Spin Dynamics: Basics of Nuclear Magnetic Resonance, Second Edition is a comprehensive and modern introduction which focuses on those essential principles and concepts needed for a thorough understanding of the subject, rather than the practical aspects. The quantum theory of nuclear magnets is presented within a strong physical framework, supported by figures.  The book assumes only a basic knowledge of complex numbers and matrices, and provides the reader with numerous worked examples and exercises to encourage understanding. With the explicit aim of carefully developing the subject from the beginning, the text starts with coverage of quarks and nucleons and progresses through to a detailed explanation of several important NMR experiments, including NMR imaging, COSY, NOESY and TROSY.  Completely revised and updated, the Second Edition features new material on the properties and distributions of isotopes, chemical shift anisotropy and quadrupolar interactions, Pake patterns, spin echoes, slice selection in NMR imaging, and a complete new chapter on the NMR spectroscopy of quadrupolar nuclei. New appendices have been included on Euler angles, and coherence selection by field gradients. As in the first edition, all material is heavily supported by graphics, much of which is new to this edition.  Written for undergraduates and postgraduate students taking a first course in NMR spectroscopy and for those needing an up-to-date account of the subject, this multi-disciplinary book will appeal to chemical, physical, material, life, medical, earth and environmental scientists. The detailed physical insights will also make the book of interest for experienced spectroscopists and NMR researchers.  • An accessible and carefully written introduction, designed to help students to fully understand this complex and dynamic subject • Takes a multi-disciplinary approach, focusing on basic principles and concepts rather than the more practical aspects • Presents a strong pedagogical approach throughout, with emphasis placed on individual spins to aid understanding • Includes numerous worked examples, problems, further reading and additional notes Praise from the reviews of the First Edition: "This is an excellent book... that many teachers of NMR spectroscopy will cherish... It deserves to be a ‘classic’ among NMR spectroscopy texts." NMR IN BIOMEDICINE "I strongly recommend this book to everyone…it is probably the best modern comprehensive description of the subject." ANGEWANDTE CHEMIE, INTERNATIONAL EDITIONTable of Contents: Preface xxi Preface to the First Edition xxiii Introduction 1 Part 1 Nuclear Magnetism 3 1 Matter 5 1.1 Atoms and Nuclei 5 1.2 Spin 5 1.3 Nuclei 9 1.4 Nuclear Spin 12 1.5 Atomic and Molecular Structure 15 2 Magnetism 23 2.1 The Electromagnetic Field 23 2.2 Macroscopic Magnetism 23 2.3 Microscopic Magnetism 25 2.4 Spin Precession 26 2.5 Larmor Frequency 29 2.6 Spin–Lattice Relaxation: Nuclear Paramagnetism 30 2.7 Transverse Magnetization and Transverse Relaxation 33 2.8 NMR Signal 36 2.9 Electronic Magnetism 36 3 NMR Spectroscopy 39 3.1 A Simple Pulse Sequence 39 3.2 A Simple Spectrum 39 3.3 Isotopomeric Spectra 42 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 48 3.7 Chemical Shifts 50 3.8 J-Coupling Multiplets 56 3.9 Heteronuclear Decoupling 59 Part 2 The NMR Experiment 63 4 The NMR Spectrometer 65 4.1 The Magnet 65 4.2 The Transmitter Section 66 4.3 The Duplexer 69 4.4 The Probe 70 4.5 The Receiver Section 72 4.6 Overview of the Radio-Frequency Section 76 4.7 Pulsed Field Gradients 77 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 5.9 Two-Dimensional Spectroscopy 105 5.10 Three-Dimensional Spectroscopy 114 Part 3 Quantum Mechanics 119 6 Mathematical Techniques 121 6.1 Functions 121 6.2 Operators 125 6.3 Eigenfunctions, Eigenvalues and Eigenvectors 131 6.4 Diagonalization 134 6.5 Exponential Operators 135 6.6 Cyclic Commutation 138 7 Review of Quantum Mechanics 143 7.1 Spinless Quantum Mechanics 143 7.2 Energy Levels 145 7.3 Natural Units 146 7.4 Superposition States and Stationary States 147 7.5 Conservation Laws 148 7.6 Angular Momentum 148 7.7 Spin 157 7.8 Spin-1/ 2 160 7.9 Higher