.1.4 Isotropie 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 Anisotropie liquids 209
9.2.5 Solids 210
9.2.6 Quadrupole interaction: sumrnary 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 215
9.3.3 Dipole-dipole coupling in liquid crystals 216
9.3.4 Dipole-dipole coupling in solids
9.3.5 Dipole-dipole interaction: summary
9.4 7-Coupling ^17
9.4.1 Isotropie 7-coupling
9.4.2 Liquid crystals and solids
9.4.3 Mechanism of the /-coupling ff
9.4.4 7-coupling: summary
9.5 Spin-Rotation Interaction
9.6 Summary of the Spin Hamiltonian Terms
Part 5 Uncoupled Spins 229
io Single Spin-1/2 23J
10.1 Zeeman Eigenstates ^
10.2 Measurement of Angular Momentum: Quantum Indeterminacy 232
10.3 Energy Levels 23
10.4 Superposition States
10.4.1 General spin states _
10.4.2 Vector notation r~:
10.4.3 Some particular states
10.4.4 Phase factors ^
10.5 Spin Precession 23J
10.5.1 Dynamics of the eigenstates _.
10.5.2 Dynamics of the superposition states
10.6 Rotating Frame 2^
10.7 Precession in the Rotating Frame
10.8 Radio-frequency Pulse 2£L
10.8.1 Rotating-frame Hamiltonian ~
10.8.2 *-pulse 2!r
10.8.3 Nutation 2^
10.8.4 Pulse of general phase TZ
10.8.5 Off-resonance effects Ö
ii Ensemble ofSpins-1/2 259
11.1 Spin Density Operator 25^
11.2 Populations and Coherences .
11.2.1 Density matrix J°J
11.2.2 Box notation 2^
11.2.3 Balls and arrows 262
11.2.4 Orders ofcoherence 2^
11.2.5 Relationships between populations and coherences ^
11.2.6 Physical interpretation of the populations 2 _
11.2.7 Physical interpretation of the coherences 2
11.3 Thermal Equilibrium Zbb t
11.4 Rotating-Frame Density Operator 268
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 Precession Without Relaxation 276
11.8 Operator Transformations 279
11.8.1 Pulse of phase 0P = 0 279
11.8.2 Pulse of phase / p = n/2 279
11.8.3 Pulse of phase 4 v=n 279
11.8.4 Pulse of phase pp = 3n/2 279
11.8.5 Pulse of general phase f p 280
11.8.6 Free precession for an interval r 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 7*i 295
12.2 Spin Echoes: Measurement of Ti 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 T p 305
12.4 Gradient Echoes 306
12.5 Slice Selection 307
12.6 NMR Imaging 309
13 Quadrupolar Nuclei 319
13.1 Spin 1 = 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 32g
13.1.10 Quadrupolar echo 331
13.2 Spin/= 3/2 m
13.2.1 Spin-3/2 energy levels ~,r
13.2.2 Populations and coherences „A
13.2.3 NMR signal ^
13.2.4 Single pulse spectrum 339
13.2.5 Spin-3/2 spectra for small quadrupole couplings 341
13.2.6 Second-order quadrupole couplings 342
13.2.7 Central transition excitation 040
13.2.8 Central transition echo ».,-
13.3 Spin 7 = 5/2 ™
13.4 Spins/= 7/2 ™
13.5 Spins/= 9/2 ™
Part 6 CoupledSpins
14 Spin-1/2 Pairs
14.1 Coupling Regimes 355
14.2 ZeemanProduct States and Superposition States 356
14.3 Spin-Pair Hamiltorüan ,c7
14.4 Pairs of Magnetically Equivalent Spins 359
14.4.1 Singletsandtriplets fl
UA.2 Energy levels £?
