Basic One- and Two-Dimensional NMR Spectroscopy

1 The Physical Basis of NMR Spectroscopy 1 1.1 Introduction 1 1.2 Nuclear Angular Momentum and Magnetic Moment 2 1.3 Nuclei in a Static Magnetic Field 4 1.3.1 Directional Quantization 4 1.3.2 Energy of the Nuclei in the Magnetic Field 4 1.3.3 Populations of the Energy Levels 6 1.3.4 Macroscopic Magnetization 6 1.4 Basic Principles of the NMR Experiment 7 1.4.1 The Resonance Condition 7 1.4.2 Basic Principle of the NMR Measurement 8 1.5 The Pulsed NMR Method 9 1.5.1 The Pulse 9 1.5.2 The Pulse Angle 10 1.5.3 Relaxation 13 1.5.4 The Time and Frequency Domains; the Fourier Transformation 14 1.5.5 Spectrum Accumulation 16 1.5.6 The Pulsed NMR Spectrometer 18 1.6 Spectral Parameters: a Brief Survey 22 1.6.1 The Chemical Shift 22 1.6.1.1 Nuclear Shielding 22 1.6.1.2 Reference Compounds and the d-Scale 24 1.6.2 Spin-Spin Coupling 26 1.6.2.1 The Indirect Spin-Spin Coupling 26 1.6.2.2 Coupling to One Neighboring Nucleus (AXSpinSystem) 27 1.6.2.3 Coupling to Two Equivalent Neighboring Nuclei (AX2 Spin System) 29 1.6.2.4 Coupling to Three or More Equivalent Neighboring Nuclei (AXn Spin System) 30 1.6.2.5 Multiplicity Rules 30 1.6.2.6 Couplings between Three Non-equivalent Nuclei (AMX Spin System) 31 1.6.2.7 Couplings between Equivalent Nuclei (An Spin Systems) 32 1.6.2.8 The Order of a Spectrum 33 1.6.2.9 Couplings between Protons and other Nuclei; 13C Satellite Spectra33 1.6.3 The Intensities of the Resonance Signals 34 1.6.3.1 1H Signal Intensities 34 1.6.3.2 13C Signal Intensities 35 1.6.4 Summary 37 1.7 “Other” Nuclides 38 1.7.1 Nuclides with Spin I = 1/2 39 1.7.2 Nuclides with Spin I > 1/2 40 Exercises 41 1.8 Bibliography for Chapter 1 41 2 The Chemical Shift 43 2.1 Introduction 43 2.1.1 Influence of the Charge Density on the Shielding 44 2.1.2 Effects of Neighboring Groups 47 2.1.2.1 Magnetic Anisotropy of Neighboring Groups 47 2.1.2.2 Ring Current Effects 49 2.1.2.3 Electric Field Effects 51 2.1.2.4 Intermolecular Interactions – Hydrogen Bonding and Solvent Effects 51 2.1.2.5 Isotope Effects 51 2.1.3 Summary 52 2.2 1H Chemical Shifts of Organic Compounds 53 2.2.1 Alkanes and Cycloalkanes 54 2.2.2 Alkenes 56 2.2.3 Arenes 56 2.2.4 Alkynes 57 2.2.5 Aldehydes 58 2.2.6 OH, SH, NH 59 2.3 13C chemical Shifts of Organic compounds 60 2.3.1 Alkanes and Cycloalkanes 61 2.3.2 Alkenes 63 2.3.3 Arenes 64 2.3.4 Alkynes 66 2.3.5 Allenes 66 2.3.6 Carbonyl and Carboxy Compounds 66 2.3.6.1 Aldehydes and Ketones 67 2.3.6.2 Carboxylic Acids and Derivatives 68 2.4 Relationships between the Spectrum and the Molecular Structure 70 2.4.1 Equivalence, Symmetry and Chirality 70 2.4.2 Homotopic, Enantiotopic and Diastereotopic Groups 74 2.4.3 Summary 77 2.5 Chemical Shifts of “Other” Nuclides 78 Exercises 83 2.6 Bibliography for Chapter 2 83 3 Indirect Spin-Spin Coupling 85 3.1 Introduction 85 3.2 H,H Coupling Constants and Chemical Structure 