MULTINUCLEAR NMR

MULTINUCLEAR NMR

EDITED BY JOAN MASON The Open University Milton Keynes, Buckinghamshire, England

PLENUM PRESS. NEW YORK AND LONDON

Library of Congress Cataloging in Publication Data

Multinuclear NMR.

Includes bibliographies and index. 1. Nuclear magnetic resonance spectroscopy. I. Mason, Joan, date.

QD96.N8M85 1987 543'.0877 ISBN-13: 978-1-4612-8999-9 e-ISBN-13: 978-1-4613-1783-8 DOl: 10.1007/978-1-4613-1783-8

First Printing-August 1987 Second Printing-October 1989

1987 Plenum Press, New York Softcover repl'int of the hardcovel'1st edition 1987 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

All rights reserved

87-12284

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

CONTRIBUTORS

J. W. Akitt School of Chemistry, University of Leeds, Leeds LS29JT, England

Keith R. Dixon Department of Chemistry, University of Victoria, Victoria, British Columbia V8W 2Y2, Canada

R. J. Goodfellow Department of Inorganic Chemistry, University of Bristol, Bristol BS8 I TS, England

Oliver W. Howarth Department of Chemistry, University of Warwick, Coventry CV 4 7 AL, England

Cynthia J. Jameson Department of Chemistry, University of Illinois, Chicago, Illinois 60680

John D. Kennedy Department of Inorganic and Structural Chemistry, University of Leeds, Leeds LS29JT, England

Brian E. Mann Department of Chemistry, University 'of Sheffield, Sheffield S37HF, England

Joan Mason Department of Chemistry, The Open University, Milton Keynes MK 7 6AA, England

H. C. E. McFarlane Department of Chemistry, Sir John Cass School of Science and Technology, City of London Polytechnic, London EC3N 2EY, England

W. McFarlane Department of Chemistry, Sir John Cass School of Science and Technology, City of London Polytechnic, London EC3N 2EY, England

Henry W. E. Rattle Biophysics Laboratories, Portsmouth Polytechnic, Portsmouth POI2DT, England

Dieter Rehder Institute of Inorganic and Applied Chemistry, University of Hamburg, D-2000 Hamburg 13, Federal Republic of Germany

PREFACE

With the power and range of modern pulse spectrometers the compass of NMR spec-troscopy is now very large for a single book-but we have undertaken this. Our book covers the Periodic Table as multinuclear spectrometers do, and introductory chapters are devoted to the essentials of the NMR experiment and its products. Primary products are chemical shifts (including anisotropies), spin-spin coupling constants, and relaxation times; the ultimate product is a knowledge of content and constitution, dynamic as well as static.

Our province is chemical and biochemical rather than physical or technical; only passing reference is made to metallic solids or unstable species, or to practical NMR spectroscopy. Our aim is depth as well as breadth, to explain the fundamental processes, whether of nuclear magnetic shielding, spin-spin coupling, relaxation, or the multiple pulse sequences that have allowed the development of high-resolution studies of solids, multidimensional NMR spectroscopy, techniques for sensitivity enhancement, and so on.

This book therefore combines the functions of advanced textbook and reference book. For reasonably comprehensive coverage in a single volume we have sum-marized the information in tables and charts, and included all leading references. Special problems are posed by the very well-studied elements, and by the enormous literature of organic and biochemical NMR, from which in vivo and medical NMR studies are now taking off. Different strategies have been adopted in the various chapters, including a "multidisciplinary" approach (e.g., coverage of inorganic and physical aspects for hydrogen and organometallic aspects for carbon), and where possible, summarizing principles, as for nitrogen, fluorine, and phosphorus. The different chapters provide references to the relevant biochemical literature, and this is the subject of our final chapters. We owe a particular debt of gratitude to the NMR reference literature listed in Chapter 1, which is constantly cited throughout the text.

The four decades of NMR spectroscopy have seen successive spurts of develop-ment following technical breakthroughs. Our book celebrates the exploration by high-(or fairly high-) resolution NMR spectroscopy, during the last decade, of more com-plex systems, more aspects of the solid state, and more regions of the periodic table. As sensitivity and resolution steadily improve, with higher field working and other advances in instrumentation, the nuclei with lower resonance frequencies or natural abundance, and/or larger quadrupole moments-which constitute so much of the NMR periodic table-are brought into the net.

The next decade will see further application of techniques for sensitivity enhancement, spectral simplification, and better recovery of spectral information content (perhaps by multidimensional NMR and multiple quantum NMR). It will also see the extension of NMR imaging of living systems to other nuclei as well as the proton, and to include spectroscopy. Thus the chemist or other scientist will have

vii

viii PREFACE

an even greater need for handbooks of first resort which can provide a quick resume of a branch of the subject. We hope our book will fulfill this role for some time to come.

Joan Mason Milton Keynes, U.K.

FOREWORD

The history of nuclear magnetic resonance spectroscopy is one of the most important, fascinating, intellectually satisfying, and, as if all that were not enough, humanly relevant in all of science. Begun by physicists, soon preempted by chemists, then embraced by biologists and most recently by physicians, NMR is a field of seemingly endless fecundity. It has, deservedly, attracted some of the most ingenious physical chemists of the postwar era.

As early as the 1920s, the existence of nuclear magnetic moments, which the quantum theory allowed one to attribute to the spin of charged nuclei, was recognized by Pauli. In the 1930s the elegant molecular beam experiments of Rabi yielded much detailed information. However, the real beginning of NMR as we know it today was in the work of Purcell, Torrey, and Pound at Harvard and Bloch, Hansen, and Packard at Stanford. In 1946, these groups independently reported that the NMR of protons could be detected in bulk materials such as paraffin and water. In 1952 Bloch and Purcell received the Nobel Prize in physics for these discoveries.

For chemists, the seminal period was the era 1949-1951 (just before I began my own graduate study), when the recognition of the chemical shift, followed by the design and manufacture of high-resolution (40 MHz for lH) spectrometers, put an awesome new instrumental tool into their hands. For many years, this new tool was mainly of interest to organic chemists, although there were some early applications of proton NMR spectroscopy to inorganic problems, as well as relatively early use of 19F, lOBjl1B, and 31p spectroscopy by inorganic chemists. The advent of practical, routine 13C spectroscopy was largely driven by the needs of organic and biological chemists, but it also opened new doors for inorganic chemists through its applications to metal carbonyls and organometallics.

However, it is the last 10 to 15 years that have seen the real flowering of NMR as a tool for the inorganic chemist. This is the result of two main developments. One is the increasing capacity of commercially available instruments to handle most of the magnetic nuclides in the periodic table in a routine fashion. The other, which is still growing in importance, is the body of techniques that allow solids to be studied at relatively high resolution.

This book, which has been planned, edited, and partially written by one of the leaders in the field of inorganic NMR, should be of tremendous value to all who face the challenge of taking maximum advantage of NMR in their inorganic research. From my examination of the proofs, I would say it is the one for taking to that fabled desert island where you can have only one book on any given subject. It contains a succinct but comprehensive summary of the principles, written crisply and with style, as well as "wall-to-wall" coverage of the periodic table. It should become the reference of first and last resort for all users and would-be users of multinuclear NMR.

F. A. Cotton Department of Chemistry Texas A&M University College Station, Texas 77843

ix

CONTENTS

Chapter 1 Introduction .......................................................... 1

Joan Mason

Chapter 2 The Parameters of NMR Spectroscopy

Cynthia 1. Jameson and Joan Mason

1. Nuclear Properties of the Elements and the Resonance Condition .......... 3 2. The Nucleus in a Chemical Environment ............................... 5

2.1. The Chemical Shift and the Shielding Tensor ........................ 6 .2.2. Dipolar (D) Coupling ........................................... 8 2.3. Indirect Spin-Spin (J) Coupling ................................... 9 2.4. Electric Quadrupole Coupling .................................... 11 2.5. Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3. The Larmor Precession and the Bloch Equations ........................ 19 4. The Fourier Transform Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5. Multipulse and Multiple Resonance Techniques ......................... 25

5.1. Double Resonance Experiments ................................... 29 5.2. Techniques for Signal Enhancement ............................... 32 5.3. Techniques in Aid of Spectral Analysis and Assignment ............... 34

6. Oriented Systems ................................................... 35 6.1. High Resolution NMR Techniques for Solids ....................... 36 6.2. Experimental Determination of Tensor Components of (J, J, D, and q ... 37

7. The NMR Time Scale ............................................... 39 8. Physical Effects on the NMR Parameters ............................... 42

8.1. Medium and Temperature Effects ................................. 42 8.2. Isotope Effects .................................................. 44 8.3. Effects of Paramagnetic Substances ................................ 44 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Chapter 3 The Chemical Shift

Cynthia 1. Jameson and Joan Mason

1. Nuclear Magnetic Shielding and the Chemical Shift ...................... 51 1.1 The Absolute Shielding Tensor .................................... 51 1.2. The Diamagnetic and Paramagnetic Contributions to Shielding ........ 52 1.3. The Relationship between (JP and the Nuclear Spin-Rotation Constant .. 53

xi

..