14.4.3 NMRspectra ^
14.4.4 Dipolarecho f^
14.5 Weakly Coupled Spin Pairs ,S
14.5.1 Weak coupling ^
14.5.2 AX spin Systems ,^4
14.5.3 Energy levels f?T
14.5.4 AX spectrum %t
14.5.5 Heteronuclearspin pairs 366
15 HomonudearAX System 359
15.1 Eigenstatesand Energy Levels 369
15.2 Density (Operator „n
15.3 Rotating Frame ZZ
15.4 Free Evolution %?
15A1 Evolution ofa spin pair 376
15.4.2 Evolution ofthe coherences 377
S pS^l^System:S^-s-sp^ s
IS 7 -JS Spirtonentations 386
15.7 ThermalEquilibrium ™
15.8 Radio-Freqi,ency Pul«** Si
15-8.2 R^hons ofthe spin denslry Operator 393
XV
15.8.3 Operator transformations 395
15.9 Free Evolution of the Product Operators 397
15.9.1 Chemical shift evolution 399
15.9.2 ./-coupling evolution 400
15.9.3 Relaxation 405
15.10 Spin Echo Sandwich 405
16 Experiments on AX Systems 409
16.1 COSY 409
16.1.1 The assignment problem 409
16.1.2 COSY pulse sequence 411
16.1.3 Theory of COSY: coherence Interpretation 411
16.1.4 Product Operator interpretation 415
16.1.5 Experimental examples 418
16.2 INADEQUATE 418
16.2.1 13C isotopomers 418
16.2.2 Pulse sequence 423
16.2.3 Theory of INADEQUATE 424
16.2.4 Coherence transfer pathways and phase cycling 429
16.2.5 Two-dimensional INADEQUATE 431
16.3 INEPT 436
16.3.1 The sensitivity of nuclear isotopes 436
16.3.2 INEPT pulse sequence 437
16.3.3 Refocused INEPT 440
16.4 Residual Dipolar Couplings 443
16.4.1 Angular information 443
16.4.2 Spin Hamiltonian 443
16.4.3 Orienting media 444
16.4.4 Doublet Splittings 446
17 Many-Spin Systems 453
17.1 Molecular Spin System 453
17.2 Spin Ensemble 454
17.3 Motionally Suppressed /-Couplings 454
17.4 Chemical Equivalence 455
17.5 Magnetic Equivalence 45g
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 46g
18.3 Superposition States
18.4 Spin Density Operator ™
18.5 Populations and Coherences
18.5.1 Coherence Orders
18.5.2 Combination coherences and simple coherences ^
18.5.3 Coherence frequencies
18.5.4 Degenerate coherences
18.5.5 Observable coherences
18.6 NMRSpectra ®1
18.7 Many-Spin Product Operators ZL
18.7.1 Construction of product Operators
18.7.2 Populations and coherences
18.7.3 Physical interpretation of product Operators 4°
18.8 Thermal Equilibrium ~;
18.9 Radio-Frequency Pulses r
18.10 Free Precession ™~
18.10.1 Chemical shift evolution rz
18.10.2 7-coupling evolution ::_
18.10.3 Relaxation *~j?
18.11 Spin Echo Sandwiches ~?
18.12 INEPT in an I2S System ™?
18.13 COSY in Multiple-Spin Systems ^}
18.13.1 AMX spectrum ^
18.13.2 Active and passive spins
18.13.3 Cross-peak multiplets f*
18.13.4 Diagonal peaks ?!
18.13.5 Linear spin Systems
18.14 TOCSY „i
49/
18.14.1 The ambiguity of COSY spectra
18.14.2 TOCSY pulse sequence .„„
18.14.3 Theory of TOCSY
Part 7 Motion and Relaxation 5°7
19 Motion 509
19.1 Motional Processes ^
19.1.1 Molecular vibrations „0
19.1.2 Local rotations of molecular groups ein
19.1.3 Molecular flexibility ™
19.1.4 Chemical exchange „1
