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 anisotropics .................... 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 time-reversal 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 НΔ 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-y 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-y 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 В The General Form of a Spin Interaction
Hamiltonian in Terms of Spherical Tensors and
Spherical Tensor Operators ........................ 337
References .................................................... 343
Index ......................................................... 344
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