Spin 162 Part 4 Nuclear Spin Interactions 169 8 Nuclear Spin Hamiltonian 171 8.1 Spin Hamiltonian Hypothesis 171 8.2 Electromagnetic Interactions 172 8.3 External and Internal Spin Interactions 177 8.4 External Magnetic Fields 177 8.5 Internal Spin Hamiltonian 182 8.6 Motional Averaging 186 9 Internal Spin Interactions 195 9.1 Chemical Shift 195 9.2 Electric Quadrupole Coupling 206 9.3 Direct Dipole–Dipole Coupling 211 9.4 J-Coupling 217 9.5 Spin–Rotation Interaction 223 9.6 Summary of the Spin Hamiltonian Terms 224 Part 5 Uncoupled Spins 229 10 Single Spin-1/2 231 10.1 Zeeman Eigenstates 231 10.2 Measurement of Angular Momentum: Quantum Indeterminacy 232 10.3 Energy Levels 233 10.4 Superposition States 234 10.5 Spin Precession 238 10.6 Rotating Frame 241 10.7 Precession in the Rotating Frame 245 10.8 Radio-frequency Pulse 247 11 Ensemble of Spins-1/2 259 11.1 Spin Density Operator 259 11.2 Populations and Coherences 261 11.3 Thermal Equilibrium 266 11.4 Rotating-Frame Density Operator 268 11.5 Magnetization Vector 269 11.6 Strong Radio-Frequency Pulse 270 11.7 Free Precession Without Relaxation 276 11.8 Operator Transformations 279 11.9 Free Evolution with Relaxation 281 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 T 1 295 12.2 Spin Echoes: Measurement of T 2 298 12.3 Spin Locking: Measurement of T 1? 305 12.4 Gradient Echoes 306 12.5 Slice Selection 307 12.6 NMR Imaging 309 13 Quadrupolar Nuclei 319 13.1 Spin I = 1 319 13.2 Spin I = 3/2 334 13.3 Spin I = 5/2 345 13.4 Spins I = 7/2 349 13.5 Spins I = 9/2 350 Part 6 Coupled Spins 353 14 Spin-1/2 Pairs 355 14.1 Coupling Regimes 355 14.2 Zeeman Product States and Superposition States 356 14.3 Spin-Pair Hamiltonian 357 14.4 Pairs of Magnetically Equivalent Spins 359 14.5 Weakly Coupled Spin Pairs 363 15 Homonuclear AX System 369 15.1 Eigenstates and Energy Levels 369 15.2 Density Operator 370 15.3 Rotating Frame 375 15.4 Free Evolution 376 15.5 Spectrum of the AX System: Spin–Spin Splitting 378 15.6 Product Operators 381 15.7 Thermal Equilibrium 389 15.8 Radio-Frequency Pulses 391 15.9 Free Evolution of the Product Operators 397 15.10 Spin Echo Sandwich 405 16 Experiments on AX Systems 409 16.1 Cosy 409 16.2 Inadequate 418 16.3 Inept 436 16.4 Residual Dipolar Couplings 443 17 Many-Spin Systems 453 17.1 Molecular Spin System 453 17.2 Spin Ensemble 454 17.3 Motionally Suppressed J-Couplings 454 17.4 Chemical Equivalence 455 17.5 Magnetic Equivalence 458 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 468 18.3 Superposition States 469 18.4 Spin Density Operator 470 18.5 Populations and Coherences 471 18.6 NMR Spectra 475 18.7 Many-Spin Product Operators 477 18.8 Thermal Equilibrium 481 18.9 Radio-Frequency Pulses 481 18.10 Free Precession 482 18.11 Spin Echo Sandwiches 485 18.12 INEPT in an I2 S System 488 18.13 COSY in Multiple-Spin Systems 491 18.14 Tocsy 497 Part 7 Motion and Relaxation 507 19 Motion 509 19.1 Motional Processes 509 19.2 Motional Time-Scales 513 19.3 Motional Effects 514 19.4 Motional Averaging 515 19.5 Motional Lineshapes and Two-Site Exchange 516 19.6 Sample Spinning 527 19.7 Longitudinal Magnetization Exchange 529 19.8 Diffusion 539 20 Relaxation 543 20.1 Types of Relaxation 543 20.2 Relaxation Mechanisms 543 20.3 Random Field Relaxation 545 20.4 Dipole–Dipole Relaxation 556 20.5 Steady-State Nuclear Overhauser Effect 566 20.6 Noesy 570 20.7 Roesy 577 20.8 Cross-Correlated Relaxation 584 Part 8 Appendices 597 Appendix A: Supplementary Material 599 A. 1 Euler Angles and Frame Transformations 599 A. 1 Definition of the Euler angles 599 A. 2 Rotations and Cyclic Commutation 604 A. 3 Rotation Sandwiches 605 A. 4 Spin-1/2 Rotation Operators 606 A. 5 Quadrature Detection and Spin Coherences 608 A. 6 Secular Approximation 611 A. 7 Quadrupolar Interaction 614 A. 8 Strong Coupling 615 A. 9 J-Couplings and Magnetic Equivalence 621 A. 10 Spin Echo Sandwiches 623 A. 11 Phase Cycling 629 A.12 Coherence Selection by Pulsed Field Gradients 649 A. 13 Bloch Equations 653 A. 14 Chemical Exchange 654 A. 15 Solomon Equations 660 A. 16 Cross-Relaxation Dynamics 662 Appendix B: Symbols and Abbreviations 665 Answers to the Exercises 681 Index 693