XII CONTENTS

1.4. Molecular Symmetry and Nuclear Magnetic Shielding ................ 54 1.5. Absolute Shielding Scales ........................................ 55 1.6. Experimental Methods of Determining the Shielding Anisotropy ....... 57

2. Theoretical Description .............................................. 59 2.1. Computational Schemes ......................................... 59 2.2. Relativistic Effects ............................................... 60 2.3. Approximate Calculations and Models ............................. 62

3. Patterns of Chemical Shifts ........................................... 64 3.1. Chemical Shift Ranges of the Nuclei ............................... 64 3.2. Scaling of Chemical Shifts ........................................ 65 3.3. General Factors in the Shielding of Main-Group and Transition Metal

Nuclei ........................................................ 65 3.4. Dependence of Nuclear Shielding on Charge Density, Oxidation State,

and Substituent Electronegativity .................................. 66 3.5. Correlations with Electronic Excitation and Ionization Energies ....... 68 3.6. Substituent Effects .............................................. 69

4. Correlations of Chemical Shifts with Other Molecular Properties .......... 75 4.1. Nuclear Quadrupole Coupling Constants ........................... 75 4.2. Van Vleck Paramagnetism, and the Electronic g Tensor .............. 75 4.3. Spin-Spin Coupling Constants and Relaxation Times ................. 76 4.4. Bond Properties ................................................ 76

5. Shifts in Paramagnetic Systems ....................................... 77 6. Effects of Intermolecular Interactions and Intramolecular'Dynamics ........ 79

6.1. Medium Effects ................................................. 79 6.2. Rovibrational Averaging and Isotope Effects ........................ 80 6.3. Dynamic Processes: Fluxional, Conformational and Exchange Equilibria 82 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Chapter 4 Spin-Spin Coupling

Cynthia 1. Jameson

1. General Considerations .............................................. 89 1.1. Mechanisms of Spin-Spin Coupling ................................ 90 1.2. Anisotropy of the Spin-Spin Coupling .............................. 92 1.3. Methods of Determining Signs of Coupling Constants ................ 93

2. Empirical Patterns of Coupling Constants .............................. 95 2.1. Signs and General Magnitudes of nK(XY) .......................... 96 2.2. Structural Factors Affecting lK .................................... 101 2.3. Structural Factors Affecting the Sign and Magnitude of 2 K ............ 106 2.4. Structural Factors Affecting the Sign and Magnitude of 3 K ............ 109

3. Effects of Intermolecular Interactions and Intramolecular Dynamics on Spin-Spin Coupling ...................................................... 110 3.1. Averaging via Rotameric Equilibria and Intramolecular Rearrangement 110 3.2. Isotope Effects .................................................. 111 3.3. Chemical Exchange and Medium Effects ........................... 112

4. Theoretical Description .............................................. 113 4.1. Computational Schemes ......................................... 113

CONTENTS xiii

4.2. Relative Importance of the Fermi Contact, Spin Dipolar and Orbital Terms ........................................................ 116

4.3. Relativistic Effects ............................................... 117 4.4. Approximate Calculations and Models ............................. 118 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 123

Chapter 5 Relaxation and Related Time-Dependent Processes

Oliver Howarth

1. Importance ........................................................ 133 2. Definitions ........................................................ 134

2.1. Macroscopic Definition of TI and T2: Bloch Equations ............... 134 2.2. Microscopic Interpretation ....................................... 135 2.3. Nuclear Overhauser Enhancement ................................. 137 2.4. Relaxation in the Rotating Frame: TIp ............................. 139

3. Microscopic Theory ................................................. 140 3.1. Spin-Lattice Relaxation .......................................... 140 3.2. Spin-Spin Relaxation ............................................ 141 3.3. Dependence of Spectral Density upon Frequency .................... 142 3.4. The Static Part V ............................................... 144 3.5. More Complete Treatments ...................................... 144

4. Specific Mechanisms ,............................................... 145 4.1. Dipole-Dipole Relaxation ........................................ 145 4.2. Scalar Interactions .............................................. 148 4.3. Shielding Anisotropy ............................................ 149 4.4. Spin-Rotation Interactions ....................................... 150 4.5. Electric Quadrupole Interactions .................................. 150

5. Methods of Measurement ............................................ 153 5.1. TI Measurements ............................................... 153 5.2. Nuclear Overhauser Enhancement Measurements .................... 154 5.3. T2 Measurement, and Other Uses of Spin Echoes .................... 154

6. Line Broadening Due to Chemical Exchange ............................ 157 6.1. T I in the Presence of Chemical Exchange ........................... 159

7. Paramagnetic Interactions ........................................... 160 7.1. Kinetics ....................................................... 160 7.2. Paramagnetic Contributions to TI and T2 .......................... 162

8. Two-Dimensional NMR ............................................. 164 8.1. Shift-Correlation Experiments .................................... 165 8.2. J-Resolved Two-Dimensional Spectroscopy ......................... 167 References ......................................................... 168

Chapter 6 Hydrogen and Its Isotopes: Hydrogen, Deuterium, and Tritium

J. W. Akitt

1. Introduction ....................................................... 171 2. Experimental Techniques ............................................ 172

xiv CONTENTS

3. Hydrogen or the Proton, or Protium .................................. 172 3.1. Strong or Weak Hydrogen Bonds ................................. 174 3.2. Ionic Solvation ................................................. 174 3.3. Chemical Shifts of Adducts ....................................... 176 3.4. Hydrogen on Carbon ............................................ 176 3.5. Hydride Protons ................................................ 177 3.6. Dynamic Processes .............................................. 180

4. Deuterium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181 4.1. Deuterium NMR in Isotropic Liquids .............................. 181 4.2. Deuterium NMR of Liquid Crystalline Phases ...................... 183 4.3. Deuterium NMR in Solids and Heterogeneous Systems ............... 184

5. Tritium ........................................................... 184 References ......................................................... 185

Chapter 7 The Alkali and Alkaline Earth Metals: Lithium, Sodium, Potassium, Rubidium, Cesium, Beryllium, Magnesium, Calcium, Strontium, and Barium

J. W. Akitt

1. Introduction to Groups I and II ...................................... 189 2. Experimental Techniques ............................................ 192 3. Aqueous Solutions of Simple Salts ..................................... 195

3.1. Nuclear Relaxation .............................................. 197 3.2. Chemical Shifts ................................................. 203

4. Mixed and Nonaqueous Solutions of Simple Salts ....................... 205 4.1. Nuclear Relaxation .............................................. 205 4.2. Chemical Shifts ................................................. 206

5. Complexes Between the Cations and Various Types of Ligands ............ 209 5.1. Complexes with Low-Molecular-Weight Compounds ................. 209 5.2. Complexes with Synthetic Polymeric Ligands ....................... 210 5.3. Complexes with Biopolymers ..................................... 210 5.4. Cations in Liquid Crystals ....................................... 211

6. Group I and II Metal Organic Compounds ............................. 212 6.1. Lithium Organic Compounds ..................................... 213 6.2. Beryllium Covalent Compounds .................................. 215 References ......................................................... 215

Chapter 8 Boron

John D. Kennedy

1. Nuclear Properties and General Considerations ......................... 221 2. Trigonal and Tetrahedral Compounds ................................. 224

2.1. Chemical Shifts ................................................. 224 2.2. Coupling Constants ............................................. 227 2.3. Relaxation Studies .............................................. 231

CONTENTS XV

3. Polyhedral Boron-Containing Species .................................. 231 3.1. General Considerations .......................................... 231 3.2. Boron Chemical Shifts ........................................... 233 3.3. Coupling Constants ............................................. 245 3.4. Relaxation Times ............................................... 248 3.5. Polyhedral Species-Nuclei Other than Boron ...................... 250 3.6. Fluxionality .................................................... 252 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 253

Chapter 9 Aluminum, Gallium, Indium, and Thallium

1. W. Akitt

1. The Nuclear Properties of AI, Ga, and In, the Quadrupolar Nuclei ........ . 2. Aluminum ....................................................... .

2.1. Operational Techniques ......................................... . 2.2. Aluminum-27 NMR Parameters ................................. . 2.3. Some Observations on the Parameters ............................ .

3. Gallium ......................................................... . 3.1. Operational Techniques ......................................... . 3.2. Gallium-69 and Gallium-71 NMR Parameters ..................... .

4. Indium .......................................................... . 4.1. Indium-115 NMR Parameters ................................... .

5. Thallium ......................................................... . References .........................................................

Chapter 10 Carbon ............................................................ .

