Spin Dynamics E-Book

Malcolm H. Levitt

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 971

Veröffentlichungsjahr: 2013

Beschreibung

Spin Dynamics: Basics of Nuclear Magnetic Resonance, Second Edition is a comprehensive and modern introduction which focuses on those essential principles and concepts needed for a thorough understanding of the subject, rather than the practical aspects. The quantum theory of nuclear magnets is presented within a strong physical framework, supported by figures. The book assumes only a basic knowledge of complex numbers and matrices, and provides the reader with numerous worked examples and exercises to encourage understanding. With the explicit aim of carefully developing the subject from the beginning, the text starts with coverage of quarks and nucleons and progresses through to a detailed explanation of several important NMR experiments, including NMR imaging, COSY, NOESY and TROSY. Completely revised and updated, the Second Edition features new material on the properties and distributions of isotopes, chemical shift anisotropy and quadrupolar interactions, Pake patterns, spin echoes, slice selection in NMR imaging, and a complete new chapter on the NMR spectroscopy of quadrupolar nuclei. New appendices have been included on Euler angles, and coherence selection by field gradients. As in the first edition, all material is heavily supported by graphics, much of which is new to this edition. Written for undergraduates and postgraduate students taking a first course in NMR spectroscopy and for those needing an up-to-date account of the subject, this multi-disciplinary book will appeal to chemical, physical, material, life, medical, earth and environmental scientists. The detailed physical insights will also make the book of interest for experienced spectroscopists and NMR researchers. * An accessible and carefully written introduction, designed to help students to fully understand this complex and dynamic subject * Takes a multi-disciplinary approach, focusing on basic principles and concepts rather than the more practical aspects * Presents a strong pedagogical approach throughout, with emphasis placed on individual spins to aid understanding * Includes numerous worked examples, problems, further reading and additional notes Praise from the reviews of the First Edition: "This is an excellent book... that many teachers of NMR spectroscopy will cherish... It deserves to be a 'classic' among NMR spectroscopy texts." NMR IN BIOMEDICINE "I strongly recommend this book to everyone...it is probably the best modern comprehensive description of the subject." ANGEWANDTE CHEMIE, INTERNATIONAL EDITION

