Introduction to Solid-State NMR Spectroscopy

Dr Melinda Duer is a senior lecturer in the Department of Chemistry at the University of Cambridge, Cambridge, UK

• Preface, xiiAcknowledgements, xv1 The Basics of NMR, 11.1 The vector model of pulsed NMR, 11.1.1 Nuclei in a static, uniform magnetic field, 21.1.2 The effect of rf pulses, 31.2 The quantum mechanical picture: hamiltonians and the Schrödinger equation, 5Box 1.1 Quantum mechanics and NMR, 6Wavefunctions, 6Operators, physical observables and expectation values, 7Schrödinger’s equation, eigenfunctions and eigenvalues, 7Spin operators and spin states, 8Dirac’s bra-ket notation, 11Matrices, 111.2.1 Nuclei in a static, uniform field, 121.2.2 The effect of rf pulses, 15Box 1.2 Exponential operators, rotation operators and rotations, 19Rotation of vectors, wavefunctions and operators (active rotations), 20Rotation of axis frames, 23Representation of rf fields, 25Euler angles, 25Rotations with Euler angles, 26Rotation of Cartesian axis frames, 271.3 The density matrix representation and coherences, 291.3.1 Coherences and populations, 301.3.2 The density operator at thermal equilibrium, 331.3.3 Time evolution of the density matrix, 341.4 Nuclear spin interactions, 371.4.1 Interaction tensors, 411.5 General features of Fourier transform NMR experiments, 431.5.1 Multidimensional NMR, 431.5.2 Phase cycling, 461.5.3 Quadrature detection, 48Box 1.3 The NMR spectrometer, 53Generating rf pulses, 53Detecting the NMR signal, 56Notes, 58References, 592 Essential Techniques for Solid-State NMR, 602.1 Introduction, 602.2 Magic-angle spinning (MAS), 612.2.1 Spinning sidebands, 622.2.2 Rotor or rotational echoes, 672.2.3 Removing spinning sidebands, 672.2.4 Setting the magic-angle and spinning rate, 722.2.5 Magic-angle spinning for homonuclear dipolar couplings, 752.3 Heteronuclear decoupling, 772.3.1 High-power decoupling, 782.3.2 Other heteronuclear decoupling sequences, 812.4 Homonuclear decoupling, 832.4.1 Implementing homonuclear decoupling sequences, 83Box 2.1 Average hamiltonian theory and the toggling frame, 86Average hamiltonian theory, 86The toggling frame and the WAHUHA pulse sequence, 892.5 Cross-polarization, 962.5.1 Theory, 972.5.2 Setting up the cross-polarization experiment, 101Box 2.2 Cross-polarization and magic-angle spinning, 1062.6 Echo pulse sequences, 110Notes, 113References, 1143 Shielding and Chemical Shift: Theory and Uses, 1163.1 Theory, 1163.1.1 Introduction, 1163.1.2 The chemical shielding hamiltonian, 1173.1.3 Experimental manifestations of the shielding tensor, 1203.1.4 Definition of the chemical shift, 1233.2 The relationship between the shielding tensor and electronic structure, 1253.3 Measuring chemical shift anisotropies, 1313.3.1 Magic-angle spinning with recoupling pulse sequences, 1323.3.2 Variable-angle spinning experiments, 1353.3.3 Magic-angle turning, 1383.3.4 Two-dimensional separation of spinning sideband patterns, 1413.4 Measuring the orientation of chemical shielding tensors in the molecular frame for structure determination, 145Notes, 149References, 1494 Dipolar Coupling: Theory and Uses, 1514.1 Theory, 1514.1.1 Homonuclear dipolar coupling, 154Box 4.1 Basis sets for multispin systems, 1564.1.2 The effect of homonuclear dipolar coupling on a spin system, 1574.1.3 Heteronuclear dipolar coupling, 1604.1.4 The effect of heteronuclear dipolar coupling on the spin system, 1624.1.5 Heteronuclear spin dipolar coupled to a homonuclear network of spins, 1634.1.6 The spherical tensor form of the dipolar hamiltonian, 164Box 4.2 The dipolar hamiltonian in terms of spherical tensor operators, 164Spherical tensor operators, 165Interaction tensors, 167The homonuclear dipolar hamiltonian under static and MAS conditions, 1674.2 Introduction to the uses of dipolar coupling, 1724.3 Techniques for measuring homonuclear dipolar couplings, 1754.3.1 Recoupling pulse sequences, 175Box 4.3 Analysis of the DRAMA pulse sequence, 180Simulating powder patterns from the DRAMA experiment, 1844.3.2 Double-quantum filtered experiments, 185Box 4.4 Excitation of double-quantum coherence under magic-angle spinning, 189The form of the reconversion pulse sequence: the need for timereversal symmetry, 