Brian E. Mann

Chapter 11 Silicon, Germanium, Tin, and Lead

John D. Kennedy and W. McFarlane

259 259 260 261 277 279 279 279 283 283 285 287

293

1. Introduction ....................................................... 305 2. Experimental Aspects ................................................ 305 3. Chemical Shifts ..................................................... 307

3.1. Isotope Effects .................................................. 307 3.2. Solvent and Temperature Effects .................................. 307 3.3. Chemical Shift Patterns .......................................... 307 3.4. Factors Influencing Shielding ..................................... 309 3.5. Chemical Shifts in Specific Classes of Compound .................... 314

4. Coupling Constants ................................................. 318 4.1. One-Bond Couplings ............................................ 318 4.2. Two-Bond Couplings ............................................ 323 4.3. Three-Bond Couplings ........................................... 325

XVI CONTENTS

5. Relaxation Behavior ................................................ 326 6. Miscellaneous and Solid State Work ................................... 327

References ......................................................... 328

Chapter 12 Nitrogen

Joan Mason

1. Nitrogen NMR Spectroscopy ......................................... 335 1.1. Nitrogen Referencing ............................................ 335 1.2. Medium Effects ................................................. 337 1.3. Solid State Measurements in High Resolution ....................... 337 1.4. Isotope Effects and Tracer Studies ................................. 340

2. 15N NMR Spectroscopy ............................................. 340 2.1. 15N Relaxation and NOE Factors ................................. 340 2.2. Sensitivity Enhancement ......................................... 344

3. 14N NMR Spectroscopy ............................................. 344 3.1. 14N Quadrupolar Relaxation ..................................... 345

4. Patterns of Nitrogen Shielding ........................................ 349 4.1. Nitrogen NMR Criteria of Structure ............................... 353 4.2. Inorganic Azines and Azenes ..................................... 355 4.3. Coordination Shifts ............................................. 356

5. Nitrogen Spin-Spin Coupling ......................................... 357 6. Dynamics ......................................................... 362 7. Biomo1ecules .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 362

References ......................................................... 362

Chapter 13 Phosphorus to Bismuth

Keith R. Dixon

1. Phosphorus-31 ..................................................... 369 1.1. Introduction ................................................... 369 1.2. Spin Lattice Relaxation (Td ...................................... 371 1.3. Chemical Shifts ................................................. 374 1.4. Coupling Constants ............................................. 390

2. Arsenic-75, Antimony-121,123 and Bismuth-209 ......................... 397 References ......................................................... 398

Chapter 14 Oxygen

H. C. E. McFarlane and W. McFarlane

1. Introduction ....................................................... 403 2. Experimental Aspects ................................................ 403 3. Chemical Shifts ..................................................... 404 4. Spin Coupling ...................................................... 408

CONTENTS

5. Relaxation Behavior ............................................... . 6. Applications ...................................................... . 7. The Solid State .................................................... .

References

Chapter 15 Sulfur, Selenium, and Tellurium

H. C. E. McFarlane and W. McFarlane

..

XVII

410 411 412 412

1. Introduction ....................................................... 417 2. Sulfur ............................................................ 417 3. Selenium and Tellurium ............................................. 421

3.1. Chemical Shifts ................................................. 421 3.2. Coupling Constants ............................................. 429 3.3. Relaxation Behavior ............................................. 431 3.4. Applications ................................................... 431 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 432

Chapter 16 Fluorine

Cynthia J. Jameson

1. 19F NMR Measurements ............................................. 437 2. 19F Chemical Shifts ................................................. 438

2.1. Absolute Shielding Scale ......................................... 438 2.2. Empirical Patterns of 19F Nuclear Shielding ......................... 440 2.3. Anisotropy of the 19F Shielding Tensor ............................. 442

3. Spin-Spin Coupling Involving 19F ..................................... 442 4. 19F Relaxation ..................................................... 445

References

Chapter 17 The Quadrupolar Halides: Chlorine, Bromine and Iodine

1. W. Akitt

1. Introduction 2. Experimental Techniques ........................................... . 3. NMR Parameters .................................................. .

3.1. Covalent Compounds .......................................... . 3.2. Ionic Solutions ................................................ . References

Chapter 18 The Noble Gases

Cynthia J. Jameson

445

447 448 448 448 455 458

1. Introduction ....................................................... 463 2. 129Xe NMR Studies of Bonding and Structure of Xenon Compounds ....... 463

...

XVIll CONTENTS

2.1. 129Xe Chemical Shifts ............................................ 466 2.2. Spin-Spin Coupling to Xenon ..................................... 469

3. Probing Nonspecific Intermolecular Interactions with Noble Gas Nuclei .... 473 3.1. Medium Shifts .................................................. 473 3.2. Relaxation Times ............................................... 473 References

Chapter 19 Early Transition Metals, Lanthanides and Actinides

Dieter Rehder

1. Introduction ...................................................... . 2. Group IIIb ....................................................... .

2.1. Scandium ..................................................... . 2.2. Yttrium ...................................................... . 2.3. Lanthanum ................................................... . 2.4. The Lanthanides ............................................... . 2.5. Actinium and the Actinides ...................................... .

3. Group IVb: Titanium, Zirconium, and Hafnium ........................ . 4. Group Vb ........................................................ .

4.1. Vanadium .................................................... . 4.2. Niobium ...................................................... . 4.3. Tantalum ..................................................... .

5. Group VIb ....................................................... . 5.1. Chromium ................................................... . 5.2. Molybdenum ................................................. . 5.3. Tungsten ..................................................... .

6. Group VIIb ....................................................... . 6.1. Manganese ................................................... . 6.2. Technetium .................................................. . 6.3. Rhenium ..................................................... . References

Chapter 20 Group VIn Transition Metals

R. 1. Goodfellow

475

479 480 480 482 483 486 486 487 488 488 493 497 497 497 499 505 507 507 511 512 512

1. Introduction ....................................................... 521 2. Observation ....................................................... 521

2.1. Relaxation Behavior ............................................. 522 2.2. Methods of Observation ......................................... 526

3. Chemical Shifts ..................................................... 531 3.1. Evaluation of Chemical Shifts ..................................... 531 3.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 534 3.3. Theoretical Approaches .......................................... 539 3.4. Empirical Correlations ........................................... 547 3.5. Effects of the Molecular Environment and Isotopes .................. 548

CONTENTS xix

4. Spin-Spin Coupling ................................................. 551 4.1. Sign Determinations ............................................. 552 References ......................................................... 554

Chapter 21 Post-Transition Metals, Copper to Mercury

R. J. Goodfellow

1. Introduction ....................................................... 563 2. Observation ....................................................... 563

2.1. 63CU and 65CU .................................................. 564 2.2. 67Zn .......................................................... 564 2.3. 107 Ag and 109 Ag ................................................. 565 2.4. 111Cd and 113Cd ................................................ 566 2.5. 197 Au ......................................................... 567 2.6. 199Hg and 201Hg ................................................ 568

3. Chemical Shifts ..................................................... 569 3.1. Results ........................................................ 569 3.2. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 579

4. Spin-Spin Coupling ................................................. 582 4.1. Sign Determinations ............................................. 584 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 584

Chapter 22 NMR Spectroscopy in Bioinorganic Chemistry

Henry W. E. Rattle

1. Introduction ....................................................... 591 2. Some Examples of Biological Applications: Isotope Shifts in 31p NMR ...... 591 3. Sodium Transport Through Membranes Using 23Na Resonance ........... 593 4. Active Site Interactions in Fluorine-Labeled IX-Chymotrypsin .............. 595 5. 113Cd Studies of Alkaline Phosphatase ................................. 596 6. 31 P NMR in Living Tissue ........................................... 597 7. Ion Binding to Cytochrome c Studied by Nuclear Magnetic Quadrupole

Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 598 8. Deuterium Label Studies of Membranes ................................ 599 9. Direct Determination of Correlation Times in Enzyme Complexes Involving

Monovalent Cations and Paramagnetic Centers ......................... 600 Index of Reviews ................................................... 601 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 603

Chapter 23 Biomedical NMR

Joan Mason

1. Biomedical NMR ................................................... 605 2. NMR Imaging ..................................................... 606

xx CONTENTS

3. Localized NMR Spectroscopy ........................................ 610 4. Further Applications ................................................ 611

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 613

Symbols and Abbreviations .............................................. 615

SI Units and Fundamental Constants ..................................... 619

Appendix: NMR Properties of the Elements ................................ 623

Index ............................................................... 631

Chapter 1

INTRODUCTION

JOAN MASON

So as to give a comprehensive account of multinuclear NMR spectroscopy, Chapter 2 describes the essentials of the NMR experiment and the spectroscopic parameters so obtained, Chapters 3 and 4 discuss the principles of nuclear magnetic shielding and spin-spin coupling, respectively, and Chapter 5, relaxation and dynamic processes in general. Chapters 6-21 ther. cover the Periodic Table from hydrogen to the transition metals and the noble gases, treating egregious elements singly and others in groups. Chapters 22 and 23 afford an introduction to the rapidly growing fields of bioinorganic and biomedical NMR, respectively, with bibliography. Symbols, abbreviations, units and physical constants are given at the end of the book; and nuclear properties of the elements, including NMR receptivities and recommended reference substances, in the Appendix.

In covering the Periodic Table we have tried to summarize voluminous (and burgeoning) literature information in tables and charts, providing as many references as possible, and certainly all key references. Many of the reported ranges of chemical shifts (or coupling constants) are growing apace as new groups of compounds are studied. Rapid growth, as for example in the direct study of many metal nuclei, has necessitated updating during the prolonged gestation of this book, and there is some diversity in effective dates of literature coverage in different chapters.

The organization of the chapters varies, reflecting differences in chemistry and in the NMR history of the nuclei. For long-studied nuclei such as 19F or 31p mainly general principles are discussed; for nitrogen, NMR criteria of structure in ligands and functional groups, and also relaxation processes, given the technical problems (and opportunities) afforded by 14N and 15N; for 13C, organo groups in metal complexes; and for 1,2,3H, inorganic and physical aspects. In some newer fields more complete coverage is possible.

