Preface XV

1 Introduction to NMR Spectroscopy 1

1.1 Our First 1D Spectrum 1

1.2 Some Nomenclature: Chemical Shifts, LineWidths, and Scalar Couplings 2

1.3 Interpretation of Spectra: A Simple Example 5

1.4 Two-Dimensional NMR Spectroscopy: An Introduction 9

Part One Basics of Solution NMR 11

2 Basicsof1DNMRSpectroscopy 13

2.1 The Principles of NMR Spectroscopy 13

2.2 The Chemical Shift 16

2.3 Scalar Couplings 17

2.4 Relaxation and the Nuclear Overhauser Effect 20

2.5 Practical Aspects 23

2.5.1 Sample Preparation 23

2.5.2 Referencing 25

2.5.3 Sensitivity and Accumulation of Spectra 27

2.5.4 Temperature Calibration 29

2.6 Problems 30

Further Reading 31

3 1H NMR 33

3.1 General Aspects 33

3.2 Chemical Shifts 34

3.2.1 Influence of Electronegativity of Substituents 35

3.2.2 Anisotropy Effects 35

3.2.3 Other Factors Affecting Chemical Shifts: Solvent, Temperature, pH, and Hydrogen Bonding 37

3.2.4 Shift Reagents 37

3.3 Spin Systems, Symmetry, and Chemical or Magnetic Equivalence 39

3.3.1 Homotopic, Enantiotopic, and Diastereotopic Protons 42

3.3.2 Determination of Enantiomeric Purity 43

3.4 Scalar Coupling 44

3.4.1 First-Order Spectra 45

3.4.2 Higher-Order Spectra and Chemical Shift Separation 47

3.4.3 Higher-Order Spectra and Magnetic Equivalence 49

3.5 1H–1H Coupling Constants 50

3.5.1 Geminal Couplings 50

3.5.2 Vicinal Couplings 50

3.5.3 Long-Range Couplings 52

3.5.4 1HCouplings to Other Nuclei 52

3.6 Problems 54

Further Reading 55

4 NMRof13C and Heteronuclei 57

4.1 Properties of Heteronuclei 57

4.2 Indirect Detection of Spin-1/2 Nuclei 59

4.3 13C NMR Spectroscopy 59

4.3.1 The 13C Chemical Shift 60

4.3.2 X,13C Scalar Couplings 64

4.3.3 Longitudinal Relaxation of 13C Nuclei 68

4.3.4 Recording 13C NMR Spectra 68

4.4 NMR of Other Main Group Elements 70

4.4.1 Main Group Nuclei with I D 1/2 71

4.4.2 Main Group Nuclei with I > 1/2 75

4.5 NMR Experiments with Transition Metal Nuclei 78

4.5.1 Technical Aspects of Inverse Experiments with I D 1/2 Metal Nuclei 79

4.5.2 Experiments with Spin I > 1/2 Transition Metal Nuclei 81

4.6 Problems 82

Further Reading 84

Part Two Theory of NMR Spectroscopy 85

5 Nuclear Magnetism – A Microscopic View 87

5.1 The Origin of Magnetism 87

5.2 Spin – An Intrinsic Property of Many Particles 88

5.3 Experimental Evidence for the Quantization of the Dipole Moment: The Stern–Gerlach Experiment 93

5.4 The Nuclear Spin and Its Magnetic Dipole Moment 94

5.5 Nuclear Dipole Moments in a Homogeneous Magnetic Field: The Zeeman Effect 96

5.5.1 Spin Precession 98

5.6 Problems 103

6 Magnetization – A Macroscopic View 105

6.1 The Macroscopic Magnetization 105

6.2 Magnetization at Thermal Equilibrium 106

6.3 Transverse Magnetization and Coherences 108

6.4 Time Evolution of Magnetization 109

6.4.1 The Bloch Equations 110

6.4.2 Longitudinal and Transverse Relaxation 112

6.5 The Rotating Frame of Reference 115

6.6 RF Pulses 117

6.6.1 Decomposition of the RF Field 118

6.6.2 Magnetic Fields in the Rotating Frame 119

6.6.3 The Bloch Equations in the Rotating Frame 120

6.6.4 Rotation of On-Resonant and Off-Resonant Magnetization under the Influence of Pulses 121

6.7 Problems 122

7 Chemical Shift and Scalar and Dipolar Couplings 125

7.1 Chemical Shielding 125

7.1.1 The Contributions to Shielding 127

7.1.2 The Chemical Shifts of Paramagnetic Compounds 131

7.1.3 The Shielding Tensor 132

7.2 The Spin–Spin Coupling 133

7.2.1 Scalar Coupling 134

7.2.2 Quadrupolar Coupling 140

7.2.3 Dipolar Coupling 141