191Analysis of the double-quantum filtered data, 195Box 4.5 Analysis of the C7 pulse sequence for exciting double-quantum coherence in dipolar-coupled spin pairs, 1964.3.3 Rotational resonance, 199Box 4.6 Theory of rotational resonance, 202Effect of H ˆ ∆ term on the density operator, 203The hamiltonian in the new rotated frame, 204The average hamiltonian, 2054.4 Techniques for measuring heteronuclear dipolar couplings, 2074.4.1 Spin-echo double resonance (SEDOR), 2074.4.2 Rotational-echo double resonance (REDOR), 208Box 4.7 Analysis of the REDOR experiment, 2104.5 Techniques for dipolar-coupled quadrupolar–spin-1–2 pairs, 2154.5.1 Transfer of population in double resonance (TRAPDOR), 2164.5.2 Rotational-echo adiabatic-passage double-resonance (REAPDOR), 2194.6 Techniques for measuring dipolar couplings between quadrupolar nuclei, 2204.7 Correlation experiments, 2214.7.1 Homonuclear correlation experiments for spin-1–2 systems, 2214.7.2 Homonuclear correlation experiments for quadrupolar spin systems, 2244.7.3 Heteronuclear correlation experiments for spin-1–2, 2264.8 Spin-counting experiments, 2274.8.1 The formation of multiple-quantum coherences, 2284.8.2 Implementation of spin-counting experiments, 231Notes, 232References, 2335 Quadrupole Coupling: Theory and Uses, 2355.1 Introduction, 2355.2 Theory, 2375.2.1 The quadrupole hamiltonian, 237Box 5.1 The quadrupole hamiltonian in terms of spherical tensor operators: the effect of the rotating frame and magic-angle spinning, 242The quadrupole hamiltonian in terms of spherical tensor operators, 242The effect of the rotating frame: first- and second-order average hamiltonians for the quadrupole interaction, 243The energy levels under quadrupole coupling, 248The effect of magic-angle spinning, 2485.2.2 The effect of rf pulses, 2495.2.3 The effects of quadrupolar nuclei on the spectra of spin-1–2 nuclei, 2525.3 High-resolution NMR experiments for half-integer quadrupolar nuclei, 2555.3.1 Magic-angle spinning (MAS), 2565.3.2 Double rotation (DOR), 2595.3.3 Dynamic-angle spinning (DAS), 2605.3.4 Multiple-quantum magic-angle spinning (MQMAS), 2635.3.5 Satellite transition magic-angle spinning (STMAS), 2685.3.6 Recording two-dimensional datasets for DAS, MQMAS and STMAS, 2755.4 Other techniques for half-integer quadrupole nuclei, 2805.4.1 Quadrupole nutation, 2825.4.2 Cross-polarization, 285Notes, 290References, 2916 NMR Techniques for Studying Molecular Motion in Solids, 2936.1 Introduction, 2936.2 Powder lineshape analysis, 2966.2.1 Simulating powder pattern lineshapes, 2976.2.2 Resolving powder patterns, 3056.2.3 Using homonuclear dipolar-coupling lineshapes – the WISE experiment, 3116.3 Relaxation time studies, 3136.4 Exchange experiments, 3166.4.1 Achieving pure absorption lineshapes in exchange spectra, 3186.4.2 Interpreting two-dimensional exchange spectra, 3206.5 2H NMR, 3226.5.1 Measuring 2H NMR spectra, 3236.5.2 2H lineshape simulations, 3286.5.3 Relaxation time studies, 3296.5.4 2H exchange experiments, 3306.5.5 Resolving 2H powder patterns, 332Notes, 334References, 335Appendix A NMR Properties of Commonly Observed Nuclei, 336Appendix B The General Form of a Spin Interaction Hamiltonian in Terms of Spherical Tensors and Spherical Tensor Operators, 337References, 343Index, 344

"Overall this is an excellent book and one that I personally will find very useful. I will recommend it to my postgraduate students and prostdoctoral research fellows for its detailed and careful explanations of a wide range of experimental methods in solid-state NMR spectroscopy.""The book is clear and straightforward...the level of detail is very impressive and the author does not shirk her duty to explain some of the most notoriously difficult concepts in this area."Chemistry World, Vol 2, No 1, January 2005 "The theoretical approaches, the description of methods and the demonstration of the applications are clearly given in this book, which can be recommended to students and researchers in physical, analytical and organic chemistry and also biology who need access to solid-state NMR for the characterization of structures and dynamics of chemical or biological compounds.”Magnetic Resonance in Chemistry, 2004, vol 42