19.1.5 Molecular rotations „-
19.1.6 Translational motion -^
19.1.7 Mechanical motion
19.2 Motional Time-Scales 5]f
19.3 Motional Effects 5JZ
19.4 Motional Averaging 5JT,
19.5 Motional Lineshapes and Two-Site Exchange
19.5.1 Slow intermediate exchange and motional broadening 518
19.5.2 Fast intermediate exchange and motional narrowing 520
19.5.3 Averaging of 7-splittings 523
19.5.4 Asymmetrie two-site exchange 524
19.5.5 Knight shift 525
19.5.6 Paramagnetic shifts 527
19.6 Sample Spinning 527
19.7 Longitudinal Magnetization Exchange 529
19.7.1 Two-dimensional exchange spectroscopy 529
19.7.2 Theory 532
19.7.3 Motional regimes 539
19.8 Diffusion 539
20 Relaxation 543
20.1 Types of Relaxation 543
20.2 Relaxation Mechanisms 543
20.3 Random Field Relaxation 545
20.3.1 Autocorrelation funetions and correlation times 545
20.3.2 Spectral density 548
20.3.3 Normalized spectral density 549
20.3.4 Transition probabilities 550
20.3.5 Thermally corrected transition probabilities 551
20.3.6 Spin-lattice relaxation 552
20.4 Dipole-Dipole Relaxation 556
20.4.1 Rotational correlation time 556
20.4.2 Transition probabilities 557
20.4.3 Solomon equations 561
20.4.4 Longitudinal relaxation 564
20.4.5 Transverse relaxation 565
20.5 Steady-State Nuclear Overhauser Effect 566
20.6 NOESY 570
20.6.1 NOESY pulse sequence 570
20.6.2 NOESY signal 570
20.6.3 NOESY spectra 573
20.6.4 NOESY and chemical exchange 575
20.6.5 Molecular strueture determination 576
20.7 ROESY 577
20.7.1 Transverse cross-relaxation 577
20.7.2 Spin locking 578
20.7.3 Transverse Solomon equations 57g
20.7.4 ROESY spectra 580
20.7.5 ROESY and chemical exchange 582
20.7.6 ROESY and TOCSY 533
20.8 Cross-Correlated Relaxation 554
20.8.1 Cross-correlation 534
20.8.2 Cross-correlation of spin interactions 585
20.8.3 Dipole-dipole cross-correlation and angular estimations 586
20.8.4 TROSY 590
Part 8 Appendices 597
Appendix A: Supplementary Material 599
599
A.l Euler Angles and Frame Transformations
A.1.1 Definition of the Euler angles
A.l.2 Euler rotations: first scheine
A.1.3 Euler rotations: second scheme
A.l.4 Euler rotation matrices .
A.1.5 Reference-frame orientations
A.l.6 Consecutive reference-frame transformations
A.1.7 Passive rotations ,„,
A.1.8 Tensor transformations 604
A.l.9 Intermediate reference frames .
A.2 Rotations and Cyclic Commutation „_
A.3 Rotation Sandwiches ,„,.
A.4 Spin-1/2 Rotation Operators „g
A.5 Quadrature Detection and Spin Coherences .
A.6 Secular Approximation ,...
A.7 Quadrupolar Interaction ,,.
A.7.1 Füll quadrupolar interaction ,.4
A.7.2 First-order quadrupolar interaction ,.j
A.7.3 Higher-order quadrupolar interactions .. ,-
A.8 Strong Coupling ,,,-
A.8.1 Strongly-coupled Spin-1/2 pairs ,^q
A.8.2 General strongly coupled Systems ,~
A.9 7-Couplings and Magnetic Equivalence ,23
A.10 Spin Echo Sandwiches ^25
A.10.1 Short-duration limit 625
A.10.2 Long-duration limit ^26
A.10.3 Two spin echo sequences ,~j