Leseprobe

Contents

Preface

Preface to the First Edition

Introduction

Part 1: Nuclear Magnetism

1 Matter

1.1 Atoms and Nuclei

1.2 Spin

1.3 Nuclei

1.4 Nuclear Spin

1.5 Atomic and Molecular Structure

1.6 States of Matter

2 Magnetism

2.1 The Electromagnetic Field

2.2 Macroscopic Magnetism

2.3 Microscopic Magnetism

2.4 Spin Precession

2.5 Larmor Frequency

2.6 Spin–Lattice Relaxation: Nuclear Paramagnetism

2.7 Transverse Magnetization and Transverse Relaxation

2.8 NMR Signal

2.9 Electronic Magnetism

3 NMR Spectroscopy

3.1 A Simple Pulse Sequence

3.2 A Simple Spectrum

3.3 Isotopomeric Spectra

3.4 Relative Spectral Frequencies: Case of Positive Gyromagnetic Ratio

3.5 Relative Spectral Frequencies: Case of Negative Gyromagnetic Ratio

3.6 Inhomogeneous Broadening

3.7 Chemical Shifts

3.8 J-Coupling Multiplets

3.9 Heteronuclear Decoupling

Part 2: The NMR Experiment

4 The NMR Spectrometer

4.1 The Magnet

4.2 The Transmitter Section

4.3 The Duplexer

4.4 The Probe

4.5 The Receiver Section

4.6 Overview of the Radio-Frequency Section

4.7 Pulsed Field Gradients

5 Fourier Transform NMR

5.1 A Single-Pulse Experiment

5.2 Signal Averaging

5.3 Multiple-Pulse Experiments: Phase Cycling

5.4 Heteronuclear Experiments

5.5 Pulsed Field Gradient Sequences

5.6 Arrayed Experiments

5.7 NMR Signal

5.8 NMR Spectrum

5.9 Two-Dimensional Spectroscopy

5.10 Three-Dimensional Spectroscopy

Part 3: Quantum Mechanics

6 Mathematical Techniques

6.1 Functions

6.2 Operators

6.3 Eigenfunctions, Eigenvalues and Eigenvectors

6.4 Diagonalization

6.5 Exponential Operators

6.6 Cyclic Commutation

7 Review of Quantum Mechanics

7.1 Spinless Quantum Mechanics

7.2 Energy Levels

7.3 Natural Units

7.4 Superposition States and Stationary States

7.5 Conservation Laws

7.6 Angular Momentum

7.7 Spin

7.8 Spin-1/2

7.9 Higher Spin

Part 4: Nuclear Spin Interactions

8 Nuclear Spin Hamiltonian

8.1 Spin Hamiltonian Hypothesis

8.2 Electromagnetic Interactions

8.3 External and Internal Spin Interactions

8.4 External Magnetic Fields

8.5 Internal Spin Hamiltonian

8.6 Motional Averaging

9 Internal Spin Interactions

9.1 Chemical Shift

9.2 Electric Quadrupole Coupling

9.3 Direct Dipole–Dipole Coupling

9.4 J-Coupling

9.5 Spin–Rotation Interaction

9.6 Summary of the Spin Hamiltonian Terms

Part 5: Uncoupled Spins

10 Single Spin-1/2

10.1 Zeeman Eigenstates

10.2 Measurement of Angular Momentum: Quantum Indeterminacy

10.3 Energy Levels

10.4 Superposition States

10.5 Spin Precession

10.6 Rotating Frame

10.7 Precession in the Rotating Frame

10.8 Radio-frequency Pulse

11 Ensemble of Spins-1/2

11.1 Spin Density Operator

11.2 Populations and Coherences

11.3 Thermal Equilibrium

11.4 Rotating-Frame Density Operator

11.5 Magnetization Vector

11.6 Strong Radio-Frequency Pulse

11.7 Free Precession Without Relaxation

11.8 Operator Transformations

11.9 Free Evolution with Relaxation

11.10 Magnetization Vector Trajectories

11.11 NMR Signal and NMR Spectrum

11.12 Single-Pulse Spectra

12 Experiments on Non-Interacting Spins-1/2

12.1 Inversion Recovery: Measurement of T1

12.2 Spin Echoes: Measurement of T2

12.3 Spin Locking: Measurement of T1ρ

12.4 Gradient Echoes

12.5 Slice Selection

12.6 NMR Imaging

13 Quadrupolar Nuclei

Part 6: Coupled Spins

14 Spin-1/2 Pairs

14.1 Coupling Regimes

14.2 Zeeman Product States and Superposition States

14.3 Spin-Pair Hamiltonian

14.4 Pairs of Magnetically Equivalent Spins

14.5 Weakly Coupled Spin Pairs

15 Homonuclear AX System

15.1 Eigenstates and Energy Levels

15.2 Density Operator

15.3 Rotating Frame

15.4 Free Evolution

15.5 Spectrum of the AX System: Spin-Spin Splitting

15.6 Product Operators

15.7 Thermal Equilibrium

15.8 Radio-Frequency Pulses

15.9 Free Evolution of the Product Operators

15.10 Spin Echo Sandwich

16 Experiments on AX Systems

16.1 COSY

16.2 INADEQUATE

16.3 INEPT

16.4 Residual Dipolar Couplings

17 Many-Spin Systems

17.1 Molecular Spin System

17.2 Spin Ensemble

17.3 Motionally Suppressed J-Couplings

17.4 Chemical Equivalence

17.5 Magnetic Equivalence

17.6 Weak Coupling

17.7 Heteronuclear Spin Systems

17.8 Alphabet Notation

17.9 Spin Coupling Topologies

18 Many-Spin Dynamics

18.1 Spin Hamiltonian

18.2 Energy Eigenstates

18.3 Superposition States

18.4 Spin Density Operator

18.5 Populations and Coherences

18.6 NMR Spectra

18.7 Many-Spin Product Operators

18.8 Thermal Equilibrium

18.9 Radio-Frequency Pulses

18.10 Free Precession

18.11 Spin Echo Sandwiches

18.12 INEPT in an I2S System

18.13 COSY in Multiple-Spin Systems

18.14 TOCSY

Part 7: Motion and Relaxation

19 Motion

19.1 Motional Processes

19.2 Motional Time-Scales

19.3 Motional Effects

19.4 Motional Averaging

19.5 Motional Lineshapes and Two-Site Exchange