No specific attention is devoted to practical NMR spectroscopy or instrumen-tation, which have been ably treated. (1-4) We acknowledge also classics of NMR spectroscopy(5-9) and other general NMR books, (1(}-17) and salute our colleagues who have aimed at a target similar to our own. (18-20) Other important texts are mentioned in appropriate chapters. We express our gratitude to the invaluable review series, (21-30) and to the NMR Abstracts. (31) Finally a tribute is in order to the achievements and promise of our chosen technique-for example, what other physical method could uncover the "chimpanzee swing" of a water molecule, from oxygen to oxygen, in sodium alumina?(32)

JOAN MASON Department of Chemistry, The Open University, Milton Keynes MK7 6AA, England,

2 CHAPTER 1

REFERENCES

1 Martm, M L, Delpuech, J -J , Martm, G J Practical NMR Spectroscopy, Heyden London, 1980 2 Shaw, D Founer Transform NMR Spectroscopy, 2nd ed, ElsevIer Amsterdam, 1984,304 pp 3 Brevard, C, Granger, P Handbook of High ResolutIOn Multinuclear NMR, WIley New York, 1981,

229 pp 4 FukushIma, E, Roeder, S B W Expenmental Pulse NMR A Nuts and Bolts Approach, Addlson-

Wesley Readmg, Massachusetts, 1981, 539 pp 5 Pople, J A, SchneIder, W G, Bernstem, H J High-resolutIOn NMR, McGraw-Hlil New York, 1959,

501 pp 6 Emsley, J W, Feeney, J, Sutchtfe, L H High ResolutIOn NMR Spectroscopy, Pergamon Oxford,

1965, Vol 1, 662 pp, Vol 2, 1154 pp 7 Camngton, A, McLachlan, A D IntroductIOn to Magnellc Resonance, Harper New York, 1967,

reIssued 1979, 266 pp 8 Shchter, C P Principles of Magnellc Resonance, 2nd ed, Spnnger-Verlag Berhn, 1978,397 pp 9 Abragam, A The Principles of Nuclear Magnetism, Oxford Umverslty Press, corr repnnt 1978,599 pp

10 Lynden-Bell, R M, Hams, R K NMR Spectroscopy, Nelson London, 1969, 160 pp 11 McLauchlan, D A Magnellc Resonance, Oxford ChemIstry Senes Oxford, 1972, 105 pp 12 Akltt, J W NMR and Chemistry, 2nd ed, Chapman and Hall London, 1983,263 pp 13 Gunther, H NMR Spectroscopy, Wliey ChIchester, 1980, 436pp 14 Becker, E D High ResolutIOn NMR, 2nd ed, AcademIC Press New York, 1980, 354 pp 15 Hams, R K NMR Spectroscopy A PhYSicochemical View, PItman London, 1983,250 pp 16 Sanders, J K M, Hunter, B K Modern NMR Spectroscopy A GUide for Chemists, 0 U P Oxford,

1987, 354pp 17 Kemp, W NMR In Chemistry a Multinuclear IntroductIOn, Macmlilan London, 1986,240 pp 18 Hams, R K, Mann, BE, Eds, NMR and the PerIOdic Table, AcademIC Press London, 1978,459 pp 19 Lambert, J B, RIddell, F G, Eds, The Multinuclear Approach to NMR Spectroscopy, NATO ASI

Senes, ReIdel Dordrecht, 1983, 548 pp 20 Laszlo, P, Ed, NMR of Newly Accessible Nuclei Chemical and BIOchemical AppitcatlOns, AcademIC

Press New York, 1983, Vol 1,298 pp, Vol 2,436 pp 21 Waugh, J S, Ed , Adv M agn Reson, AcademIC Press New York, 1965-22 Mooney, E F, Webb, G A, successIve Eds, Ann Rep NMR Spectrose AcademIC Press New York,

1968-23 Berhner, L J, Reuben, J, Eds, BIOI Magn Reson, Plenum New York, 1978-24 Bradbury, J H, Ed, Bull Magn Reson, Frankhn InstItute Press Phliadelphla, 1979-25 C P Poole, Ed, Magn Reson Rev, Gordon and Breach, London, 1977-26 DIehl, P, Fluck, E, Kosfeld, R, Eds, NMR-Baslc Principles and Progress, Spnnger-Verlag Berhn,

1969-27 Kaufman, L, Crooks, L E, Marguhs, A R, Eds, NMR Imaging In MediCine, Igaku-Shom New

York, 1981-28 Hams, R K, Abraham, R J, Webb, G A, successIve Eds , Nucl Magn Reson, Spec Per Rep Chern

Soc London, 1972-29 Emsley, J W, Feeney, J, SutchfTe, L H, Eds, Progr NMR Spectrosc, Pergamon, Oxford, 1966-30 Greenwood, N N, Ebsworth, E A V, Adams, D M, DavIdson, G, successIve Eds , Spectrosc Props

Inorg Organomet Cpds, Spec Per Rep Chern Soc London, 1968-, Mann, B E "NMR Spec-troscopy," p 1

31 NMR (ChemIcal Aspects), CA Selects, ChemIcal Abstracts, Columbus, OhIO, Nottmgham, UK 32 Kuhns, P L, RIchter, L J, ConradI, M S J Chern Phys 1982, 76, 6-9

Chapter 2

THE PARAMETERS OF NMR SPECTROSCOPY

CYNTHIA 1. JAMESON and JOAN MASON

1. NUCLEAR PROPERTIES OF THE ELEMENTS AND THE RESONANCE CONDITION

Many nuclei have spin angular momentum, since protons and neutrons have this property, although the nucleons couple to produce nuclei without spin when an even number of each kind is present, as in 12C, 160, 28Si, 32S, etc. The nuclear angular momentum has an associated magnetic field, comparable to the magnetic field produced by an electric current in a loop. A nuclear spin thus behaves as a magnetic dipole, which tends to align with an applied magnetic field and to interact with neighboring dipoles. The magnetic moment p, which determines tl).e potential energy E of the nuclear magnetic dipole in a magnetic field of strength (or flux density) Bo, is defined by

E= -p'Bo (1)

Nuclear spin angular momentum, given by the vector I, has total magnitude Ii[/(/ + 1)]1/2, where I is the nuclear spin quantum number, and Iii is the maximum observable component of I in any selected direction (since not all of the angular momentum is along anyone direction). The observable components of I are M/l, where M[ is the magnetic quantum number and takes the values I, (I - 1 ), ... , ( - I + 1), ( - I). Nuclei such as 12C with 1=0 are nonmagnetic and so cannot be observed by NMR. Magnetic nuclei have half-integral values of 1(1/2,3/2,5/2, ... ) corresponding to an odd number of nucleons, or, less commonly, integral values of I corresponding to an odd number both of protons and of neutrons eH, 6Li, lOB, 14N, 50V, ... ). All nuclei with I>! behave as electric quadrupoles as well as magnetic dipoles.

The magnetism of a nucleus is usefully described in terms of its magnetogyric ratio y, the proportionality constant which relates the nuclear magnetic moment J1 to the nuclear spin angular momentum I:

y = p/I = p/Ii [/(l + 1)] 1/2

CYNTHIA 1. JAMESON Department of Chemistry, University of Illinois, Chicago, Illinois 60680. JOAN MASON Department of Chemistry, The Open University, Milton Keynes MK76AA, England.

3

4 CHAPTER 2

or

y = Jl//Il (2) where Jl is the maximum observable component of the vector J1 (and is the value often quoted). (I) For most magnetic nuclei J1 and I are parallel vectors and y is positive, but some nuclei ('5N, 170, 29Si) have J1 and I antiparallel (as for the electron) and y negative, which can sometimes be disadvantageous.

Nuclear magnetic moments Jl are expressed in units of JlN' the nuclear magneton:

where

and e is the elementary charge, mp the proton mass, and gN the nuclear g jactor, the counterpart of the g factor (with values close to 2) relating an electron's magnetic moment to its spin angular momentum. The magnetic moment of an electron is the Bohr magneton

JlB= ell/2me = 9.2740 x 10- 24 J T- 1

where me is the electron mass. Thus the proton, the smallest nucleus, has a magnetic moment which is 658 times smaller than that of the electron. Physical consequences of this disparity are, for example, the use of radiofrequencies for NMR as opposed to microwave frequencies for ESR spectroscopy, and the large perturbations of NMR systems if unpaired electrons are present.

From equations (1) and (2), and the quantization of I into observable com-ponents Mjll along the direction of the magnetic field Bo, we have

(3)

The (2/ + 1) values of M j ranging from - / to + / thus correspond to different nuclear magnetic energy levels separated by the Zeeman splitting yllBo, as shown in Figure 1 for a nucleus with / = 3/2. In NMR spectroscopy we induce transitions of the nuclear spin between these levels by the use of electromagnetic radiation, and monitor the absorption. The magnitudes of magnetogyric ratios and practical field strengths Bo are such as to require radiofrequency (rf) radiation, with frequency (v) in the range

E

L..----.so

3 .......... ----"2

1 --------------- -,

1 +,

--------------- + {

Figure 1. Zeeman splitting for a nucleus with spin 1=3/2, l' > O.

THE PARAMETERS OF NMR SPECTROSCOPY 5

50-500 MHz or so. The selection rule is AM[= 1, so that for a single bare nucleus all the transitions have the same energy AE as in Figure 1:

AE = hv = yliBo (4) Equation (4) is the resonance condition which has to be satisfied by the applied fre-quency in order for absorption to be a maximum. The frequency Vo = yBo/2n is the Larmor frequency for that nuclear species in the field Bo.

In NMR as in other forms of spectroscopy net absorption of electromagnetic radiation can occur owing to the greater population of the lower energy levels com-pared to the upper ones, at thermal equilibrium. But the very small splitting of nuclear energy levels, about 10- 25 J, makes NMR much less sensitive than optical spec-troscopy. The Boltzmann law gives the ratio of populations

n2/nj = exp(hvo/kT) = exp(yIiBo/kT) ~ 1 + yIiBo/kT. Thus for l3C in a field of 2.35 T at ambient temperatures the ratio is 1.000004. Luckily measurements at radiofrequencies can be made with very great accuracy.