87 3.2.1 Geminal Couplings 2J(H,H) 87 3.2.1.1 Dependence on Bond Angle 87 3.2.1.2 Substituent Effects 88 3.2.1.3 Effects of Neighboring π-Electrons 88 3.2.2 Vicinal Couplings 3J(H,H) 89 3.2.2.1 Dependence on the Dihedral Angle 90 3.2.2.2 Substituent Effects 94 3.2.3 H,H Couplings in Aromatic Compounds 95 3.2.4 Long-range Couplings 96 3.3 C,H Coupling Constants and Chemical Structure 97 3.3.1 C,H Couplings through One Bond 1J(C,H) 97 3.3.1.1 Dependence on the s-Fraction 97 3.3.1.2 Substituent Effects 98 3.3.2 C,H Couplings through Two or More Bonds 99 3.3.2.1 Geminal Couplings (i.e. 2J(C,H) in H-C-13C) 99 3.3.2.2 Vicinal Couplings (i.e. 3J(C,H) in H-C-C-13C) 99 3.3.2.3 Long-range Couplings 3+nJ(C,H) 100 3.3.3 C,H Couplings in Benzene Derivatives 100 3.4 C,C Coupling Constants and Chemical Structure 101 3.5 Correlations between C,H and H,H Coupling Constants 101 3.6 Coupling Mechanisms 103 3.6.1 The Electron-Nuclear Interaction 103 3.6.2 H,D Couplings 105 3.6.3 Relationship between the Coupling and the Lifetime of a Spin State 106 3.6.4 Couplings through Space 106 3.7 Couplings of “Other” Nuclides (Heteronuclear Couplings) 107 Exercises 109 3.8 Bibliography for Chapter 3 109 4 Spectrum Analysis and Calculations 111 4.1 Introduction 111 4.2 Nomenclature 113 4.2.1 Systematic Notation for Spin Systems 113 4.2.2 Chemical and Magnetic Equivalence 114 4.3 Two-Spin Systems 116 4.3.1 The AX Spin System 116 4.3.2 The AB Spin System 118 4.4 Three-Spin Systems 120 4.4.1 The AX2, AK2, AB2 and A3 Spin Systems 120 4.4.2 The AMX and ABX Spin Systems 121 4.5 Four-Spin Systems 123 4.5.1 A2X2 and A2B2 Spin Systems 123 4.5.2 The AA ′XXl′ and AA ′BBl′ Spin Systems 124 4.6 Spectrum Simulation and Iteration 125 4.7 Analysis of 13C NMR Spectra 126 Exercises 127 4.8 Bibliography for Chapter 4 127 5 Double Resonance Experiments 129 5.1 Introduction 129 5.2 Spin Decoupling in ‑H NMR Spectroscopy 130 5.2.1 Simplification of Spectra by Selective Spin Decoupling 130 5.2.2 Suppression of a Solvent Signal 132 5.3 Spin Decoupling in 13C NMR Spectroscopy 133 5.3.1 1H Broad-band Decoupling 133 5.3.2 The Gated Decoupling Experiment 135 5.3.3 1H Off-Resonance Decoupling 136 5.3.4 Selective Decoupling in 13C NMR Spectroscopy 137 Exercises 138 5.4 Bibliography for Chapter 5 138 6 Assignment of 1H and 13C Signals 139 6.1 Introduction 139 6.2 1H NMR Spectroscopy 140 6.2.1 Defining the Problem 140 6.2.2 Empirical Correlations for Predicting Chemical Shifts 141 6.2.2.1 Alkanes (Shoolery’s Rule) 141 6.2.2.2 Alkenes 142 6.2.2.3 Benzene Derivatives 143 6.2.3 Decoupling Experiments 145 6.2.4 Altering the Chemical Structure of the Sample 145 6.2.5 Effects of Solvent and Temperature 146 6.2.6 Shift Reagents 147 6.2.6.1 Lanthanide Shift Reagents (LSRs) 147 6.2.6.2 Chiral Lanthanide Shift Reagents 150 6.3 13C NMR Spectroscopy 152 6.3.1 Defining the Problem 152 6.3.2 Empirical Correlations for Predicting Approximate