19.6 Sample Spinning

19.7 Longitudinal Magnetization Exchange

19.8 Diffusion

20 Relaxation

20.1 Types of Relaxation

20.2 Relaxation Mechanisms

20.3 Random Field Relaxation

20.4 Dipole–Dipole Relaxation

20.5 Steady-State Nuclear Overhauser Effect

20.6 NOESY

20.7 ROESY

20.8 Cross-Correlated Relaxation

Part 8: Appendices

Appendix A: Supplementary Material

A.1 Euler Angles and Frame Transformations

A.2 Rotations and Cyclic Commutation

A.3 Rotation Sandwiches

A.4 Spin-1/2 Rotation Operators

A.5 Quadrature Detection and Spin Coherences

A.6 Secular Approximation

A.7 Quadrupolar Interaction

A.8 Strong Coupling

A.9 J-Couplings and Magnetic Equivalence

A.10 Spin Echo Sandwiches

A.11 Phase Cycling

A.12 Coherence Selection by Pulsed Field Gradients

A.13 Bloch Equations

A.14 Chemical Exchange

A.15 Solomon Equations

A.16 Cross-Relaxation Dynamics

Appendix B: Symbols and Abbreviations

Answers to the Exercises

Supplemental Images

Index

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Library of Congress Cataloging-in-Publication Data

Levitt, Malcolm H.

Spin dynamics : basics of nuclear magnetic resonance / Malcolm H. Levitt.

– 2nd ed.

p. cm.

Includes bibliographical references.

ISBN 978-0-470-51118-3 (hb : acid-free paper) – ISBN 978-0-470-51117-6 (pbk : acid-free paper)

1. Nuclear spin. 2. Nuclear magnetic resonance. I. Title.

QC793.3.S6L47 2007

538’.362-dc22

2007022146

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 9780470511183 HB

9780470511176 PB

To my mother and father

Preface

In this second edition I have tried to address some of the deficiencies of the first edition, but without disturbing the structure of the text too much. I have now included an overview of the NMR of quadrupolar nuclei, given the important subject of pulsed field gradients more prominence, and addressed the subject of spin-1/2 pairs in solids more thoroughly. It is a complex task to revise a large book, and I am not sure whether I have been successful. Let’s see what you think.

I am very grateful to all the people who pointed out errors in the first edition, which I hope to have corrected in this new version. These include Juan Alberdi, Bernard Ancian, Stefan Berger, Tom Bloemberg, Geoffrey Bodenhausen, Dave Bryce, Shidong Chu, Andre Dorsch, Nick Higham, Vladimir Hnizdo, Eric Johnson, Alan Kenwright, Karel Klika, Olivier Lafon, Linda Lai, Young Lee, Phil Lucht, Slobodan Macura, P. K. Madhu, Ian Malcolm, Arnold Maliniak, Emi Miyoshi, Gareth Morris, Norbert Müller, Juan Paniagua, Tanja Pietrass, Tatyana Polynova, E. J. Pone, Jan Rainey, Michael Roehrl, David Siminovitch, Chunpen Thomas, Bill Wallace, John Waugh, and Steven Wimperis. I also thank Zosia Beckles for help with the initial computer spadework.

As always, my research group and our research visitors have been a constant source of inspiration and enthusiasm. So I thank Giancarlo Antonioli, Jacco van Beek, Pauline Brouillaud, Darren Brouwer, Marina Carravetta, Maria Concistre, Andre Dorsch, Axel Gansmüller, Natala Ivchenko, Ole Johannessen, Per-Eugen Kristiansen, Linda Lai, P. K. Madhu, Salvatore Mamone, Ildefonso Marín-Montesinos, Giulia Mollica, and Giuseppe Pileio for your input. Many of the new sections in this book have derived from our group discussions.

Special thanks to Geoffrey Bodenhausen and Angelika Sebald for giving detailed criticism on the text. Thanks to P. K. Madhu for the photograph from India.

Fiona Woods and Andy Slade at Wiley have been patient, encouraging and helpful during the preparation of this edition.

As usual, I take sole responsibility for any errors and omissions.

Finally, I thank my wife and daughter Latha and Leela again, for their renewed patience and support.

Technical Details

The book was written on Apple Macintosh© computers. The text was written in LaTeX©, using a large number of self-programmed macros. Most of the diagrams were drawn by the author using a combination of Mathematica© and Adobe Illustrator©. Errata and supplementary notes are available through the website www.mhl.soton.ac.uk

Preface to the First Edition

This book has a long prehistory. It began approximately 12 years ago, when I was persuaded by my friend (and squash court enemy) Jim Sudmeier, to give a short series of lectures on the basics of NMR at Tufts University in Boston, MA. The lectures were probably not a tremendous success, but I was inspired to write up the material as some sort of short book. I was naive enough to feel that I could probably cover the basics in perhaps 100 pages using a minimum of equations. I worked on this ‘proto-book’ for over a year in Cambridge, England, before I realised that I was only scratching the surface of the subject and that I was not yet prepared for the task.