The signal strength is proportional to the net magnetization, which is given by(2)

for a collection of N nuclear moments. In addition the voltage induced in the detector system increases as the resonance frequency. Depending on the instrumentation, the sensitivity to NMR detection increases with increasing "1 3 , P, and B6/2 For comparing different nuclei, the receptivity R is defined as the product of the natural abundance A of the magnetic isotope (expressed as a percentage) and the sensitivity at constant field, taken as proportional to "1 3/(/+ 1 )y,2) The values given in the Appendix are those of Re, relative to that of l3C:

To overcome the intrinsically low sensitivity, NMR signals are accumulated from a series of repeated experiments. Since the signal-to-noise ratio increases only as In, where n is the number of experiments, a factor x in receptivity corresponds to a factor x2 in time of accumulation. Of peculiar importance is the rate of reestablishment of the Boltzmann distribution (thermal equilibrium) since the repetition rate depends on this. NMR spectroscopy differs from optical spectroscopy in not being able to rely on spon-taneous emission of radiation, since the probability of this depends on v3 and is extremely low at radiofrequencies. (When the populations of the nuclear magnetic energy levels become equalized, the NMR signal is said to be saturated.) Nor can reestablishment of Boltzmann populations be as fast as the molecular collisions which relax vibrational and rotational states. In NMR only local magnetic fields fluctuating at the Larmor frequency can induce radiationless transfers between nuclear magnetic energy levels (relaxation).

2. THE NUCLEUS IN A CHEMICAL ENVIRONMENT

The main parameters of NMR spectroscopy, the nuclear magnetic shielding, the indirect spin-spin (J) coupling, and the direct dipolar (D) coupling, are all tensor

6 CHAPTER 2

quantities, since the environment in which the nucleus finds itself is generally not spherically symmetric. Each parameter therefore consists of a 3 x 3 array of tensor components, in principle. In practice, depending on the symmetry, some of the num-bers may be equal and some zero (and in any case only the diagonal elements are important in the analysis of spectra). The NMR parameters are tensors because they are molecular properties arising from the interaction of the nuclear spin vector I with another vector, i.e., with Bo (shielding), with I via a nuclear electric quadrupole (quadrupole coupling), or with another nuclear spin I' (D or J coupling). If all these couplings were evident in the NMR spectrum this would be very complicated indeed. It is greatly simplified in liquid or gas phase measurements (although a wealth of information is then lost) because the disordered motion of a molecule, with rapid rotations interrupted by frequent and random collisions, allows it to sample all possible orientations with equal probability, on the NMR time scale. The isotropic average of the tensor is equal to one-third of the trace, which is the sum of the com-ponents along the diagonal of the array. The direct dipolar coupling D and the quadrupole coupling e2qQ are isotropically averaged to zero (their tensors have zero trace) so only the averaged value of the shielding and the (indirect) spin-spin coupling constants contribute to the positions of the NMR spectral lines in fluid phase spectra.

2.1. The Chemical Shift and the Shielding Tensor

Much of the chemical information in NMR spectra arises from chemical shifts due to the local magnetic fields generated at the nucleus by the circulations of the surrounding electrons induced by the applied field. If the resulting magnetic fields oppose the applied field (Bo) the effect is to shield or screen the nucleus from it, and vice versa. The nucleus then experiences an effective field given by

where (J, the nuclear magnetic shielding, is expressed in units of 10- 6, or parts per million (ppm). The (J tensor elements reflect the symmetry of the electronic environ-ment of the nucleus, depending on the bond type, an averaged value ((j av) being observed in fluid phases.

The resonance condition of equation (4) then becomes

Vo = yBo(1- (J)/2rc

The shielding constant (J is given by quantum mechanical calculations relative to the bare nucleus, which is not a practical reference. Chemical shifts are commonly measured relative to a standard substance, such as tetramethyl silane (TMS), used for iH, 13C, and 29Si. The chemical shift is defined by IUPAC convention(3) as

(5)

which can be related to the shielding difference in the limit (j ~ 1. Then b ~ (j ref - (j S' where the subscript s refers to the sample and ref to the reference. The opposite signs of (j (shielding) and b (shift) can be a source of confusion in the literature. Before 1972 shifts were commonly defined with the opposite sign and more recently there has been a tendency to report shift tensors with either sign, which is unfortunate.

In the continuous wave (CW) mode, resonances can be observed with the fre-

THE PARAMETERS OF NMR SPECTROSCOPY 7

quency held constant and the field varied (field sweep). Observation of a more shielded nucleus then requires a higher field, giving rise to terms such as "high-field resonance" for higher shielding and vice versa. Usage has now been standardized to refer to the frequency-sweep mode, with the field held constant, so that higher shielding should be described in terms of lower frequencies rather than higher fields.

Since the use of reference substances poses practical problems, an alternative which is gaining ground is to refer to an absolute frequency. On the E scale the stan-dard frequency for a given nucleus (X) is the one observed at a field strength (2.35 T) in which TMS protons (under standard conditions) resonate at exactly 100 MHz. (E is the upper case Greek letter xi.) Thus

The chemical shift is then

and Ex values for the elements are given in the Appendix. For some nuclei e95pt for example) an arbitrary frequency has been taken as reference because of problems with standard solutions.

This frequency in practice is not as "absolute" as we should like. TMS shifts are temperature dependent, and temperatures are not always accurately reproduced. Further, a bulk susceptibility correction which depends on the shape of the container and its orientation relative to the magnetic field must be made (Section 8.1).

The shielding tensor for a linear molecule has only three nonzero components, of which only two are independent. Clearly, the electronic circulations induced in such a molecule will be different if it is placed parallel or perpendicular to the magnetic field. In this case there are two independent quantities, 0"11 and 0" -1, which characterize the nuclear shielding. In a nuclear site with no symmetry at all there are nine different components of G, (4-6) but the off-diagonal components have negligible effect on the spectrum (except perhaps for the heaviest nuclei). In fluid phases only the isotropic average is observed:

but the separate elements can be observed in the spectra of oriented systems (cf. Sec-tion 6) or molecular beams. (4.7) Single-crystal studies can give the tensor elements (relative to a standard or to 0" av), and the orientation of the principal axes. Polycrystalline samples give characteristic line shapes (as in Figure 2a) from which the tensor elements can be read off or obtained by computer simulation. Figure 2b shows a powder pattern for a nucleus in an axially symmetric location with 0" 11 = 0" 22 = 0" -1' and 0"33=0"11' the anisotropy being defined as ,10"=0"11-0"-1' or more generally, ,10"= 0" 33 - (0"22 + 0" 11 )/2, the elements being conventionally taken as 0" 33 ~ 0" 22 ~ 0" 11. The asymmetry is defined as YJ = (0"22 - 0" 11 )/( 0" 33 - 0" av), which is zero for axially symmetric systems.

Substituent effects in organic molecules are well defined by J3C tensor elements. Thus for the carbonyl group RCOX, where X = H, R, OH, OR etc., 0" 11 and 0"33 vary rather little, the sensitivity to the substituent X being concentrated in 0"22. (8) Similarly, experimental values of tensor elements afford a more stringent test of calculated shieldings than do the isotropic shifts (Chapter 3).

8

0'" V.L

- to -. ----"-- ", (""ml, RELATIVE TO H!S

a b

CHAPTER 2

r ;:::::====:;:OI-, ,. r------,I.'

-R

- - 0>0

---

Figure 2. Line shapes for polycrystalline samples showing principal elements of the shielding tensor. (a) Asymmetric e1p in a diethylphosphonate); (b) axially symmetric (l3C in [MO(CO)6]); (c) axially sym-metric, with dipolar coupling to one spin 1= 1 (l3C in NH4 NCS). Spectra reproduced with permission from j, Chern, Phys, 1983,78, 5384; Chern, Phys, Lett, 1985, 122, 545; and R. E. Wasylishen,(8"

2.2. Dipolar (D) Coupling The presence of neighboring magnetic nuclei alters the local field and therefore

the energies of a nucleus. The direct dipolar interaction energy between any two magnetic moments J11 and J12 separated by a vector r is

and for nuclear magnetic dipoles this is

which is written in abbreviated form as

where D is the direct (through space) dipolar coupling tensor. We can see that D depends only on the relative position coordinates of nuclei 1 and 2.

The effect of the dipolar interaction on the NMR spectrum depends on the angle () which the internuclear vector makes with the magnetic field Bo. From the II' D 12 interaction six different kinds of terms arise, of which only two contribute in first order, both having the factor (3 cos 2 () - 1 )/r3. The r- 3 dependence means that the dipolar coupling is strong at close approach and falls off quite steeply with distance.

THE PARAMETERS OF NMR SPECTROSCOPY 9

The same factor appears in the classical picture, in which the dipolar field B D at a dis-tance r from a magnet with moment J-lz in the field direction is given by

(6) The isotropic average of 3 cos 2 () - 1 over all orientations is zero, so the dipolar

interactions do not contribute to line positions in a liquid phase NMR spectrum (cf. the fact that the trace of D is zero).

