00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page i NMR for Physical and Biological Scientists 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page ii 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page iii 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 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page iv Vice President Denise Schanck Senior Editor Robert L. Rogers Associate Editor Summers Scholl Senior Publisher Jackie Harbor Production Editor Karin Henderson Cover Designer Aktiv Typesetter Phoenix Photosetting Printer RR Donnelly © 2007 by Garland Science, a member of the Taylor & Francis Group, LLC This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. ®Mathematica is a registered trademark of Wolfram Research, Inc. ®Mathcad is a registered trademark of Mathsoft Engineering & Education, Inc. ®MATLAB is a registered trademark of The Mathworks, Inc. 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 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page v To our children, Elizabeth and Theodore and our parents, Eugene and Mary Pochapsky and Bob and Mary Ann Sondej 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page vi 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page vii 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 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page viii 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 00-Pochapsky-Pre-cpp 31/7/06 2:00 pm Page ix 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