Chemical Shifts 154 6.3.2.1 Alkanes 154 6.3.2.2 Alkenes 157 6.3.2.3 Benzene Derivatives 158 6.3.3 Decoupling Experiments 159 6.3.4 T1 Measurements 160 6.3.5 Chemical Changes to the Sample 160 6.3.6 Solvent and Temperature Effects and Shift Reagents 161 6.4 Computer-aided Assignment of 13C NMR Spectra 161 6.4.1 Searching for Identical or Related Compounds 161 6.4.2 Spectrum Prediction 162 Exercises 164 6.5 Bibliography for Chapter 6 165 7 Relaxation 167 7.1 Introduction 167 7.2 Spin-Lattice Relaxation of 13C Nuclei (T1) 168 7.2.1 Relaxation Mechanisms 168 7.2.2 Experimental Determination of T1; the Inversion Recovery Experiment 170 7.2.3 Relationships between T1 and Chemical Structure 174 7.2.3.1 Influence of Protons in CH, CH2 and CH3 Groups 174 7.2.3.2 Influence of Molecular Size 175 7.2.3.3 Segmental Mobilities 176 7.2.3.4 Anisotropy of the Molecular Mobility 176 7.2.4 Suppression of the Water Signal 177 7.3 Spin-Spin Relaxation (T2) 177 7.3.1 Relaxation Mechanisms 177 7.3.2 Experimental Determination of T2; the Spin-Echo Experiment 179 7.3.3 Line-widths of NMR Signals 183 Exercises 185 7.4 Bibliography for Chapter 7 185 8 One-Dimensional NMR Experiments using Complex Pulse Sequences 187 8.1 Introduction 187 8.2 Basic Techniques Using Pulse Sequences and Pulsed Field Gradients 188 8.2.1 The Effect of the Pulse on the Longitudinal Magnetization (Mz) 189 8.2.2 The Effect of the Pulse on the Transverse Magnetization Components (Mx′, My′) 190 8.2.3 Spin-Locking 193 8.2.4 The Effect of Pulsed Field Gradients on the Transverse Magnetization 195 8.3 The J-Modulated Spin-Echo Experiment 199 8.4 The Pulsed Gradient Spin-Echo Experiment 208 8.5 Signal Enhancement by Polarization Transfer 210 8.5.1 The SPI Experiment 210 8.5.2 The INEPT Experiment 213 8.5.3 The Reverse INEPT Experiment with Proton Detection 221 8.6 The DEPT Experiment 226 8.7 The Selective TOCSY Experiment 230 8.8 The One-Dimensional INADEQUATE Experiment 233 Exercises 237 8.9 Bibliography for Chapter 8 237 9 Two-Dimensional NMR Spectroscopy 239 9.1 Introduction 239 9.2 The Two-Dimensional NMR Experiment 240 9.2.1 Preparation, Evolution and Mixing, Data Acquisition 240 9.2.2 Graphical Representation 244 9.3 Two-Dimensional J-Resolved NMR Spectroscopy 245 9.3.1 Heteronuclear Two-Dimensional J-Resolved NMR Spectroscopy 245 9.3.2 Homonuclear Two-Dimensional J-Resolved NMR Spectroscopy 249 9.4 Two-Dimensional Correlated NMR Spectroscopy 254 9.4.1 Two-Dimensional Heteronuclear (C,H)-Correlated NMR Spectroscopy (HETCOR or C,H-COSY) 255 9.4.2 Two-Dimensional Homonuclear (H,H)-Correlated NMR Spectroscopy (H,H-COSY; Long-Range COSY) 263 9.4.3 Reverse Two-Dimensional Heteronuclear (H,C)-Correlated NMR Spectroscopy (HSQC; HMQC) 271 9.4.4 The Gradient-Selected (gs-)HMBC Experiment 276 9.4.5 The TOCSY Experiment 281 9.4.6 Two-Dimensional Exchange NMR Spectroscopy: The Experiments NOESY ROESY and EXSY 284 9.5 The