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NMR for Physical and
Biological Scientists
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NMR for Physical and
Biological Scientists
Thomas C. Pochapsky and
Susan Sondej Pochapsky
Brandeis University
Waltham, Massachusetts
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
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Vice President Denise Schanck
Senior Editor Robert L. Rogers
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© 2007 by Garland Science, a member of the Taylor & Francis Group, LLC
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ISBN 0 8153 4103 2
Library of Congress Cataloging-in-Publication Data
Pochapsky, Thomas C.
NMR for physical and biological scientists/Thomas C. Pochapsky and Susan Sondej Pochapsky.
p. ; cm.
Includes bibliographical references and index.
ISBN 0-8153-4103-2 (alk. paper)
1. Nuclear magnetic resonance spectroscopy. 2. Nuclear magnetic resonance. I.
Pochapsky, Susan Sondej. II. Title.
[DNLM: 1. Magnetic Resonance Spectroscopy. QU 25 P739n 2006]
QP 519.9.N83P63 2006
543′.66–dc22
2006019638
Published in 2007 by Garland Science, member of the Taylor & Francis Group, LLC,
270 Madison Avenue, New York, NY 10016, USA and
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN, UK.
Printed in the United States of America on acid-free paper.
10 9 8 7 6 5 4 3 2 1
Taylor & Francis Group, an informa buisness Visit our web site at http//www.garlandscience.com
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To our children, Elizabeth and Theodore
and our parents, Eugene and Mary Pochapsky and Bob and Mary Ann Sondej
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CONTENTS
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, 23
ensemble behavior and coupling
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 29
and chemical shift
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 43
decoupling
Interaction between nuclear spins and radio-frequency (RF) 44
EMR: 1. RF decoupling
Problems 47
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viii Contents
3. Elementary aspects of NMR: II. Fourier transform NMR 49
Interaction between nuclear spins and RF: 2. 49
A single spin in the rotating frame of reference
Interaction between nuclear spins and RF: 3. 54
An ensemble of spins in the rotating frame of reference
Detection of an NMR signal 55
Time-domain detection in the NMR experiment: the 58
free induction decay and quadrature detection
Digitization of the free induction decay 61
Fourier transformation: time-domain FID to frequency-domain 63
spectrum
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, 80
window functions and apodization
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 (T ) relaxation and the sensitivity of the 95
1
NMR experiment
Transverse (T ) relaxation and the spin-echo experiment 98
2
Chemical shift and J-coupling evolution during the spin echo 104
Mechanisms of nuclear spin relaxation in liquids and the spectral 104
density function
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 T1relaxation: chemical shift anisotropy, 117
spin-rotation and paramagnetic effects
Quadrupolar relaxation 119
Selective and nonselective T measurement and multi-exponential 119
1
decay of coherence
Problems 120
References 122
5. Classical and quantum descriptions of NMR experiments 123
in liquids
The classical approach: the Bloch equations of motion for 123
macroscopic magnetization
Classical description of a pulsed NMR experiment 126
A quantum mechanical description of NMR of a single spin in an 128
isotropic liquid
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Contents ix
A quantum mechanical description of NMR of coupled spins in an 129
isotropic liquid
The time-dependent nuclear spin Hamiltonian operator and 143
solutions to the time-dependent Schrödinger equation
Problems 144
References 146
6. Density operator and product operator descriptions of 147
NMR experiments in liquids
An ensemble of identical spins at equilibrium: an introduction to 147
the density matrix formalism
Expansion of the density matrix for an uncoupled spin in terms 150
of Cartesian angular momentum operators
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 155
operator bases
Evolution of Cartesian operators under the influence of pulses, 157
chemical shift and J-coupling
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 167
coherence selection
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 180
experiment
Other multiple-quantum filters in COSY 186
Multiple-quantum spectroscopy 186
π
Effect of 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 204
composite pulse decoupling
Problems 209
References 213
8. Heteronuclear correlations in NMR 215
Heteronuclear polarization transfer and the INEPT experiment 216
Refocused INEPT 221
