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High Resolution NMR
Theory and Chemical Applications
THIRD EDITION
Edwin D. Becker National Institutes of Health
Bethesda, Maryland
Academic Press San Diego London Boston New York
Sydney Tokyo Toronto
Contents
Preface to the T h i r d Ed i t ion xv
1 Introduction
1.1 Origins and Early History of N M R 2 1.2 High Resolution N M R : An Overview 5 1.3 Additional Reading and Resources 12
2 TheTheoryofNMR 2.1 Nuclear Spin and Magnetic Moment 13 2.2 Theoretical Descriptions of N M R 14
Transitions between Stationary State Energy Levels 15
Classical Mechanical Treatment 15
The Density Matrix 15
Product Operators 16
2.3 Steady-State Quantum Mechanical Description 16 The Hamiltonian Operator 16
SpinWave Functions 17
Spectral Transitions 18
2.4 Effect of the Boltzmann Distribution 19 2.5 Spin-Lattice Relaxation 20
Saturation 22
Other Non-Boltzmann Distributions 22
LmeWidths 23
2.6 Precession of Nuclear Magnetic Moments 24 Macroscopic Magnetization 26
2.7 Classical Mechanical Description of N M R 27 The Bloch Equations 30
Contents
2.8 Magnetization in the Rotating Frame 32 2.9 Methods of Obtaining N M R Spectra 33
Adiabatic Passage 33
Slow Passage 34
Absorption and Dispersion 35
Radio Frequency Pulses 35
Pulse Sequences 37
2.10 Dynamic Processes 39 Qualitative Evaluation 40
Quantitative Treatments 42
2.11 Terniinology, Symbols, Units, and Conventions 43 Symbols 43
Magnetic Field and Magnetic Induction 44
Signs of Rotations 44
Frequency Units 45
2.12 Additional Reading and Resources 46 2.13 Problems 46
Instrumentation and Techniques
3.1 Advantages of Pulse Fourier Transform N M R 49 3.2 Basic N M R Apparatus 51 3.3 Requirenients for High Resolution N M R 52
Homogeneity 53
Stability 55
3.4 Detection of N M R Signals 56 3.5 Phase Cycling 57 3.6 Fourier Transformation of the FID 60 3.7 Data Acquisition 61
Acquisition Rate 61
Acquisition Time 67
3.8 Data Processing 68 Zero-Filling 69 Phase Correction and Spectral Presentation 69
Interpolation by Linear Prediction 70
3.9 Digital Filtering 72 Sensitivity Enhancement 72
Resolution Enhancement 74
3.10 Alternatives to Fourier Transformation 74 3.11 Sensitivity and Size of Sample 75
Instrumental Sensitivity 75
Radiation Damping 76
Time Averaging 77
Sample Tubes 78
Control of Sample Temperature 79
3.12 Useful Solvents 79
Contents vii
3.13 Additional Reading and Resources 80 3.14 Problems 81
Chemical Shifts
4.1 The Origin of Chemical Shifts 83 4.2 Theoryof Chemical Shifts 84
Ab Initio Calculations of Chemical Shielding 85
Absolute and Relative Shieldings 86
4.3 Measurement of Chemical Shifts 87 Chemical Shift Scales 88
Internal and External References 89
Effect of Bulk Magnetic Susceptibility 90
Substitution of Sample and Reference 91
Reference Compounds 92
4.4 Empirical Correlations of Chemical Shifts 94 4.5 SomeAspects of Proton Chemical Shifts 94
Effect of Electron Density 94
Magnetic Anisotropy 99
Ring Currents 102
Solvent Effects 103
Hydrogen Bonding 105
4.6 Nuclei OtherThan Hydrogen 107 Nitrogen 107
Carbon-13 107
4.7 Compilations of Spectral Data and Empirical Estiniates of Chemical Shifts 108
4.8 Isotope Effects 109 4.9 Effects of Molecular Asymmetry 109 4.10 Paramagnetic Species 112
Lanthanide Shift Reagents 113
4.11 Additional Reading and Resources 114 4.12 Problems 115
Coupling between Pairs of Spins 5.1 Origin of Spin Coupling Interactions 119
Magnetic Dipolar Interactions 120
Electron-Coupled Spin—Spin Interactions 120
5.2 General Aspects of Spin—Spin Coupling 122 Signs of Coupling Constants 123 Some Observed Coupling Constants 123
Reduced Coupling Constants 125
5.3 Theory of Spin-Spin Coupling 128 5.4 Correlation of Coupling Constants with Other
Physical Properties 129
vii i Contents