The situation changed in Stockholm where I became involved in teaching an intensive course each year on NMR to third-year undergraduates. Over a period of around seven years I built up a large set of handwritten lecture notes. The experience of teaching made me realise how difficult it is to keep the subject accessible while still imparting something useful to those students wishing to continue into NMR research. Over many years I experimented with various permutations of the material until I ended up with a set of notes which form the basis of this book.

The bulk of the final writing was done in India where I enjoyed the hospitality of Professor Anil Kumar at the Indian Institute of Science in Bangalore for three months.

The book which emerged is still not precisely the one I wanted to write: I wanted to communicate the beauty and usefulness of NMR in a rather simple and non-mathematical way. In the end, I did not succeed at all in keeping down the number of equations. Teaching showed me that equations are simply the only way to present the subject clearly. Nevertheless, although some of the mathematics may look a little frightening to the uninitiated, I think none of it is truly difficult. Most workers in NMR, including myself, have somehow learnt to muddle through the mathematics without any formal training, and the mathematics given here is just a distillation of my own muddling.

The one thing more discouraging to students than anything else is bad terminology and notation, especially when its defects are not pointed out plainly. Faced with a confusing but accepted term, many students draw the conclusion that the problem lies in their own stupidity, rather in the true cause, which is often simple carelessness by its originators, amplified by uncritical perpetuation. This problem falls into a general pattern of teaching science as if everything is already understood and ‘engraved in stone’. I care too much about NMR to accept such a static view of the subject and I have tried to combat the most offending eyesores in this book. Some of these suggestions may be controversial with established workers in the field. Nevertheless, I stand by these suggestions and hope that they will catch on in time. I point out the following items here: (i) I consistently distinguish between ‘rate’ (the change in something over a small time interval, divided by the duration of that interval) and ‘rate constant’ (a factor appearing in a rate equation); (ii) I consistently distinguish between ‘time’ (needs no explanation) and ‘time constant’ (inverse of a rate constant); (iii) I consistently distinguish between a ‘time point’ and an ‘interval’ (which is the separation between two time points); (iv) I use the notation t for a time point, and τ for an interval (with the single exception of the evolution interval in a two-dimensional experiment, for which I use the widespread notation t1); (v) I consistently use the correct physical sign for the nuclear Larmor frequency, the correct physical sign for the spectral frequency axes, and the correct sign for all spin interactions; (vi) I change the sign of the cross-relaxation rate constant in the Solomon equations (Chapter 20), so as to bring it into line with a kinetic description; (vii) I avoid terminology such as ‘emission peak’, ‘rotating-frame experiment’, ‘phase-sensitive 2D experiment’, and ‘time-reversal experiment’ which are widely used in the field but which have no physical basis. I also avoid terminological fossils such as ‘low field’ and ‘high field’, whose original physical basis has been undermined by the development of NMR methodology, leaving them sadly marooned in a world in which they no longer make sense.

I have also not shied away from minor modifications of conventions for the sake of clarity. For example, I consistently use a deshielding convention for all elements of the chemical shift tensor, instead of using the deshielding convention for the isotropic chemical shift and the shielding convention for the chemical shift anisotropy, which seems to be the standard practice.

I have also introduced some novel notation, for example the ‘box notation’ for coherences in a weakly coupled system. I have personally used this notation for many years, and know that it is useful and that it works. However, I have only rarely used it in a scientific paper. Here, I am taking the opportunity of exposing it to a wider audience.

In one exceptional case I have allowed the convenience of the final equations, and consistency with most of the existing literature, to overrule the transparency of the physics: I have imposed mathematically positive rotations for r.f. pulses (the ‘Ernst convention’) by manipulating the definition of the rotating frame in a messy way.

Although I have tried to take care, I am sure that this book contains many remaining inconsistencies, and will be very grateful to be informed about them.

Another point of contention may be my presentation of quantum mechanics. In order to make NMR comprehensible I attack vigorously the widespread view that spin-1/2 particles only have two ‘allowed orientations’ (up and down). Quantum mechanics says no such thing but it is surprising how emotionally this view can be defended. Emotions may also be inflamed over my very ‘physical’ discussion of the dynamics of single spins. I have been told in all seriousness that quantum mechanics ‘forbids’ any such discussions. My view is that quantum mechanics is not understood in its completeness by anyone and that the field is wide open to any physical interpretation, as long as that interpretation is demonstrably useful in a particular situation. The interpretation presented in Chapter 9 and the following chapters is neither radical nor original, but is nevertheless very useful for understanding NMR. I am fully aware that this physical picture runs into trouble in certain situations (such as the observation of non-local entangled spin states, as in the Einstein–Rosen–Podolosky paradox). Nevertheless, the ‘arrow’ picture of a single spin is demonstrably useful over the limited domain of NMR, and I regularly use it myself in thinking about old experiments and developing new ones.