7.3 Problems 144

Further Reading 145

8 A Formal Description of NMR Experiments: The Product Operator Formalism 147

8.1 Description of Events by Product Operators 148

8.2 Classification of Spin Terms Used in the POF 149

8.3 Coherence Transfer Steps 151

8.4 An Example Calculation for a Simple 1D Experiment 152

Further Reading 153

9 A Brief Introduction into the Quantum-Mechanical Concepts of NMR 155

9.1 Wave Functions, Operators, and Probabilities 155

9.1.1 Eigenstates and Superposition States 156

9.1.2 Observables of Quantum-Mechanical Systems and Their Measured Quantities 157

9.2 Mathematical Tools in the Quantum Description of NMR 158

9.2.1 Vector Spaces, Bra’s, Ket’s, and Matrices 158

9.2.2 Dirac’s Bra–Ket Notation 159

9.2.3 Matrix Representation of State Vectors 160

9.2.4 Rotations between State Vectors can be Accomplished with Tensors 161

9.2.5 Projection Operators 162

9.2.6 Operators in the Bra–Ket Notation 163

9.2.7 Matrix Representations of Operators 165

9.3 The Spin Space of Single Noninteracting Spins 166

9.3.1 Expectation Values of the Spin-Components 168

9.4 Hamiltonian and Time Evolution 169

9.5 Free Precession 169

9.6 Representation of Spin Ensembles – The Density Matrix Formalism 171

9.6.1 Density Matrix at Thermal Equilibrium 173

9.6.2 Time Evolution of the Density Operator 173

9.7 Spin Systems 175

9.7.1 Scalar Coupling 176

Part Three Technical Aspects of NMR 179

10 The Components of an NMR Spectrometer 181

10.1 The Magnet 181

10.1.1 Field Homogeneity 182

10.1.2 Safety Notes 183

10.2 Shim System and Shimming 184

10.2.1 The Shims 184

10.2.2 Manual Shimming 185

10.2.3 Automatic Shimming 186

10.2.4 Using Shim Files 187

10.2.5 Sample Spinning 187

10.3 The Electronics 187

10.3.1 The RF Section 188

10.3.2 The Receiver Section 189

10.3.3 Other Electronics 189

10.4 The Probehead 189

10.4.1 Tuning and Matching 190

10.4.2 Inner and Outer Coils 191

10.4.3 Cryogenically Cooled Probes 191

10.5 The Lock System 192

10.5.1 The 2H Lock 192

10.5.2 Activating the Lock 193

10.5.3 Lock Parameters 194

10.6 Problems 194

Further Reading 194

11 Acquisition and Processing 195

11.1 The Time Domain Signal 197

11.2 Fourier Transform 199

11.2.1 Fourier Transform of Damped Oscillations 199

11.2.2 Intensity, Integral, and Line Width 200

11.2.3 Phases of Signals 201

11.2.4 Truncation 202

11.2.5 Handling Multiple Frequencies 202

11.2.6 Discrete Fourier Transform 203

11.2.7 Sampling Rate and Aliasing 204

11.2.8 How Fourier Transformation Works 205

11.3 Technical Details of Data Acquisition 209

11.3.1 Detection of the FID 209

11.3.2 Simultaneous and Sequential Sampling 210

11.3.3 Digitizer Resolution 213

11.3.4 Receiver Gain 214

11.3.5 Analog and Digital Filters 215

11.3.6 Spectral Resolution 216

11.4 Data Processing 217

11.4.1 Digital Resolution and Zero Filling 217

11.4.2 Linear Prediction 219

11.4.3 Pretreatment of the FID: Window Multiplication 220

11.4.4 Phase Correction 227

11.4.5 Magnitude Mode and Power Spectra 229

11.4.6 Baseline Correction 230

11.5 Problems 231

Further Reading 232

12 Experimental Techniques 233

12.1 RF Pulses 233

12.1.1 General Considerations 234

12.1.2 Hard Pulses 235

12.1.3 Soft Pulses 236

12.1.4 Band-Selective RF Pulses 237

12.1.5 Adiabatic RF Pulses 238

12.1.6 Composite Pulses 240

12.1.7 Technical Considerations 241

12.1.8 Sources and Consequences of Pulse Imperfections 243

12.1.9 RF Pulse Calibration 244

12.1.10 Transmitter Pulse Calibration 245