5.5 Effect of Exchange 132 5.6 Spin Decoupling and Double Resonance 133 5.7 Additional Reading and Resources 134 5.8 Problems 135
6 Stmcture and Analysis of Complex Spectra 6.1 Symmetry and Equivalence 140 6.2 Notation 142 6.3 Energy Levels and Transitions in an AX System 143
Case I. N o Coupling between A and X 144
Case Il.Weak Coupling 145
6.4 Quantum Mechanical Treatment 145 Nuclear Spin Basis Functions 146 The Spin Hamiltonian 146
Energy Levels and Eigenfunctions 147
6.5 The Two-Spin System without Coupling 148 6.6 Factoring the Secular Equation 150 6.7 Two Coupled Spins 151
Wave Functions 153
Selection Rules and Intensities 153
6.8 The AB Spectrum 154 Frequencies of Lines 154
Intensities of Lines 156
6.9 AX, AB, and A2 Spectra 157 Magnetically Equivalent Nuclei 158
6.10 "First-Order" Spectra 158 6.11 Symmetry of Spin Wave Functions 161 6.12 General Procedures for Simulating Spectra 163 6.13 Three-Spin Systems 164
ABC 164
A2B 164
ABX 165
AMX 168
6.14 Relative Signs of Coupling Constants 168 6.15 Some Consequences of Strong Coupling and
Chemical Equivalence 171 6.16 "Satellites" from Carbon-13 and Other Nuclides 175 6.17 The AA'BB'and AA'XX'Systems 176 6.18 Additional Reading and Resources 177 6.19 Problems 178
7 Spectra ofSolids
7.1 Spin Interactions in Solids 184 7.2 Dipolar Interactions 184
Contents ix
7.3 "Scalar Coupimg" 187 7.4 The HeteronuclearTwo-Spin System 187 7.5 Dipolar Decoupling 189 7.6 Cross Polarization 190 7.7 The HomonuclearTwo-Spin System 191 7.8 Line Narrowing by Multiple Pulse Methods 192 7.9 Anisotropy of the Chemical Shielding 194 7.10 Magic Angle Spinning 195
Spinning Sidebands and Recoupling Techniques 197
7.11 Quadrupole Interactions and Line-Narrowing Methods 198 7.12 Other Aspects of Line Shapes 200 7.13 Orientation Effects in Liquids: Liquid Crystals 201 7.14 Additional Reading and Resources 203 7.15 Problems 203
Relaxation 8.1 Molecular Motions and Processes for Relaxation
in Liquids 206 8.2 Nuclear Magnetic Dipole Interactions 209 8.3 Nuclear Overhauser Effect 212 8.4 Relaxation via Chemical Shielding Anisotropy 215 8.5 Electric Quadrupole Relaxation 216 8.6 Scalar Relaxation 217 8.7 Spin-Rotation Relaxation 219 8.8 Relaxation by Paramagnetic Substances 220 8.9 Other Factors Affecting Relaxation 221 8.10 Additional Reading and Resources 224 8.11 Problems 224
Pulse Sequences 9.1 The Spin Echo 228
Effect of Chemical Shifts and Spin Coupling 228
Enhancement of Signal/Noise Ratio 231
90° Echoes 231
Gradient-Recalled Echo 232
Effect of Motion on an Echo 232
9.2 The Carr—Purcell Pulse Sequence 233 Effect of Diffusion and Exchange 233
Measurement of Molecular Diffusion 233
9.3 Correcting for Pulse Imperfections 234 The M e i b o o m - Gill Method 235 Composite Pulses 235
x Contents
9.4 SpinLocking 236 Relaxation in the Rotating Frame 236
9.5 Selective Excitation 237 DANTE 238 BIRD Pulse and X-Filters 239
Solvent Suppression 241
9.6 Decoupling 242 9.7 Polarization Transfer Methods 243
Selective Population Transfer 244
INEPT 244
Antiphase Magnetization 247
Spectral Editing by INEPT 248
9.8 Additional Reading and Resources 249 9.9 Problems 249
10 Two-Dimensional NMR 10.1 General Aspects of2D Spectra 251
The Basic 2D Experimental Procedure 252
Behavior of Magnetization and N M R Signals 253
A Real Exaniple: Chemical Exchange and Cross Relaxation 256
10.2 A Survey of Basic 2D Experiments 259 _f-Resolved Spectra 259
2D Experiments in Solids 262
Correlation via Spin Coupling 263
Isotropie Mixing 265
NOESY and ROESY 267
INADEQUATE 267
Indirect Detection 268
10.3 Data Acquisition and Processing 268 Effects of Modulation during the Evolution Period 269
Processing of Time Response Signals 270
States and TPPI Methods 272
Axial Peaks 273