A.10.4 Heteronuclear spin echo sequences ,«9
A.ll Phase Cycling ,2o
A.ll.l Coherence transfer pathways rnn
A.11.2 Coherence transfer amplitudes 631
A.ll.3 Coherence Orders and phase shifts 632
A.11.4 The pathway phase ^
A.11.5 Asumtheorem fi34
A.11.6 Pathway selection I ,,c
A.11.7 Pathway selection II 637
A.11.8 Pathway selection III ?3g
A.l 1.9 Selection of a Single pathway I .,9
A.11.10 Selection of a Single pathway II ^q
A.ll.ll Dual pathway selection f,-,
A.11.12 InternalphasesI Vg
A.11.13 Internal phases II ^
A.ll.14 Nested phase cycles I Mc
A.11.15 Nested phase cycles n ^g
A.11.16 Differentwaysofconstructing phase cycles
A.12 Coherence Selection by Pulsed Field Gradients 649
A.12.1 Field gradient dephasing 649
A.12.2 Pathway phase 651
A.12.3 Coherence transfer echoes 652
A.12.4 Pathway selection 652
A.12.5 Heteronuclear coherence transfer echoes 652
A.13 Bloch Equations 653
A.14 Chemical Exchange 654
A.14.1 The incoherent dynamics 655
A.14.2 The coherent dynamics 655
A.14.3 The spectrum 656
A.14.4 Longitudinal magnetization exchange 658
A.15 Solomon Equations 660
A.16 Cross-Relaxation Dynamics 662
Appendix B: Symbols and Abbreviations 665
Answers to the Exercises 681
Index 693
|
| adam_txt |
Preface xxi
Preface to the First Edition xxiii
Introduction i
Parti Nuclear Magnet ism 3
i 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
2 Magnetism 23
2.1 The Electromagnetic Field ^
2.2 Macroscopic Magnetism
2.3 Microscopic Magnetism
2.4 Spin Precession
2.5 Larmor Frequency
2.6 Spin-Lattice Relaxation: Nuclear Paramagnetism M
2.7 Transverse Magnetization and Transverse Relaxation 33
2.8 NMR Signal ^
2.9 Electronic Magnetism
3 NMRSpectroscopy 39
3.1 A Simple Pulse Sequence
3.2 A Simple Spectrum
3.3 Isotopomeric Spectra
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
3.7 Chemical Shifts ^°
3.8 /-Coupling Multiplets 56
3.9 Heteronuclear Decoupling
Part 2 The NMR Experiment 63
4 The NMR Spectrometer 65
4.1 The Magnet 65
4.2 The Transmitter Section
4.2.1 The Synthesizer: radio-frequency phase shifts
4.2.2 The pulse gate: radio-frequency pulses
4.2.3 Radio-frequency amplifier
4.3 The Duplexer ^
4.4 The Probe 70
4.5 The Receiver Section '
4.5.1 Signal preamplifier
4.5.2 The quadrature receiver
4.5.3 Analogue-digital conversion
4.5.4 Signal phase shifting
4.6 Overview of the Radio-Frequency Section L?
4.7 Pulsed Field Gradients ''
4.7.1 Magnetic field gradients „g
4.7.2 Field gradient coils l!
4.7.3 Field gradient control :
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
5.8.1 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 114
Part 3 Quantum Mechanics 119
6 Mathematical Techniques 121
6.1 Functions 121
6.1.1 Continuous functions 121
6.1.2 Norrnalization 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 Herrnitian 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 Eigeflfunctions of commuting Operators: non-degenerate case 132
