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