Zero-Filling and Digital Filtering 274
10.4 Sensitivity Considerations 274 Signal/Noise in 1D and 2D Spectra 275
Noise andArtifacts Peculiar to 2D Spectra 276
Experiment Repetition Rate 276
10.5 Additional Reading and Resources 277 10.6 Problems 277
1 1 Density Matrix and Product Operator Formalisms 11.1 The Density Matrix 280
Expectation Values and Ensemble Averaging 280
Properties of the Density Matrix 282
C o n t e n t s x i
Evolution of the Density Matrix 283
Exponential Operators 285
Notations for the Density Matrix and Its Subsets 286
11.2 Transformations of the Density Matrix 287 Transformation to the Rotating Frame 287
The Effect of a Radio Frequency Pulse 287
11.3 The One-Spin System 289 Effect ofa 90° Pulse 291
Effect of Free Precession 292
11.4 The Two-Spin System 293 Eigenfunctions and Energy Levels 293
Equilibrium Density Matrix 294
Effect ofa Selective 90° Pulse 294
Evolution of the Density Matrix 296
Effect ofa Nonselective 90° Pulse 297
Effect of Strong Coupling 297
11.5 INEPT and Related Pulse Sequences 298 Density Matrix Treatment of INEPT 298
Polarization Transfer 301
Multiple Quantum Coherence 301
11.6 Product Operators 302 Density Matrix and Spin Operators 303
Properties of Product Operators 305
An Example: INEPT 309
An Example: Solid Echo 310
11.7 Coherence Transfer Pathways 311 Phase Cycling 312
Coherence Order Diagrams 313
Use of Pulsed Field Gradients 315
11.8 Additional Reading and Resources 316 11.9 Problems 316
12 Selected ID, 2D, and 3D Experiments: A Further Look
12.1 Spectral Editing 317 APT 318
INEPT 319
DEPT 319
12.2 Double Quantum Filtering Experiments 322 Double Quantum Filters 323
INADEQUATE 323
Proton-Detected INADEQUATE 326
O t h e r U s e s o f D Q F 326
12.3 COSY 327 Coherence Pathways 327
Detection and Spectral Display 330
xi i C o n t e n t s
DQF-COSY 330
ft)rDecoupled COSY 332
OtherVariantsofCOSY 333
12.4 Heteronuclear Correlation by Indirect Detection 334 HSQC 335
H M Q C 337
HMBC 338
12.5 Three- and Four-Dimensional N M R 339 Spectral Editing in the Third Dimension 339
Correlation byTriple Resonance Experiments 343
12.6 Additional Reading and Resources 345 12.7 Problems 346
1 3 Eluädation ofMolecular Structure and Macromolecular Conformation
13.1 Organic Structure Elucidation 348 Features o f ] H Spectra 348
Features of 13C Spectra 351
Spectral Editing 352
13.2 Application of Some Useful 2D Methods 352 Proton-Proton Correlations 353
Heteronuclear Correlations 353
Other Useful 2D Experiments 353
13.3 Structure and Configuration of Polymers 355 13.4 Three-Dimensional Structure of Biopolymers 358
Computational Strategy 359
Spectral Assignment 361
N M R and Structure Determination 363
13.5 Additional Reading and Resources 367
1 4 NMR Imaging and Spatially Localized Spectroscopy
14.1 Use of Magnetic Field Gradients to Produce Images 369 14.2 Use of 2D N M R Methods in Imaging 371
Slice Selection 373
RepetitionTime 373
14.3 k Space; Echo Planar Imaging 374 14.4 Factors Affecting Image Contrast 375
Relaxation Times 376
Diffusion 377
Flow 377
Magnetic Susceptibility 378
14.5 Chemical Shift Imaging and in Vivo Spectroscopy 378 14.6 N M R Imaging in Solids 379 14.7 Additional Reading and Resources 380
C o n t e n t s x i i i
Appendix A
Properties of Common Nuclear Spins 381
Appendix B
ABXandAA'XX' Spectra 385 B.l The ABX System 385
Structure of the Spectrum 385
Analysis of an ABX Spectrum 388
B.2 The AA'XX'System 389 Structure of the Spectrum 389 Analysis of an A A ' X X ' Spectrum 390
Appendix C
Review of Relevant Mathematics 393 C. 1 Complex Numbers 393 C.2 Trigonometrie Identities 394 C.3 Vectors 394 C.4 Matrices 395
Appendix D
Spin Matrices 397 D.l One Spin 397 D.2 Two-Spin System 397
Appendix E
Selected Answers to Problems 401
References 411
Index 417