Preface ...................................................... xiii
Symbols and fundamental constants ............................. xxi
1. What is spectroscopy? ....................................... 1
A semiclassical description of spectroscopy ................. 2
Damped harmonics ............................................ 5
Quantum oscillators ......................................... 6
The spectroscopic experiment ................................ 9
Ensembles and coherence ..................................... 9
Types of spectroscopy ...................................... 10
Practical considerations in spectroscopy ................... 12
Acquiring a spectrum ....................................... 14
Resolution: the problem of line width ...................... 17
Line shape ................................................. 20
Problems ................................................... 20
2. Elementary aspects of NMR: I. Introduction to spins,
ensemble behavior and coupling ............................. 23
Nuclear and electronic spin ................................ 23
The quantum picture of nuclear spin ........................ 24
The "spinning top" model of nuclear spin ................... 26
Spin-state populations in ensembles ........................ 28
Information available from NMR: 1. Nuclear shielding and
chemical shift ......................................... 29
Information available from NMR: 2. Scalar coupling ......... 34
Information available from NMR: 3. Dipolar coupling ........ 37
Information available from NMR: 4. Dynamics ................ 40
J-coupling time scale, decoupling experiments and
exchange decoupling .................................... 43
Interaction between nuclear spins and radio-frequency
(RF) EMR: 1. RF decoupling ............................. 44
Problems ................................................... 47
3. Elementary aspects of NMR: II. Fourier transform NMR ....... 49
Interaction between nuclear spins and RF: 2. A single
spin in the rotating frame of reference ................ 49
Interaction between nuclear spins and RF: 3. An ensemble
of spins in the rotating frame of reference ............ 54
Detection of an NMR signal ................................. 55
Time-domain detection in the NMR experiment: the free
induction decay and quadrature detection ............... 58
Digitization of the free induction decay ................... 61
Fourier transformation: time-domain FID to
frequency-domain spectrum .............................. 63
Discrete Fourier transformation ............................ 67
Spectral phasing ........................................... 73
RF pulses and pulse phase .................................. 74
Pulse power and off-resonance effects from RF pulses ....... 76
Phase cycling: improved quadrature detection using
CYCLOPS ................................................ 77
Factors affecting spectral quality and appearance:
shimming, window functions and apodization ............. 80
After the fact: window functions and zero filling .......... 81
Linear prediction .......................................... 85
Problems ................................................... 89
References ................................................. 93
4. Nuclear spin relaxation and the nuclear Overhauser
effect ..................................................... 95
Longitudinal (T1) relaxation and the sensitivity of the
NMR experiment ......................................... 95
Transverse (T2) relaxation and the spin-echo experiment .... 98
Chemical shift and J-coupling evolution during the spin
echo .................................................. 104
Mechanisms of nuclear spin relaxation in liquids and the
spectral density function ............................. 104
Dipolar relaxation and the nuclear Overhauser effect ...... 108
NOE measurements, indirect NOEs and saturation transfer ... 111
Heteronuclear NOE and the Solomon equation ................ 114
Other contributions to T1 relaxation: chemical shift
anisotropy, spin-rotation and paramagnetic effects .... 117
Quadrupolar relaxation .................................... 119
Selective and nonselective T1 measurement and
multi-exponential decay of coherence .................. 119
Problems .................................................. 120
References ................................................ 122
5. Classical and quantum descriptions of NMR experiments in
liquids ................................................... 123
The classical approach: the Bldch equations of motion
for macroscopic magnetization ......................... 123
Classical description of a pulsed NMR experiment .......... 126
A quantum mechanical description of NMR of a single spin
in an isotropic liquid ................................ 128
A quantum mechanical description of NMR of coupled spins
in an isotropic liquid ................................ 129
The time-dependent nuclear spin Hamiltonian operator and
solutions to the time-dependent Schrödinger
equation .............................................. 143
Problems .................................................. 144
References ................................................ 146
6. Density operator and product operator descriptions of
NMR experiments in liquids ................................ 147
An ensemble of identical spins at equilibrium:
an introduction to the density matrix formalism ....... 147
Expansion of the density matrix for an uncoupled spin in
terms of Cartesian angular momentum operators ......... 150
Weakly coupled ensembles and the weak-coupling
approximation ......................................... 152
Single-element operators for a two-spin system ............ 154
Interconversion between the single-element and the
Cartesian operator bases .............................. 155
Evolution of Cartesian operators under the influence of
pulses, chemical shift and J-coupling ................. 157
Evolution of operators with weak J-coupling ............... 158
Analysis of a simple NMR spectrum using product
operators ............................................. 161
Problems .................................................. 163
References ................................................ 165
7. Multidimensional NMR: homonuclear experiments and
coherence selection ....................................... 167
A simple two-dimensional NMR experiment ................... 168
Coherence transfer in multidimensional NMR ................ 171
The COSY experiment ....................................... 172
Quadrature detection in multidimensional NMR .............. 175
Axial peaks ............................................... 178
Phase cycling and coherence order selection:
the DQF-COSY experiment ............................... 180
Other multiple-quantum filters in COSY .................... 186
Multiple-quantum spectroscopy ............................. 186
Effect of π pulses on coherence ........................... 189
Pulsed-field gradients for coherence selection ............ 190
The gradient COSY experiment .............................. 193
"Zero-quantum filtered COSY": NOESY and incoherent
transfer .............................................. 197
Rotating frame NOEs: CAMELSPIN and ROESY .................. 200
Spin-locking experiments for coherence transfer: TOCSY
and composite pulse decoupling ........................ 204
Problems .................................................. 209
References ................................................ 213
8. Heteronuclear correlations in NMR ......................... 215
Heteronuclear polarization transfer and the INEPT
experiment ............................................ 216
Refocused INEPT ........................................... 221
Two-dimensional polarization transfer: HETCOR ............. 223
Sensitive nucleus (inverse) detection of an insensitive
nucleus: the double INEPT or HSQC experiment .......... 223
Multiple-quantum approaches to heteronuclear correlation:
DEPT and HMQC ......................................... 228
Gradient coherence selection in heteronuclear
correlation NMR ....................................... 230
Phase-sensitive gradient coherence selection experiments
for heteronuclear correlations ........................ 233
Sensitivity enhancement in gradient coherence selection
experiments ........................................... 235
Problems .................................................. 238
References ................................................ 240
9. Building blocks for multidimensional NMR and special
considerations for biological applications of NMR ......... 241
Polarization transfer ..................................... 248
Solvent suppression ....................................... 248
Frequency-labeling periods and constant time NMR
experiments ........................................... 251
Shaped and selective pulses ............................... 256
Composite pulse decoupling and spin-locking ............... 258
Dealing with very large biomolecules in solution:
deuteration and direct 13C detection .................. 262
Interference patterns in heteronuclear relaxation:
TROSY ................................................. 263
Problems .................................................. 270
References ................................................ 271
10. NMR under anisotropic conditions: NMR in the solid state
and ordered fluids ........................................ 273
Anisotropy in NMR: chemical shielding and dipolar
coupling .............................................. 273
Resolving the solid-state NMR spectrum: magic angle
spinning (MAS) and high-power 1H decoupling ........... 278
Cross-polarization for signal enhancement of dilute
spins and spin-spin correlations ...................... 280
Selective reintroduction of dipolar couplings between
dilute spins: rotational resonance, RFDR, and REDOR ... 283
Heteronuclear two-dimensional techniques in solid-state
NMR ................................................... 287
Solid-state NMR using oriented samples: PISEMA ............ 289
Bringing a little order to solution NMR: residual
dipolar couplings and CSA in ordered fluids ........... 293
Analysis of residual dipolar couplings .................... 298
Problems .................................................. 299
References ................................................ 301
11. Relaxation revisited: dynamic processes and
paramagnetism ............................................. 303
Time scales of molecular motion, dynamic processes and
relaxation ............................................ 303
The spectral density revisited ............................ 306
Experimental measurement of heteronuclear relaxation
parameters in proteins ................................ 310
Model-free analysis of spin relaxation .................... 311
Chemical exchange and motion on slow and intermediate
time scales (10-6s-10-1s) .............................. 312
Measurement of Rex ........................................ 314
Quadrupolar relaxation .................................... 316
Hyperfine interactions and paramagnetic shifts of
nuclear spins ......................................... 319
Paramagnetic relaxation of nuclear spins .................. 324
Relaxation and the density matrix ......................... 325
Problems .................................................. 326
References ................................................ 327
12. Diffusion, imaging, and flow .............................. 329
Magnetic field inhomogeneity, T2(macro) and diffusion
measurement by NMR .................................... 329
Basic imaging concepts: phase and frequency encoding of
position in a macroscopic sample ...................... 331
Spatially selective pulses ................................ 333
Spatial equivalents of NMR parameters ..................... 334
Basic two-dimensional imaging sequences ................... 335
k-Space ................................................... 336
Contrast and contrast agents, relaxation, and flow ........ 337
Rapid-scan MRI: echo-planar imaging and one-shot
methods ............................................... 341
Problems .................................................. 342
References ................................................ 343
Appendix A. Time-dependent perturbations ...................... 345
The time-dependent Schrödinger equation and
superposition states .................................. 345
Hilbert space, eigenvectors, and superposition of
states ................................................ 346
Perturbation theory: time-dependent perturbations of the
Hamiltonian ........................................... 347
Semiclassical interactions between EMR and quantum
oscillators using perturbation theory ................. 350
Appendix B. Density matrix formalism and the relaxation
supermatrix ............................................... 353
A density matrix description of the 1H, 15N HMQC
experiment ............................................ 353
RF pulses ................................................. 355
Time evolution of the density matrix with chemical shift
and coupling .......................................... 358
Semiclassical relaxation theory and the Redfield
relaxation matrix ..................................... 361
Index ......................................................... 365
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