In solids or liquid crystals in which nuclear positions are maintained relative to the applied field, the direct interaction of the magnetic dipoles may be observed in the NMR spectrum. A magnetic nucleus X with spin 1 has (21 + 1) orientations in the magnetic field, splitting the resonance of a neighbor Y at a distance r into a (2/ + 1) multiplet, the splitting depending on YxYy(3 cos2 () - 1 )/r3. For example, the + 1, 0, - 1 components of 14N split the resonance of 13C in NCS - ion in Figure 2c, and from the apparent dipolar coupling constant R = 1295 Hz, the effective C-N bond length -1/3 = 1.19 0.01 A is obtained. (8a) Because of their high y, protons have large dipolar coupling constants, and splittings may be 102-105 Hz. Usually the resonances are greatly broadened by unresolved couplings to neighbors with a range of distances and orientations.

2.3. Indirect Spin-Spin (1) Coupling A coupling between nuclei which does not average to zero in liquids is the

indirect spin-spin coupling or J coupling; in fact the total (dipolar) interaction between nuclear,magnetic moments is YI Y2n2I1 . (J + D)' 12 , For oriented molecules the components of (J + D) are evident in the spectrum. In isotropic phases only the average of J is observed, and this is nonzero because the interaction is by way of the electrons in the bonds between the nuclei. Whereas D contains structural information in the form of internuclear distances, which may be intermolecular, J contains bond-related structural information. Thus the observation of a J coupling is proof positive of a chemical bond that is long-lived on the NMR time scale.

Indeed, important information on connectivity within a molecule is carried by the symmetrical multiplet splittings (in high-resolution spectra) due to J coupling of nearby none qui valent nuclear spins. (The coupling of equivalent spins, with the same chemical shift, splits the energy levels but not the signals, as the transitions have the same energy.) The splittings (J/Hz, where J is the coupling constant) are independent of the applied field, as expected for an intramolecular interaction. Indirect (e.g., double irradiation) methods show that the coupling constant can be positive or negative, but the sign is not normally evident in the NMR spectrum.

There are three main mechanisms for indirect or J coupling, all mediated by the valence electrons. The most important involves the Fermi contact interaction of an s electron with the nucleus (with which p, d, ... electrons have no contact). This can be envisaged in terms of the Dirac vector model. (9) For simplicity we can consider the HF molecule, since both nuclei have spin 1/2 and positive magnetogyric ratios y. The bonding pair of electrons must have anti parallel spins (af3) by the Pauli principle, and their motions are correlated such that if the one with a spin is near one nucleus, the one with f3 spin is likely to be near the other. Within each nucleus the magnetic moments of the nucleus and the electron are more stable when parallel, so that the spins are antiparallel (since the electron has a negative y). The nuclear spins are

10 CHAPTER 2

therefore coupled, having a lower energy when anti parallel than when parallel, in which case the difference hJ is defined as positive (Figure 3). For HF, J has the rather large value of + 530 Hz, (reflecting the large magnetogyric ratios of IH and 19F) observed in the molecular beam.

A two-bond coupling, as of IH and 19F in CH3 F, arises because the bonding elec-trons on carbon are the more stable when their spins are parallel, as in H ':!! C I!::. F, by Hund's rule of maximum multiplicity. Thus the parallel configuration of the IH and 19F spins is now the more stable, corresponding to a negative sign for 2JHF . This model therefore suggests that n J coupling constants are positive for odd values of n and negative for even n, and that n J decreases with increase in n (as the Hund rule is not exclusive). These conclusions have some general validity, particularly for alkanes, but the exceptions show that the reality is more complicated than the model.

The other spin-spin coupling mechanisms involve interactions mediated by p, d, ... electrons. The orbital term JAB arises from the perturbation of the magnetic field due to the electron's orbital motion by the nucleus A, this perturbation being experienced by the nucleus B, and vice versa. The spin-dipolar term JS;B arises from the direct interaction of the magnetic dipole of the nucleus A with that of the orbital electron, which then interacts with nucleus B, and vice versa. The observed coupling constant is then the sum of the Fermi contact term fe, which usually dominates, and rand .rd , which are of course insignificant for hydrogen. These components can be evaluated only by theoretical calculations, which show the importance of non bonding as well as of (J and n bonding electrons (r and .rd are larger when there is multiple bonding). (10)

For all coupling mechanisms the contribution to JAB is proportional to the product Y A YB' Thus the coupling constant for H2 can be obtained from that of HD, to which it is related by the ratio YH/yo. For comparisons involving different nuclei it is convenient to use a reduced coupling constant K, defined as

Kxy = 4n2 Jxylhyxi'Y

where J is in Hz and Kin N A -2 m -3. Spin-spin coupling in HD produces a doublet in 2D resonance but a triplet in I H

resonance, as the proton interacts with three orientations of the deuteron (/ = 1). All components of the multiplet have near-equal intensity because of the near-equal populations of the nuclear energy levels of the deuteron. Similarly for a nucleus A, coupled to two X spins with 1= 1, the 9 combinations of Ml for the X spins are

1, 1 1, 1, -1 -1, -1, -1 0, 1 -1,1 0, -1

0,0 giving I: M 1: 2 1

-1 -2

Number of combinations: 1 2 3 2 1

The result is a quintet with intensities in the ratio 1:2:3:2:1. In general, the coupling of any number of A nuclei to n equivalent I spins gives a

multiplet with (2nI + 1) lines in the A spectrum. For 1= 1/2 the relative intensities are given by the coefficients of the binomial expansion of (a + brand by the Pascal triangle, and correspondingly for I> 1/2. The numbers in a row of the triangle give the relative intensities, for n equivalent X spins. Each number in the triangles (for n > 0) can be obtained as the sum of the (2nI + 1) nearest neighbors in the line above, with zero for empty spaces.

THE PARAMETERS OF NMR SPECTROSCOPY 11

hJ positive

H iJ a F Figure 3. Splitting of lH energy level in HF by spin-spin coupling to 19F, mediated by the Fermi contact interaction.

n 1= 1/2 1= 1 1=3/2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 121 1 2 3 2 1 2 3 4 3 2 1 3 133 1 1 3 6 7 6 3 1 1 3 6 10 12 12 10 6 3 1 4 1 464 1 1 4 10 16 19 16 10 4 1 1 4 10 20 31 40 44 40 31 20 10 4 1

These simple rules break down if the chemical shift in frequency units between the coupled nuclei becomes comparable with J. The spectrum is then called "second order": there are shifts of intensity from the wings to the center, compared with a first-order spectrum, and further splittings. (11) The calculations of high-resolution spectra in the isotropic phase are a beautiful and straightforward application of quantum mechanics, and have been worked out in detail for systems of spin!(12,13) and for quadrupolar nuclei. (14-16) Analytical solutions of this problem are in smaller demand now that higher-field working can restore first-order conditions.

Spin-spin coupling constants are different for members of a chemically equivalent set if magnetic nonequivalence is present. In. CF 2 = CH 2, for example, 3 J HF( cis) is dif-ferent from 3 J HF( trans), because of the difference in coupling pathways. The spectra of magnetically nonequivalent systems are complex even in the limit of very high fields (see Figure 4). Computer calculations can be used to determine the chemical shifts and the magnitudes (even the relative signs in some cases) of J by iterative fitting of frequency separations and intensities. (18,19)

2.4. Electric Quadrupole Coupling

All nuclei with I> 1/2 have an ellipsoidal distribution of charge, as shown in Figure 5, and an electric quadrupole moment eQ; values of Q are given in the Appen-dix. Q is positive if the nucleus is prolate (lengthened) in the direction of its spin angular momentum, negative if oblate (flattened). The unit is 10- 28 m2 = 1 barn (after Fermi's exclamation at the first measurement of a nuclear cross section, that it was as big as a barn). Indeed, a nucleus with 1 = n/2 may have a 2n moment which is magnetic for n odd, and electric for n even. Thus nuclei with I~ 3/2 may have a magnetic octupole and those with I~ 2 an electric hexadecapole moment, and so on, although effects of these are rarely observed.

Electrostatic energy is minimized by appropriate alignment of a quadrupole in a field gradient (in contrast to dipolar energy, which depends directly on the field). In a molecule, there is an electric field gradient (efg) at the nucleus because of asymmetry

12 CHAPTER 2

500 Hz

Figure 4. Example of magnetic inequivalence in a chemically equivalent system.(l7) The 31p spectrum of cis-[PdCI2{PF(OPhhhJ in which the protons are decoupled is that of an [AXJ2 spin system, inequivalent because the P-F couplings are unequal. The spectrum is drastically different from the simple 1 :2: 1 triplet which would have been observed for an A2X2 spin system.

in the local charge distribution due to the electrons and other nuclei. The energy of a nuclear quadrupole is quantized according to its orientation in the efg even in the absence of an external magnetic field. Transitions are induced by a radiofrequency, in so-called "pure quadrupole" or nuclear quadrupole resonance, NQR (Figure 6). But since transitions of one multipole change the electromagnetic environment of another, the magnetic dipole and electric quadrupole are strongly coupled. When a quadrupolar nucleus is placed in a magnetic field so that the nuclear spin is.quantized along the magnetic field direction rather than the efg symmetry axis, the nuclear magnetic energy levels depend on both the efg and the field Bo.

Like cr, J, and D, the efg is a tensor, and like D it is traceless: the isotropic average of energy terms involving the efg is zero. Thus in the liquid phase the positions of the lines in the NMR spectrum are not affected by the nuclear quadrupole coupling; NMR (and NQR) studies of quadrupolar splittings must be done in the solid state, often at low temperature. In the liquid phase the changes in the local efg with molecular motions induce transitions between the different M j states, and this is quadrupolar relaxation (Section 2.5.4). If very rapid, it causes broadening of the NMR line, which is related to Heisenberg's uncertainty principle. Because of the very

8 G G

0 e----8L e G $-"8 : :1 2q q G .... Gq 8 0 G

eO qP

Figure 5. Two forms of electric quadrupole oriented in an electric field gradient. eQ = qf2.