i 6.3.5 Eigeflfunctions of commuting Operators: degenerate case 132
t 6.3.6 Eigenfunctions of commuting Operators: summary 133
I 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 13°
6.6.1 Definition of cyclic commutation 138
6.6.2 Sandwich formula 139
7 Review of Quantum Mechanics *43
7.1 Spinless Quantum Mechanics 143
7.1.1 The State of the particle I43
7.1.2 The equation of motion 144
7.1.3 Experimental observations 144
7.2 Energy Levels 145
7.3 Natural Units I46
7.4 Superposition States and Stationary States 14^
7.5 Conservation Laws 14^
7.6 Angular Momentum 148
7.6.1 Angular momentum Operators 14"
7.6.2 Rotation Operators U9
7.6.3 Rotation Sandwiches
7.6.4 Angular momentum eigenstates and eigenvalues 1^
7.6.5 The angular momentum eigenstates 1^
7.6.6 Shift Operators I54
7.6.7 Matrix representations of the angular momentum Operators 156
7.7 Spin I57
7.7.1 Spin angular momentum Operators i0
7.7.2 Spin rotation Operators
7.7.3 Spin Zeeman basis ^
7.7A Trace 159
7.8 Spin-1/2 l60
7.8.1 Zeeman eigenstates 1^
7.8.2 Angular momentum Operators
7.8.3 Spin-1/2 rotation Operators 160
7.8.4 Unity Operator l61
7.8.5 Shift Operators 161
7.8.6 Projection Operators
7.8.7 Ket-bra notation 162
7.9 Higher Spin 162
7.9.1 Spin/ = 1 163 !
7.9.2 Spin 7 = 3/2 164 i
7.9.3 Higher spins 165 i
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 Statte 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 190
9 Internal Spin Interactions 195
9.1 Chemical Shirt 195
9.1.1 Chemical shift tensor 196
9.1.2 Principal axes 197
9.1.3 Principal values 198
9.1.4 Isotropie 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 Anisotropie liquids 209
9.2.5 Solids 210
9.2.6 Quadrupole interaction: sumrnary 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 215
9.3.3 Dipole-dipole coupling in liquid crystals 216
9.3.4 Dipole-dipole coupling in solids
9.3.5 Dipole-dipole interaction: summary
9.4 7-Coupling ^17
9.4.1 Isotropie 7-coupling
9.4.2 Liquid crystals and solids
9.4.3 Mechanism of the /-coupling ff
9.4.4 7-coupling: summary
9.5 Spin-Rotation Interaction
9.6 Summary of the Spin Hamiltonian Terms
Part 5 Uncoupled Spins 229
io Single Spin-1/2 23J
10.1 Zeeman Eigenstates "^
10.2 Measurement of Angular Momentum: Quantum Indeterminacy 232
10.3 Energy Levels 23
10.4 Superposition States
10.4.1 General spin states _
10.4.2 Vector notation r~:
10.4.3 Some particular states
10.4.4 Phase factors ^
10.5 Spin Precession 23J
10.5.1 Dynamics of the eigenstates _.
10.5.2 Dynamics of the superposition states
10.6 Rotating Frame 2^
10.7 Precession in the Rotating Frame
10.8 Radio-frequency Pulse 2£L
10.8.1 Rotating-frame Hamiltonian ~
10.8.2 *-pulse 2!r
10.8.3 Nutation 2^
10.8.4 Pulse of general phase TZ
10.8.5 Off-resonance effects Ö
ii Ensemble ofSpins-1/2 259
11.1 Spin Density Operator 25^
11.2 Populations and Coherences .
11.2.1 Density matrix J°J
11.2.2 Box notation 2^
11.2.3 Balls and arrows 262
11.2.4 Orders ofcoherence 2^
11.2.5 Relationships between populations and coherences ^
11.2.6 Physical interpretation of the populations 2 _
11.2.7 Physical interpretation of the coherences 2
11.3 Thermal Equilibrium Zbb t
11.4 Rotating-Frame Density Operator 268
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 Precession Without Relaxation 276
11.8 Operator Transformations 279
11.8.1 Pulse of phase 0P = 0 279
11.8.2 Pulse of phase / p = n/2 279
11.8.3 Pulse of phase 4 v=n 279
11.8.4 Pulse of phase pp = 3n/2 279
11.8.5 Pulse of general phase f p 280
11.8.6 Free precession for an interval r 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 7*i 295
12.2 Spin Echoes: Measurement of Ti 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 T\p 305
12.4 Gradient Echoes 306
12.5 Slice Selection 307
12.6 NMR Imaging 309
13 Quadrupolar Nuclei 319
13.1 Spin 1 = 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 32g
13.1.10 Quadrupolar echo 331
13.2 Spin/= 3/2 m
13.2.1 Spin-3/2 energy levels ~,r
13.2.2 Populations and coherences „A
13.2.3 NMR signal ^
13.2.4 Single pulse spectrum 339
13.2.5 Spin-3/2 spectra for small quadrupole couplings 341
13.2.6 Second-order quadrupole couplings 342
13.2.7 Central transition excitation 040
13.2.8 Central transition echo ».,-
13.3 Spin 7 = 5/2 ™
13.4 Spins/= 7/2 ™
13.5 Spins/= 9/2 ™
Part 6 CoupledSpins
14 Spin-1/2 Pairs
14.1 Coupling Regimes 355
14.2 ZeemanProduct States and Superposition States 356
14.3 Spin-Pair Hamiltorüan ,c7
14.4 Pairs of Magnetically Equivalent Spins 359
14.4.1 Singletsandtriplets fl
UA.2 Energy levels £?