12.1.11 Decoupler Pulse Calibration (13C and 15N) 246

12.2 Pulsed Field Gradients 247

12.2.1 Field Gradients 247

12.2.2 Using Gradient Pulses 248

12.2.3 Technical Aspects 250

12.3 Phase Cycling 251

12.3.1 The Meaning of Phase Cycling 251

12.4 Decoupling 255

12.4.1 How Decoupling Works 255

12.4.2 Composite Pulse Decoupling 256

12.5 Isotropic Mixing 257

12.6 Solvent Suppression 257

12.6.1 Presaturation 258

12.6.2 Water Suppression through Gradient-Tailored Excitation 259

12.6.3 Excitation Sculpting 260

12.6.4 WET 260

12.6.5 One-Dimensional NOESY with Presaturation 260

12.6.6 Other Methods 261

12.7 Basic 1D Experiments 262

12.8 Measuring Relaxation Times 262

12.8.1 Measuring T1 Relaxation – The Inversion-Recovery Experiment 262

12.8.2 Measuring T2 Relaxation – The Spin Echo 263

12.9 The INEPT Experiment 266

12.10 The DEPT Experiment 268

12.11 Problems 270

13 The Art of Pulse Experiments 271

13.1 Introduction 271

13.2 Our Toolbox: Pulses, Delays, and Pulsed Field Gradients 272

13.3 The Excitation Block 273

13.3.1 A Simple 90ý Pulse Experiment 273

13.3.2 The Effects of 180ý Pulses 273

13.3.3 Handling of Solvent Signals 274

13.3.4 A Polarization Transfer Sequence 275

13.4 The Mixing Period 277

13.5 Simple Homonuclear 2D Sequences 278

13.6 Heteronuclear 2D Correlation Experiments 279

13.7 Experiments for Measuring Relaxation Times 281

13.8 Triple-Resonance NMR Experiments 283

13.9 Experimental Details 284

13.9.1 Selecting the Proper Coherence Pathway: Phase Cycles 284

13.9.2 Pulsed Field Gradients 286

13.9.3 N-Dimensional NMR and Sensitivity Enhancement Schemes 288

13.10 Problems 289

Further Reading 289

Part Four Important Phenomena and Methods in Modern NMR 291

14 Relaxation 293

14.1 Introduction 293

14.2 Relaxation: The Macroscopic Picture 293

14.3 The Microscopic Picture: Relaxation Mechanisms 294

14.3.1 Dipole–Dipole Relaxation 295

14.3.2 Chemical Shift Anisotropy 297

14.3.3 Scalar Relaxation 298

14.3.4 Quadrupolar Relaxation 298

14.3.5 Spin–Spin Rotation Relaxation 299

14.3.6 Paramagnetic Relaxation 299

14.4 Relaxation and Motion 299

14.4.1 A Mathematical Description of Motion: The Spectral Density Function 300

14.4.2 NMR Transitions That Can Be Used for Relaxation 302

14.4.3 The Mechanisms of T1 and T2 Relaxation 303

14.4.4 Transition Probabilities 304

14.4.5 Measuring Relaxation Rates 306

14.5 Measuring 15N Relaxation to Determine Protein Dynamics 306

14.5.1 The Lipari–Szabo Formalism 307

14.6 Measurement of Relaxation Dispersion 310

14.7 Problems 313

15 The Nuclear Overhauser Effect 315

15.1 Introduction 315

15.1.1 Steady-State and Transient NOEs 318

15.2 The Formal Description of the NOE: The Solomon Equations 318

15.2.1 Different Regimes and the Sign of the NOE: Extreme Narrowing and Spin Diffusion 320

15.2.2 The Steady-State NOE 321

15.2.3 The Transient NOE 324

15.2.4 The Kinetics of the NOE 324

15.2.5 The 2D NOESY Experiment 325

15.2.6 The Rotating-Frame NOE 327

15.2.7 The Heteronuclear NOE and the HOESY Experiment 329

15.3 Applications of the NOE in Stereochemical Analysis 330

15.4 Practical Tips for Measuring NOEs 332

15.5 Problems 333

Further Reading 334

16 Chemical and Conformational Exchange 335

16.1 Two-Site Exchange 335

16.1.1 Fast Exchange 338

16.1.2 Slow Exchange 340

16.1.3 Intermediate Exchange 340

16.1.4 Examples 342

16.2 Experimental Determination of the Rate Constants 344

16.3 Determination of the Activation Energy by Variable-Temperature NMR Experiments 346

16.4 Problems 348

