Introduction to Solid-State NMR Spectroscopy

Preface, xii Acknowledgements, xv 1 The Basics of NMR, 1 1.1 The vector model of pulsed NMR, 1 1.1.1 Nuclei in a static, uniform magnetic field, 2 1.1.2 The effect of rf pulses, 3 1.2 The quantum mechanical picture: hamiltonians and the Schrödinger equation, 5 Box 1.1 Quantum mechanics and NMR, 6 Wavefunctions, 6 Operators, physical observables and expectation values, 7 Schrödinger’s equation, eigenfunctions and eigenvalues, 7 Spin operators and spin states, 8 Dirac’s bra-ket notation, 11 Matrices, 11 1.2.1 Nuclei in a static, uniform field, 12 1.2.2 The effect of rf pulses, 15 Box 1.2 Exponential operators, rotation operators and rotations, 19 Rotation of vectors, wavefunctions and operators (active rotations), 20 Rotation of axis frames, 23 Representation of rf fields, 25 Euler angles, 25 Rotations with Euler angles, 26 Rotation of Cartesian axis frames, 27 1.3 The density matrix representation and coherences, 29 1.3.1 Coherences and populations, 30 1.3.2 The density operator at thermal equilibrium, 33 1.3.3 Time evolution of the density matrix, 34 1.4 Nuclear spin interactions, 37 1.4.1 Interaction tensors, 41 1.5 General features of Fourier transform NMR experiments, 43 1.5.1 Multidimensional NMR, 43 1.5.2 Phase cycling, 46 1.5.3 Quadrature detection, 48 Box 1.3 The NMR spectrometer, 53 Generating rf pulses, 53 Detecting the NMR signal, 56 Notes, 58 References, 59 2 Essential Techniques for Solid-State NMR, 60 2.1 Introduction, 60 2.2 Magic-angle spinning (MAS), 61 2.2.1 Spinning sidebands, 62 2.2.2 Rotor or rotational echoes, 67 2.2.3 Removing spinning sidebands, 67 2.2.4 Setting the magic-angle and spinning rate, 72 2.2.5 Magic-angle spinning for homonuclear dipolar couplings, 75 2.3 Heteronuclear decoupling, 77 2.3.1 High-power decoupling, 78 2.3.2 Other heteronuclear decoupling sequences, 81 2.4 Homonuclear decoupling, 83 2.4.1 Implementing homonuclear decoupling sequences, 83 Box 2.1 Average hamiltonian theory and the toggling frame, 86 Average hamiltonian theory, 86 The toggling frame and the WAHUHA pulse sequence, 89 2.5 Cross-polarization, 96 2.5.1 Theory, 97 2.5.2 Setting up the cross-polarization experiment, 101 Box 2.2 Cross-polarization and magic-angle spinning, 106 2.6 Echo pulse sequences, 110 Notes, 113 References, 114 3 Shielding and Chemical Shift: Theory and Uses, 116 3.1 Theory, 116 3.1.1 Introduction, 116 3.1.2 The chemical shielding hamiltonian, 117 3.1.3 Experimental manifestations of the shielding tensor, 120 3.1.4 Definition of the chemical shift, 123 3.2 The relationship between the shielding tensor and electronic structure, 125 3.3 Measuring chemical shift anisotropies, 131 3.3.1 Magic-angle spinning with recoupling pulse sequences, 132 3.3.2 Variable-angle spinning experiments, 135 3.3.3 Magic-angle turning, 138 3.3.4 Two-dimensional separation of spinning sideband patterns, 141 3.4 Measuring the orientation of chemical shielding tensors in the molecular frame for structure determination, 145 Notes, 149 References, 149 4 Dipolar Coupling: Theory and Uses, 151 4.1 Theory, 151 4.1.1 Homonuclear dipolar coupling, 154 Box 4.1 Basis sets for multispin systems, 156 4.1.2 The effect of homonuclear dipolar coupling on a spin system, 157 4.1.3 Heteronuclear dipolar coupling, 160 4.1.4 The effect of heteronuclear dipolar coupling on the spin system, 162 4.1.5 Heteronuclear spin dipolar coupled to a homonuclear network of spins, 163 4.1.6 The spherical tensor form of the dipolar hamiltonian, 164 Box 4.2 The dipolar hamiltonian in terms of spherical tensor operators, 164 Spherical tensor operators, 165 Interaction tensors, 167 The homonuclear dipolar hamiltonian under static and MAS conditions, 167 4.2 Introduction to the uses of dipolar coupling, 