14.4.3 NMRspectra ^
14.4.4 Dipolarecho f^
14.5 Weakly Coupled Spin Pairs ,S
14.5.1 Weak coupling ^
14.5.2 AX spin Systems ,^4
14.5.3 Energy levels f?T
14.5.4 AX spectrum %t
14.5.5 Heteronuclearspin pairs 366
15 HomonudearAX System 359
15.1 Eigenstatesand Energy Levels 369
15.2 Density (Operator „n
15.3 Rotating Frame ZZ
15.4 Free Evolution %?
15A1 Evolution ofa spin pair 376
15.4.2 Evolution ofthe coherences 377
S pS^l^System:S^-s-sp^ s
IS 7 -JS Spirtonentations 386
15.7 ThermalEquilibrium ™
15.8 Radio-Freqi,ency Pul«** Si
15-8.2 R^hons ofthe spin denslry Operator 393
XV
15.8.3 Operator transformations 395
15.9 Free Evolution of the Product Operators 397
15.9.1 Chemical shift evolution 399
15.9.2 ./-coupling evolution 400
15.9.3 Relaxation 405
15.10 Spin Echo Sandwich 405
16 Experiments on AX Systems 409
16.1 COSY 409
16.1.1 The assignment problem 409
16.1.2 COSY pulse sequence 411
16.1.3 Theory of COSY: coherence Interpretation 411
16.1.4 Product Operator interpretation 415
16.1.5 Experimental examples 418
16.2 INADEQUATE 418
16.2.1 13C isotopomers 418
16.2.2 Pulse sequence 423
16.2.3 Theory of INADEQUATE 424
16.2.4 Coherence transfer pathways and phase cycling 429
16.2.5 Two-dimensional INADEQUATE 431
16.3 INEPT 436
16.3.1 The sensitivity of nuclear isotopes 436
16.3.2 INEPT pulse sequence 437
16.3.3 Refocused INEPT 440
16.4 Residual Dipolar Couplings 443
16.4.1 Angular information 443
16.4.2 Spin Hamiltonian 443
16.4.3 Orienting media 444
16.4.4 Doublet Splittings 446
17 Many-Spin Systems 453
17.1 Molecular Spin System 453
17.2 Spin Ensemble 454
17.3 Motionally Suppressed /-Couplings 454
17.4 Chemical Equivalence 455
17.5 Magnetic Equivalence 45g
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 46g
18.3 Superposition States
18.4 Spin Density Operator ™
18.5 Populations and Coherences
18.5.1 Coherence Orders
18.5.2 Combination coherences and simple coherences ^
18.5.3 Coherence frequencies
18.5.4 Degenerate coherences
18.5.5 Observable coherences
18.6 NMRSpectra ®1
18.7 Many-Spin Product Operators ZL
18.7.1 Construction of product Operators
18.7.2 Populations and coherences
18.7.3 Physical interpretation of product Operators 4°
18.8 Thermal Equilibrium ~;
18.9 Radio-Frequency Pulses r\
18.10 Free Precession ™~
18.10.1 Chemical shift evolution rz
18.10.2 7-coupling evolution ::_
18.10.3 Relaxation *~j?
18.11 Spin Echo Sandwiches ~?
18.12 INEPT in an I2S System ™?
18.13 COSY in Multiple-Spin Systems ^}
18.13.1 AMX spectrum ^
18.13.2 Active and passive spins
18.13.3 Cross-peak multiplets f*
18.13.4 Diagonal peaks ?!
18.13.5 Linear spin Systems
18.14 TOCSY „i
49/
18.14.1 The ambiguity of COSY spectra '
18.14.2 TOCSY pulse sequence .„„
18.14.3 Theory of TOCSY
Part 7 Motion and Relaxation 5°7
19 Motion 509
19.1 Motional Processes ^
19.1.1 Molecular vibrations „0
19.1.2 Local rotations of molecular groups ein
19.1.3 Molecular flexibility ™
19.1.4 Chemical exchange „1
19.1.5 Molecular rotations „-
19.1.6 Translational motion -^
19.1.7 Mechanical motion
19.2 Motional Time-Scales 5]f
19.3 Motional Effects 5JZ
19.4 Motional Averaging 5JT,
19.5 Motional Lineshapes and Two-Site Exchange
19.5.1 Slow intermediate exchange and motional broadening 518
19.5.2 Fast intermediate exchange and motional narrowing 520
19.5.3 Averaging of 7-splittings 523
19.5.4 Asymmetrie two-site exchange 524
19.5.5 Knight shift 525
19.5.6 Paramagnetic shifts 527
19.6 Sample Spinning 527
19.7 Longitudinal Magnetization Exchange 529
19.7.1 Two-dimensional exchange spectroscopy 529
19.7.2 Theory 532
19.7.3 Motional regimes 539
19.8 Diffusion 539
20 Relaxation 543