Two-Dimensional INADEQUATE Experiment 289 9.6 Summary of Chapters 8 and 9 294 Exercises 295 9.7 Bibliography for Chapter 9 295 10 The Nuclear Overhauser Effect 297 10.1 Introduction 297 10.2 Theoretical Background 298 10.2.1 The Two-Spin System 298 10.2.2 Enhancement Factors 301 10.2.3 Multi-Spin Systems 302 10.2.4 From the One-Dimensional to the Two-Dimensional Experiments, NOESY and ROESY 303 10.3 Experimental Aspects 305 10.4 Applications 306 Exercises 311 10.5 Bibliography for Chapter 10 311 11 Dynamic NMR Spectroscopy (DNMR) 313 11.1 Introduction 313 11.2 Quantitative Calculations 317 11.2.1 Complete Line-shape Analysis 317 11.2.2 The Coalescence Temperature TC and the corresponding Rate constant kC 319 11.2.3 Activation Parameters 320 11.2.3.1 The Arrhenius Activation Energy EA 320 11.2.3.2 The Free Enthalpy of Activation ΔG 321 11.2.3.3 Estimating the Limits of Error 322 11.2.4 Rate Constants in Reactions with Intermediate Stages 323 11.2.5 Intermolecular Exchange Processes 324 11.3 Applications 325 11.3.1 Rotation about CC Single Bonds 325 11.3.1.1 C(sp3)-C(sp3) Bonds 326 11.3.1.2 C(sp2)-C(sp3) Bonds 326 11.3.1.3 C(sp2)-C(sp2) Bonds 327 11.3.2 Rotation about a Partial Double Bond 327 11.3.3 Inversion at Nitrogen and Phosphorus Atoms 329 11.3.4 Ring Inversion 330 11.3.5 Valence Tautomerism 333 11.3.6 Keto-Enol Tautomerism 334 11.3.7 Intermolecular Proton Exchange 335 11.3.8 Reactions and Equilibration Processes 337 Exercises 340 11.4 Bibliography for Chapter 11 340 12 Synthetic Polymers 343 12.1 Introduction 343 12.2 The Tacticity of Polymers 343 12.3 Polymerization of Dienes 347 12.4 Copolymers 348 12.5 Solid-State NMR Spectroscopy of Polymers 349 Exercises 352 12.6 Bibliography for Chapter 12 352 13 NMR Spectroscopy in Biochemistry and Medicine 355 13.1 Introduction 355 13.2 Elucidating Reaction Pathways in Biochemistry 355 13.2.1 Syntheses using Singly 13C-Labeled Precursors 356 13.2.1.1 Low Levels of 13C Enrichment 356 13.2.1.2 High Levels of 13C Enrichment 357 13.2.2 Syntheses using Doubly 13C-Labeled Precursors 358 13.3 Biopolymers 360 13.3.1 Peptides and Proteins 361 13.3.1.1 Sequence Analysis 362 13.3.1.2 The Three-Dimensional Structure of Proteins 363 13.3.2 Polynucleotides 365 13.3.3 Oligosaccharides and Polysaccharides 367 13.4 Saturation Transfer Difference NMR Spectroscopy (STD) 371 Exercises 372 13.5 Bibliography for Chapter 13 372 14 In vivo NMR Spectroscopy in Biochemistry and Medicine 375 14.1 Introduction 375 14.2 High-Resolution in vivo NMR Spectroscopy 376 14.2.1 The Problem and its Solution 376 14.2.2 31 PNMR Experiments 377 14.2.3 1H and 13C NMR Experiments 380 14.3 Magnetic Resonance Tomography 381 14.3.1 Basic Principles and Experimental Considerations 381 14.3.2 Applications 387 14.4 Magnetic Resonance Spectroscopy, 1H MRS 391 Exercises 393 14.5 Bibliography for Chapter 14 393 Solutions 395 Subject Index 407 Index of Compounds 411