172 4.3 Techniques for measuring homonuclear dipolar couplings, 175 4.3.1 Recoupling pulse sequences, 175 Box 4.3 Analysis of the DRAMA pulse sequence, 180 Simulating powder patterns from the DRAMA experiment, 184 4.3.2 Double-quantum filtered experiments, 185 Box 4.4 Excitation of double-quantum coherence under magic-angle spinning, 189 The form of the reconversion pulse sequence: the need for timereversal symmetry, 191 Analysis of the double-quantum filtered data, 195 Box 4.5 Analysis of the C7 pulse sequence for exciting double-quantum coherence in dipolar-coupled spin pairs, 196 4.3.3 Rotational resonance, 199 Box 4.6 Theory of rotational resonance, 202 Effect of H ˆ ∆ term on the density operator, 203 The hamiltonian in the new rotated frame, 204 The average hamiltonian, 205 4.4 Techniques for measuring heteronuclear dipolar couplings, 207 4.4.1 Spin-echo double resonance (SEDOR), 207 4.4.2 Rotational-echo double resonance (REDOR), 208 Box 4.7 Analysis of the REDOR experiment, 210 4.5 Techniques for dipolar-coupled quadrupolar–spin-1–2 pairs, 215 4.5.1 Transfer of population in double resonance (TRAPDOR), 216 4.5.2 Rotational-echo adiabatic-passage double-resonance (REAPDOR), 219 4.6 Techniques for measuring dipolar couplings between quadrupolar nuclei, 220 4.7 Correlation experiments, 221 4.7.1 Homonuclear correlation experiments for spin-1–2 systems, 221 4.7.2 Homonuclear correlation experiments for quadrupolar spin systems, 224 4.7.3 Heteronuclear correlation experiments for spin-1–2, 226 4.8 Spin-counting experiments, 227 4.8.1 The formation of multiple-quantum coherences, 228 4.8.2 Implementation of spin-counting experiments, 231 Notes, 232 References, 233 5 Quadrupole Coupling: Theory and Uses, 235 5.1 Introduction, 235 5.2 Theory, 237 5.2.1 The quadrupole hamiltonian, 237 Box 5.1 The quadrupole hamiltonian in terms of spherical tensor operators: the effect of the rotating frame and magic-angle spinning, 242 The quadrupole hamiltonian in terms of spherical tensor operators, 242 The effect of the rotating frame: first- and second-order average hamiltonians for the quadrupole interaction, 243 The energy levels under quadrupole coupling, 248 The effect of magic-angle spinning, 248 5.2.2 The effect of rf pulses, 249 5.2.3 The effects of quadrupolar nuclei on the spectra of spin-1–2 nuclei, 252 5.3 High-resolution NMR experiments for half-integer quadrupolar nuclei, 255 5.3.1 Magic-angle spinning (MAS), 256 5.3.2 Double rotation (DOR), 259 5.3.3 Dynamic-angle spinning (DAS), 260 5.3.4 Multiple-quantum magic-angle spinning (MQMAS), 263 5.3.5 Satellite transition magic-angle spinning (STMAS), 268 5.3.6 Recording two-dimensional datasets for DAS, MQMAS and STMAS, 275 5.4 Other techniques for half-integer quadrupole nuclei, 280 5.4.1 Quadrupole nutation, 282 5.4.2 Cross-polarization, 285 Notes, 290 References, 291 6 NMR Techniques for Studying Molecular Motion in Solids, 293 6.1 Introduction, 293 6.2 Powder lineshape analysis, 296 6.2.1 Simulating powder pattern lineshapes, 297 6.2.2 Resolving powder patterns, 305 6.2.3 Using homonuclear dipolar-coupling lineshapes – the WISE experiment, 311 6.3 Relaxation time studies, 313 6.4 Exchange experiments, 316 6.4.1 Achieving pure absorption lineshapes in exchange spectra, 318 6.4.2 Interpreting two-dimensional exchange spectra, 320 6.5 2H NMR, 322 6.5.1 Measuring 2H NMR spectra, 323 6.5.2 2H lineshape simulations, 328 6.5.3 Relaxation time studies, 329 6.5.4 2H exchange experiments, 330 6.5.5 Resolving 2H powder patterns, 332 Notes, 334 References, 335 Appendix A NMR Properties of Commonly Observed Nuclei, 336 Appendix B The General Form of a Spin Interaction Hamiltonian in Terms of Spherical Tensors and Spherical Tensor Operators, 337 References, 343 Index, 344