20.1 Types of Relaxation 543
20.2 Relaxation Mechanisms 543
20.3 Random Field Relaxation 545
20.3.1 Autocorrelation funetions and correlation times 545
20.3.2 Spectral density 548
20.3.3 Normalized spectral density 549
20.3.4 Transition probabilities 550
20.3.5 Thermally corrected transition probabilities 551
20.3.6 Spin-lattice relaxation 552
20.4 Dipole-Dipole Relaxation 556
20.4.1 Rotational correlation time 556
20.4.2 Transition probabilities 557
20.4.3 Solomon equations 561
20.4.4 Longitudinal relaxation 564
20.4.5 Transverse relaxation 565
20.5 Steady-State Nuclear Overhauser Effect 566
20.6 NOESY 570
20.6.1 NOESY pulse sequence 570
20.6.2 NOESY signal 570
20.6.3 NOESY spectra 573
20.6.4 NOESY and chemical exchange 575
20.6.5 Molecular strueture determination 576
20.7 ROESY 577
20.7.1 Transverse cross-relaxation 577
20.7.2 Spin locking 578
20.7.3 Transverse Solomon equations 57g
20.7.4 ROESY spectra 580
20.7.5 ROESY and chemical exchange 582
20.7.6 ROESY and TOCSY 533
20.8 Cross-Correlated Relaxation 554
20.8.1 Cross-correlation 534
20.8.2 Cross-correlation of spin interactions 585
20.8.3 Dipole-dipole cross-correlation and angular estimations 586
20.8.4 TROSY 590
Part 8 Appendices 597
Appendix A: Supplementary Material 599
599
A.l Euler Angles and Frame Transformations
A.1.1 Definition of the Euler angles
A.l.2 Euler rotations: first scheine
A.1.3 Euler rotations: second scheme
A.l.4 Euler rotation matrices .
A.1.5 Reference-frame orientations
A.l.6 Consecutive reference-frame transformations
A.1.7 Passive rotations ,„,
A.1.8 Tensor transformations 604
A.l.9 Intermediate reference frames .
A.2 Rotations and Cyclic Commutation „_
A.3 Rotation Sandwiches ,„,.
A.4 Spin-1/2 Rotation Operators „g
A.5 Quadrature Detection and Spin Coherences .
A.6 Secular Approximation ,.
A.7 Quadrupolar Interaction ,,.
A.7.1 Füll quadrupolar interaction ,.4
A.7.2 First-order quadrupolar interaction ,.j
A.7.3 Higher-order quadrupolar interactions . ,-
A.8 Strong Coupling ,,,-
A.8.1 Strongly-coupled Spin-1/2 pairs ,^q
A.8.2 General strongly coupled Systems ,~\
A.9 7-Couplings and Magnetic Equivalence ,23
A.10 Spin Echo Sandwiches ^25
A.10.1 Short-duration limit 625
A.10.2 Long-duration limit ^26
A.10.3 Two spin echo sequences ,~j
A.10.4 Heteronuclear spin echo sequences ,«9
A.ll Phase Cycling ,2o
A.ll.l Coherence transfer pathways rnn
A.11.2 Coherence transfer amplitudes 631
A.ll.3 Coherence Orders and phase shifts 632
A.11.4 The pathway phase ^
A.11.5 Asumtheorem fi34
A.11.6 Pathway selection I ,,c
A.11.7 Pathway selection II 637
A.11.8 Pathway selection III ?3g
A.l 1.9 Selection of a Single pathway I .,9
A.11.10 Selection of a Single pathway II ^q
A.ll.ll Dual pathway selection f,-,
A.11.12 InternalphasesI Vg
A.11.13 Internal phases II ^
A.ll.14 Nested phase cycles I Mc
A.11.15 Nested phase cycles n ^g \
A.11.16 Differentwaysofconstructing phase cycles \
A.12 Coherence Selection by Pulsed Field Gradients 649
A.12.1 Field gradient dephasing 649
A.12.2 Pathway phase 651
A.12.3 Coherence transfer echoes 652
A.12.4 Pathway selection 652
A.12.5 Heteronuclear coherence transfer echoes 652
A.13 Bloch Equations 653
A.14 Chemical Exchange 654
A.14.1 The incoherent dynamics 655
A.14.2 The coherent dynamics 655
A.14.3 The spectrum 656
A.14.4 Longitudinal magnetization exchange 658
A.15 Solomon Equations 660
A.16 Cross-Relaxation Dynamics 662
Appendix B: Symbols and Abbreviations 665
Answers to the Exercises 681
Index 693 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Levitt, Malcolm H. |
| author_facet | Levitt, Malcolm H. |
| author_role | aut |