Further Reading 349

17 Two-Dimensional NMR Spectroscopy 351

17.1 Introduction 351

17.2 The Appearance of 2D Spectra 352

17.3 Two-Dimensional NMR Spectroscopy: How Does It Work? 354

17.4 Types of 2D NMR Experiments 357

17.4.1 The COSY Experiment 358

17.4.2 The TOCSY Experiment 359

17.4.3 The NOESY Experiment 362

17.4.4 HSQC and HMQC Experiments 364

17.4.5 The HMBC Experiment 365

17.4.6 The HSQC-TOCSY Experiment 366

17.4.7 The INADEQUATE Experiment 367

17.4.8 J-Resolved NMR Experiments 368

17.5 Three-Dimensional NMR Spectroscopy 370

17.6 Practical Aspects of Measuring 2D Spectra 370

17.6.1 Frequency Discrimination in the Indirect Dimension: Quadrature Detection 370

17.6.2 Folding in 2D Spectra 376

17.6.3 Resolution in the Two Frequency Domains 377

17.6.4 Sensitivity of 2D NMR Experiments 378

17.6.5 Setting Up 2D Experiments 379

17.6.6 Processing 2D Spectra 380

17.7 Problems 381

18 Solid-State NMR Experiments 383

18.1 Introduction 383

18.2 The Chemical Shift in the Solid State 384

18.3 Dipolar Couplings in the Solid State 386

18.4 Removing CSA and Dipolar Couplings: Magic-Angle Spinning 387

18.5 Reintroducing Dipolar Couplings under MAS Conditions 388

18.5.1 An Alternative to Rotor-Synchronized RF Pulses: Rotational Resonance 390

18.6 Polarization Transfer in the Solid State: Cross-Polarization 391

18.7 Technical Aspects of Solid-State NMR Experiments 393

18.8 Problems 394

Further Reading 394

19 Detection of Intermolecular Interactions 395

19.1 Introduction 395

19.2 Chemical Shift Perturbation 397

19.3 Methods Based on Changes in Transverse Relaxation (Ligand-Observe Methods) 398

19.4 Methods Based on Changes in Cross-Relaxation (NOEs) (Ligand-Observe or Target-Observe Methods) 400

19.5 Methods Based on Changes in Diffusion Rates (Ligand-Observe Methods) 403

19.6 Comparison of Methods 404

19.7 Problems 405

Further Reading 406

Part Five Structure Determination of Natural Products by NMR 407

20 Carbohydrates 419

20.1 The Chemical Nature of Carbohydrates 419

20.1.1 Conformations of Monosaccharides 422

20.2 NMR Spectroscopy of Carbohydrates 423

20.2.1 Chemical Shift Ranges 423

20.2.2 Systematic Identification by NMR Spectroscopy 424

20.2.3 Practical Tips: The Choice of Solvent 429

20.3 Quick Identification 430

20.4 A Worked Example: Sucrose 430

Further Reading 437

21 Steroids 439

21.1 Introduction 439

21.1.1 The Chemical Nature 440

21.1.2 Proton NMR Spectra of Steroids 441

21.1.3 Carbon Chemical Shifts 443

21.1.4 Assignment Strategies 444

21.1.5 Identification of the Stereochemistry 447

21.2 A Worked Example: Prednisone 449

Further Reading 456

22 Peptides and Proteins 457

22.1 Introduction 457

22.2 The Structure of Peptides and Proteins 458

22.3 NMR of Peptides and Proteins 461

22.3.1 1HNMR 461

22.3.2 13C NMR 464

22.3.3 15N NMR 467

22.4 Assignment of Peptide and Protein Resonances 469

22.4.1 Peptides 470

22.4.2 Proteins 473

22.5 A Worked Example: The Pentapeptide TP5 476

Further Reading 480

23 Nucleic Acids 481

23.1 Introduction 481

23.2 The Structure of DNA and RNA 482

23.3 NMR of DNA and RNA 486

23.3.1 1HNMR 486

23.3.2 13C NMR 489

23.3.3 15NNMR 490

23.3.4 31P NMR 490

23.4 Assignment of DNA and RNA Resonances 492

23.4.1 Unlabeled DNA/RNA 492

23.4.2 Labeled DNA/RNA 496

Further Reading 498

Appendix 499

A.1 The Magnetic H and B Fields 499

A.2 Magnetic Dipole Moment and Magnetization 500

A.3 Scalars, Vectors, and Tensors 501

A.3.1 Properties of Matrices 504

Solutions 507

Index 525