THE PARAMETERS OF NMR SPECTROSCOPY

E

1

" = 0

.' .

------

" =F 0

..!. X7l 1

~)( (1 7]/3)

Figure 6. "Pure quadrupole" transitions for a nucleus with 1= 1 where X is NQCC.

13

frequent transitions, the lifetime bt in the excited state is short, and this gives an uncertainty bE in the energy:

(bE)(bt)~n/2

which corresponds to an uncertainty in the frequency (bE = h bv). The magnitude of the quadrupolar interaction is therefore of great importance to NMR spectroscopy.

The nuclear quadrupole coupling constant (NQCC) is a tensor quantity related to the efg tensor. In frequency units

where q zz is the maximum component of the efg tensor q with principal components in the order Iqzzl ~ Iqyyl ~ Iqxxl. The efg tensor is specified by all three components, or else by the largest, qZZ' and an asymmetry parameter which lies between 0 and 1, being defined by

Since the NQCC depends not only on the nuclear quadrupole moment Q, but also on the chemical environment of the nucleus, quadrupole couplings can vary greatly for the same nucleus. Moreover, the NQCC tensor contains useful chemical information on the disposition of bonding and non bonding electrons which determine the efg. Thus for 14N, with 1= 1, the NQCC is small (a few kHz) in the symmetrical environ-ment of the ammonium ion 14NHt, small also in linear groups (as in R - N =: C), but larger (about 9 MHz) in very asymmetric locations, as in NHF 2'

NQCC values generally range from 106 to 109 Hz, tending to be larger for heavier nuclei. For small molecules e2qQ and '1 can be measured as hyperfine splittings in molecular beam magnetic or electric resonance, or by microwave spectroscopy, since the nuclear spin is coupled to the angular momentum of the rotating molecule. Quadrupole splitting is observed also in Mossbauer spectroscopy. NQR spectroscopy has become a more sensitive technique in recent years. (20) Pulsed double resonance methods can give high-resolution spectra for light nuclei such as 2H or 170, even in natural abundance, and even for frozen liquid samples which are not amenable to dif-fraction methods because of the lack of long-range order. Thus organic and biomolecules can now be studied, as well as heavier nuclei, with NQR usefully com-plementing NMR spectroscopy.

14 CHAPTER 2

In solid-state NMR spectroscopy the quadrupolar interaction, if less than 100 kHz, say, can be taken as a perturbation of the Zeeman interaction (the "high-field case"). (2) Perturbation theory then gives the contribution to the energy (for axial symmetry of the efg, with '1 = 0) as follows:

in first order, E(1) = e2qQh(3 cos2 e - I )[3M; - 1(/ + I )]/8/(21 - I); in second order, E(2) is a more complex expression in (e2qQ)2jy and M;. Whereas the (zero-order) resonance condition for a quadrupolar nucleus gives a single line at the Larmor frequency Vo for AM/= l, the first-order quadrupolar interaction gives a series of 21 lines with quadrupolar shifts vQ such that (for '1 = 0)

v = Vo + vQ for the transition M/--+ M/-I

where

Thus a spin-l nucleus eH, 6Li, 14N) gives a doublet with the splitting (for '1 = 0)

For half-integral spins (l = 3/2,5/2, ... ) the frequency of the central line (+! --+ -!) is unchanged to first order, since the expression for v Q vanishes if M/ =!; the other two lines appear as symmetrical satellites (Figure 7). The intensities are in the ratio 3:4:3 for spin 3/2, 5:8:9:8:5 for spin 5/2, and so onY) The satellites are broadened by molecular motions or crystal imperfections, and for large splittings may disappear out of the observable range.

Second-order quadrupolar interactions may be observed if the quadrupole coupling is larger, relative to the Zeeman splitting. The second-order interaction shifts the entire line ( +! --+ -!) but leaves the separation of the satellites unchanged (the components are equally spaced when the energies depend on an odd power of M/). An interesting example of a second-order quadrupole coupling is that of the 27 Al (l = 5/2) spectrum of AIN. Because of the high (hexagonal) symmetry the first-order quadrupolar interac-tion is absent. Only the (+! --+ -!) transitions were observed giving the NQCC as 280 kHz for the aluminum. (21)

(-t -})

l ________ ., I ,

. .. xJ4

Figure 7. First-order quadrupole coupling for a nucleus with 1=3/2, Y > 0, and axial symmetry. (a) Zeeman splitting with and without quadrupolar shifts; (b) broadened powder spectrum. X is NQCC.

THE PARAMETERS OF NMR SPECTROSCOPY 15

For some time the measurement of quadrupole splittings in NMR spectra lay effectively in the domain of the physicist, but recent advances are making chemical applications less difficult. Linewidths of a few kilohertz due to dipolar, quadrupolar, or anisotropy broadening may be reduced to 100 Hz or less by the use of higher fields (the second-order interaction is inversely proportional to the field), and by techniques such as high-power irradiation or magic angle spinning, which are discussed in Sec-tions 5 and 6. With the appropriate instrumentation, quadrupole couplings of 1 MHz or less (as for 2H or 14N) are well resolved. Thus a range of e2qQ and 11 values has now been recorded for 14NHt in different crystals, the variations in efg arising from distortion of the N-H bonds, notably by hydrogen bonding to oxygen. (22)

2.5. Relaxation

The importance of relaxation in NMR spectroscopy may be illustrated by the story of C. 1. Gorter, who failed to discover nuclear magnetic resonance in bulk matter in the 1930s and 1940s largely because-owing to the long relaxation time of his specimens(23)-the resonances saturated. Equally hazardous are relaxation times that are too short, as the resonances may then be broadened out of existence by the uncer-tainty in the energy.

As mentioned in Section 1, spontaneous emission is rare at radiofrequencies. In spin-lattice relaxation, nuclei transfer spin energy to the medium or "lattice" by a matching of Larmor frequencies, notably by the rotating fields of nearby magnetic nuclei as the molecules tumble in Brownian motion. These fields can have large local values at any instant, although they average to zero overall. The proton is highly effec-tive because of its large magnetogyric ratio and close approach. Much more effective are unpaired electrons, and paramagnetic materials may only be present in small amounts in NMR experiments. In solids at low temperatures spin-lattice relaxation can be very slow indeed in the absence of paramagnetic impurities.

Relaxation processes follow an exponential law in principle, the rate depending on the excess (n) of excited nuclei compared to the number at thermal equilibrium:

dnldt= -niT

so that the excess at time t after an excitation is given by

nt = no exp( - tiT) where n = no at t = O. T is a time constant characteristic of the system, such that the relaxation rate is T- 1 T I , the spin-lattice relaxation time, gives the rate at which the magnetization M z in the direction of the applied field Bo returns to its equilibrium value after excitation, by loss of spin energy to other degrees of freedom. TI is thus a longitudinal relaxation time, and a corresponding transverse relaxation time T2 is defined by the rate of loss of magnetization in the xy plane. (24)

In nonviscous liquids, Tl and T2 are approximately equalized by the molecular motions. They are not necessarily equal, since the radiofrequency (applied in the x direction) which induces the nuclear transitions also makes the nuclei precess in phase in the xy plane, the spectrometer observes the rate of loss of the phase-coherence, and this rate may differ from that of the longitudinal relaxation. Thus another name for T2 is the spin-spin relaxation time, because of the contribution from the exchange of spin energy between adjacent antiparallel nuclei, with loss of the phase coherence induced

16 CHAPTER 2

by the excitation, and increase in entropy, but no loss of spin energy to the lattice. This spin exchange is an important mechanism of relaxation and line-broadening in solids, in which the nuclei maintain their relative positions, and T J values may be long. In these circumstances T2 ~ T J On the other hand, very efficient spin-lattice relaxation (electron-nuclear, J coupling to a quadrupolar nucleus, or chemical exchange) can shorten T J relative to T2

The natural shape of the NMR signal is Lorentzian, as for damped oscillations, and the line width at half-height is given by

A further contribution to the linewidth and to T2 is made by the range of the static dipolar fields in solids, and of the local fluctuating fields in liquids. These may rein-force or oppose the applied field, and so correspond to a range of resonance frequen-cies. In practice an effective T2 value called Tt is obtained from the observed linewidth, and includes also the contribution from instrumental imperfections, par-ticularly the inhomogeneity of the applied field. (This is a problem for high-resolution NMR spectroscopy, and is reduced by sample spinning.)

2.5.1. Dipole-Dipole Relaxation

Various sources of local fields which can induce relaxation are given in Table 1, the observed relaxation rate Ti(~bs) being the sum of the rates contributed by the mechanisms that are operative.

The major relaxation mode for spin-! nuclei, if one or both have large enough y values, is by direct dipole-dipole interaction DD with neighboring spins in random motion (rotations, translations, and collisions) and sometimes in molecular fluxions or chemical exchange. Detailed mathematical description of the motion is complex, (2) particularly when rotations are anisotropic. It is usefully approximated in terms of average values of an angular frequency OJ and a correlation time, during which a local field is maintained or "remembered." From the range of frequencies that are present, relaxation occurs at the Larmor frequency OJo = yBo.