| author_sort | Levitt, Malcolm H. |
| author_variant | m h l mh mhl |
| building | Verbundindex |
| bvnumber | BV022720678 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.3.S6 |
| callnumber-search | QC793.3.S6 |
| callnumber-sort | QC 3793.3 S6 |
| callnumber-subject | QC - Physics |
| classification_rvk | UM 3500 VE 8600 VG 9500 |
| classification_tum | PHY 517f CHE 244f CHE 160f |
| ctrlnum | (OCoLC)141380283 (DE-599)DNB 2007022146 |
| dewey-full | 538/.362 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 538 - Magnetism |
| dewey-raw | 538/.362 |
| dewey-search | 538/.362 |
| dewey-sort | 3538 3362 |
| dewey-tens | 530 - Physics |
| discipline | Chemie / Pharmazie Physik Chemie |
| discipline_str_mv | Chemie / Pharmazie Physik Chemie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV022720678 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:29:58Z |
| indexdate | 2024-07-09T21:04:28Z |
| institution | BVB |
| isbn | 9780470511176 9780470511183 0470511176 |
| language | English |
| lccn | 2007022146 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015926414 |
| oclc_num | 141380283 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-92 |
| owner_facet | DE-20 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-29T DE-92 |
| physical | XXV, 714 S., [5] Bl. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| spelling | Levitt, Malcolm H. Verfasser aut Spin dynamics basics of nuclear magnetic resonance Malcolm H. Levitt 2. ed. Chichester Wiley 2008 XXV, 714 S., [5] Bl. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nuclear spin Nuclear magnetic resonance Magnetische Kernresonanz (DE-588)4037005-7 gnd rswk-swf NMR-Spektroskopie (DE-588)4075421-2 gnd rswk-swf Spindynamik (DE-588)4417075-0 gnd rswk-swf NMR-Spektroskopie (DE-588)4075421-2 s DE-604 Magnetische Kernresonanz (DE-588)4037005-7 s Spindynamik (DE-588)4417075-0 s http://www.loc.gov/catdir/toc/ecip0719/2007022146.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015926414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levitt, Malcolm H. Spin dynamics basics of nuclear magnetic resonance Nuclear spin Nuclear magnetic resonance Magnetische Kernresonanz (DE-588)4037005-7 gnd NMR-Spektroskopie (DE-588)4075421-2 gnd Spindynamik (DE-588)4417075-0 gnd |
| subject_GND | (DE-588)4037005-7 (DE-588)4075421-2 (DE-588)4417075-0 |
| title | Spin dynamics basics of nuclear magnetic resonance |
| title_auth | Spin dynamics basics of nuclear magnetic resonance |
| title_exact_search | Spin dynamics basics of nuclear magnetic resonance |
| title_exact_search_txtP | Spin dynamics basics of nuclear magnetic resonance |
| title_full | Spin dynamics basics of nuclear magnetic resonance Malcolm H. Levitt |
| title_fullStr | Spin dynamics basics of nuclear magnetic resonance Malcolm H. Levitt |
| title_full_unstemmed | Spin dynamics basics of nuclear magnetic resonance Malcolm H. Levitt |
| title_short | Spin dynamics |
| title_sort | spin dynamics basics of nuclear magnetic resonance |
| title_sub | basics of nuclear magnetic resonance |
| topic | Nuclear spin Nuclear magnetic resonance Magnetische Kernresonanz (DE-588)4037005-7 gnd NMR-Spektroskopie (DE-588)4075421-2 gnd Spindynamik (DE-588)4417075-0 gnd |
| topic_facet | Nuclear spin Nuclear magnetic resonance Magnetische Kernresonanz NMR-Spektroskopie Spindynamik |
| url | http://www.loc.gov/catdir/toc/ecip0719/2007022146.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015926414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT levittmalcolmh spindynamicsbasicsofnuclearmagneticresonance |