The function 2,j(1 + OJ2,~) which gives the dependence of T J on the fluctuating local fields has a maximum value (relaxation is most efficient) at OJ'c ~ 1. Thus T J is shortest for 'c ~ 10- 8 s, at NMR operating frequencies of ca. 108 Hz: it is most favorable, in fact, for large molecules such as lighter polymers, or biomolecules. Spin-! nuclei which are difficult to observe because relaxation is too slow (J83W for example) may be easier to study in very viscous solution.

For faster molecular motions TlDo lengthens, and becomes independent of fre-quency for OJ'c < 1 (i.e., ,~1O- 8 s). This is called the extreme narrowing condition, as T2 then becomes equal to T J , and the fast motions average the local fields, the range of which contributes to line broadening (this is motional narrowing). T2 depends on ,)(1 + OJ2,~) as T J does, but the contribution to T2 from dephasing of the spins requires an additional '( dependence that is independent of frequency OJ.

For slower molecular motions (OJ, > 1) T2 decreases further, then levels off as the dipolar interactions approach those in solids. TJ , however, increases from its minimum value, and becomes dependent on OJ 2 Thus high-field working may be dis-advantageous for large molecules because of long relaxation times.

Mec

ham

sm

Dlp

ole-

2

nJ

Quad

rupo

lar (Q

)

Tabl

e 1.

M

echa

msm

s o

f Spm

-Lat

tlce

Rel

axat

IOn

Rat

e de

pend

ence

a

For

spm

-! n

ucl

elb

nsJI;J

I~rIS6

,< N

sJl;JI

~/DRls

whe

re D

=kT

/6V'

1m

NsJl7J

l~rrrk

6,< (r

ot)

N sJ

l; Jl~r

r/ DR

IS (t

ransl)

IC

zkT'

t SR

whe

re C

OCJlI

Jl

rB~(

AoY '

c

S(S+

1) P

'eJ[

1 +

('ex

Aw)2

J

S(S

+ l)

PT q

/[1 +

('qA

w)ZJ

For

spm

>!

nucl

ei

[(NQC

C)2(

l +'1

2/3)

(21+

3)/1

2(2/

-1)]

'<

Exam

ples

S=

)H

0z,

rela

xatIO

n re

age

nts

P4

195 p

t m

pla

nar

com

plex

es

13C7

9Br

All

I> 1

/2 n

ucl

ei

Com

men

ts

ns IS

the

nu

mbe

r o

f S

nu

clei

N

s IS

co

ncen

trat

IOn

R)s I

S th

e di

stan

ce o

f clo

sest

app

roac

h D

= (D

) + D

s)/2

IS th

e m

utu

al t

rans

latIO

nal

dif-

fUSI

On

coef

fiCie

nt

for

sphe

ncal

m

ole

cule

s o

f v

olu

me

V '1m

= m

lcro

vlsc

oslty

'" 0

16

x m

acro

vls

cosl

ty fo

r pur

e liq

uids

'<

I = 'r

) + "

I,

whe

re "

IS

the

corr

elat

IOn

time

for

the

un

pair

ed e

lect

ron

1 IS

the

mo

men

t o

f m

ertI

a, C

the

spm

-rot

atlO

n co

upl

ing

co

nst

ant

(or t

enso

r ele

men

ts t

here

of)

TdT

z=

7/

6

'ex

IS t

he e

xcha

nge

lifet

ime

Aw

IS t

he d

iffer

ence

m re

son

an

ce f

requ

enci

es o

f 1

an

d S

spm

s

NQC

C =

eZq

Q/h,

'1 IS

the

asy

mm

etry

par

amet

er

a Fo

r lIq

UId

s In

the

ex

trem

e n

arr

ow

Ing

lImIt

(02

r2 ~

1) N

ote

that

co

rrel

atIO

n tIm

es r

fo

r dI

ffere

nt re

laxa

tIOn

mecha

msm

s are

no

t n

ecess

an

ly th

e sa

me

All

rota

tIO

nal c

orr

ela

tIOn

tImes

r

depe

nd o

n

(vlsc

oslty

/kT)

h Th

e fa

ctor

/(1

+ I

) = 3/

4 ha

s be

en o

mIt

ted

~ ;: i ~ ; ~ ~ o ~ --.....I

18 CHAPTER 2

2.5.2. Relaxation by Paramagnetic Agents

Most efficient in dipole-dipole relaxation is an unpaired electron, with its large magnetic moment (f.1B/f.1N= 1836). If close to a nuclear spin (in a free radical or paramagnetic ion, say), the electron-nuclear interaction may outweigh the Zeeman effect and ESR replaces NMR spectroscopy. If less close, the effective electron magnetic moment replaces y s in the dipole-dipole relaxation rate (see Table 1), and 1:; I includes a contribution from the relaxation of the electron. There is a contact con-tribution also if the unpaired electron is close enough to the resonant nucleus. (25) Paramagnetic materials may be present incidentally-dissolved oxygen for example, or transition metal impurities as from a nickel spatula-or they may be deliberately added, for example to promote relaxation when this is too slow (as in unprotonated materials). For nonpolar solvents, a fairly nonspecific unreactive relaxation reagent is [Cr(pd)3]' * which does not broaden or shift the lines unduly; suitable lanthanide ions may be used in polar solvents. Relaxation reagents which form complexes with the species of interest may be used to probe particular centers in the molecule; the exchange rate 1: All may then contribute to 1:;1.(26)

2.5.3. Other Mechanisms of Relaxation for Spin-! Nuclei Other relaxation mechanisms come into play when dipole-dipole relaxation is less

efficient. The spin-rotation (SR) interaction is important for spin-! nuclei in smaller molecules, particularly in the gas phase. The nucleus experiences magnetic fields due to the differential rotation of charge with the molecular frame, and fluctuations of these fields, as with collisions, induce relaxation. This mechanism is distinguished by increase in the rate with increase in temperature and with decrease in viscosity, in con-trast to the mechanisms depending on molecular tumbling. This is because the mechanism is more effective with increased population of the higher rotational states. The rate depends on the spin-rotation coupling tensor (C) and its anisotropy (as the square) and appropriate moments of inertia (I), values of which may be available from rotational spectroscopy.

Anisotropy in the shielding of a nucleus affords a mechanism of relaxation with molecular tumbling, and may be observed for 13C in metal carbonyls, transition metals in planar complexes, etc. The shielding anisotropy (SA) relaxation rate depends on B6, and may be monitored by measurements at different field strengths. At higher fields it may be large enough to broaden the resonance with loss of spin-spin coupling if 1: c is large, as in solutions of planar complexes of 195Pt, for which Aa was measured as ca. 103 ppm in the solid state. (27)

Scalar or J coupling of the observed nucleus to a neighboring spin S which is fluctuating rapidly with 1: -I > J washes out the splitting and can induce relaxation. (2) This scalar relaxation may arise through chemical exchange of the spin S, with

1:~ I> J. Scalar relaxation of the second kind is observed if the S spin is relaxing rapidly because quadrupolar, and has a Larmor frequency close to that of the /( =!) spin, as in 13C_79Br.

* pd is 2,4-pentanedionate, (CH3COCHCOCH 3)-.

THE PARAMETERS OF NMR SPECTROSCOPY 19

2.5.4. Quadrupolar Relaxation For the inorganic or organometallic chemist the most important relaxation

mechanism may well be the quadrupolar relaxation of I>! nuclei. This normally dominates over all other mechanisms, so that Tq( = TI ~ T2 ) determines the linewidth. As described in Section 2.4, relaxation of the nuclear electric quadrupole with changes in the local electric field gradient (efg) also relaxes the nuclear spin. The consequent line broadening, with loss of information from spin-spin coupling and smaller chemical shifts, has inhibited NMR studies of quadrupolar nuclei.

The rate of quadrupolar relaxation (Table 1) increases as the square of the NQCC. Line broadening due to a large value of Q may be offset by a large I value, the line-broadening jactor(28) being

where j(l) = (21 + 3)/12(21 -1)

the function of I decreasing from 5 for 1=1 to 0.075 for 1=9/2. Since the quadrupolar relaxation rate increases also with To the lines are usually

broadened significantly by increase in viscosity, and higher temperatures are then advantageous.

Because of the dependence on the efg, high-resolution spectroscopy is possible for fairly weakly quadrupolar nuclei if the electronic environment is sufficiently symmetric. Examples are 2H, 6,7Li, 9Be, 14N, 170, or 133CS. Indeed, quadrupolar relaxation for aqueous 6Li + is so inefficient that relaxation times of 1000 s have been observed. (29) Asymmetry of the efg is marked for atoms carrying lone pair electrons with s charac-ter. Thus 14N lines are sharp for NHt but quite broad (W1/2 ca. 200 Hz) for pyridine. The lines for monocovalent bromine or iodine are usually broadened out of existence, but can be observed for aqueous 1- and 14 , for example, because of the high local symmetry (Chapter 17).

3. THE LARMOR PRECESSION AND THE BLOCH EQUATIONS

To understand the potentialities of FT pulsed NMR spectroscopy(30,31) (and to see the full significance of the two relaxation times TI and T 2 ) we need to consider the precession of the nuclear spins. In Figure 8 the nuclear spin angular momentum is shown as a vector at an angle to the z axis such that its projection takes the values

z

'J---y

x

Figure 8. Orientation of a nuclear spin vector,

20 CHAPTER 2

M[ = -I, ... , + I. According to the uncertainty principle, if the z component is specified, then the x and y components are undetermined: the vector may be oriented in any direction at the same angle to the z axis, and so lies somewhere on the surface of a cone.

If a magnetic field Bo is then applied in the z direction the spin vector