Since NMR is an enormous subject, I have had to select only a very few experiments for detailed discussion. Both my selection of topics and the very basic level at which many of these are treated will probably annoy the specialists. For this I can only apologize. I could simply manage no more material at this stage.

One point on which I am personally dissatisfied is how little I manage to say about solid-state NMR, which is my own main research interest. I had considered having a brief review of the field in a single chapter. However, I decided against that, since it became rapidly clear that I could not maintain a comparable depth of discussion without greatly increasing the size of the book. So I will have to defer the treatment of solid-state NMR to another time, maybe another book.

One remark on my literature referencing: I have been very sparse, and have generally tried to restrict myself to sources that I think will be useful to the reader. The references do not indicate the priority of some group in a particular area.

There are many people other than myself who have contributed to this book. As I mentioned above, the whole thing grew out of a series of lecture notes. Those notes would never have condensed into a useful form without the participation and probing questions of the students I have taught in Stockholm, including Kai Ulfstedt-Jäkel, Tomas Hirsch, Baltzar Stevensson and Clas Landersjö. There are many others: unfortunately I don’t remember all of your names, but I do thank you if you read this. I did learn a lot from you all.

I do remember those students who went on to be my graduate students and co-workers, and I have relied over the years on your enthusiasm, support, and amazing hard work. Many of you have also made very specific and useful suggestions about this material. So thanks again to Zhiyan Song, Xiaolong Feng, Dick Sandstrom, Oleg Antzutkin, Mattias Eden, Torgny Karlsson, Andreas Brinkmann, Marina Carravetta, Xin Zhao, Lorens van Dam and Natala Ivchenko. I have also enjoyed the visits of many wonderful scientists, all of whom have contributed to this book in one way or another, at least in spirit. These include Young K. Lee, S. C. Shekar, K. D. Narayanan, Michael Helmle, Clemens Glaubitz, Angelika Sebald, Stefan Dusold, Peter Verdegem, Sapna Ravindranathan, Pratima Ramasubrahmanyan, Colan Hughes, Henrik Luthman, Jörn Schmedt auf der Günne and P. K. Madhu. I am extremely grateful to the critical reading and detailed suggestions of Gottfried Otting, Gareth Morris, Ole Johannessen, Arnold Maliniak, Dick Sandström, Maurice Goldman, Colan Hughes and Ad Bax. Thanks also to Melinda Duer for ploughing through the first (aborted) version of the book. I am also very grateful to Sapna Ravindranathan, Gottfried Otting, Warren Warren, Jianyun Lu and Ad Bax for supplying some of the figures. Special thanks to Anil Kumar for your hospitality in Bangalore and many delightful discussions. Very special thanks to Jozef Kowalewski for many years of invaluable support in Stockholm and for your constructive comments on the text.

Special thanks to Angelika Sebald for a very large number of insightful and constructive suggestions. Your knowledge and enthusiasm has been an inspiration.

In addition, I would like to thank Ray Freeman and Richard Ernst, from whom I learnt to think about NMR in two very different ways.

Although many people have commented on the text of this book, I take sole responsibility for any errors and omissions.

Finally, I thank my wonderful wife Latha and daughter Leela for your patience, understanding, advice, encouragement and help, as I climbed this personal mountain.

Introduction

Commonplace as such experiments have become in our laboratories, I have not yet lost that sense of wonder, and delight, that this delicate motion should reside in all ordinary things around us, revealing itself only to him who looks for it.

E. M. Purcell, Nobel Lecture, 1952

In December 1945, Purcell, Torrey and Pound detected weak radio-frequency signals generated by the nuclei of atoms in ordinary matter (in fact, about 1 kg of paraffin wax). Almost simultaneously, Bloch, Hansen and Packard independently performed a different experiment in which they observed radio signals from the atomic nuclei in water. These two experiments were the birth of the field we now know as nuclear magnetic resonance (NMR).

Before then, physicists knew a lot about atomic nuclei, but only through experiments on exotic states of matter, such as found in particle beams or through energetic collisions in accelerators. How amazing to detect atomic nuclei using nothing more sophisticated than a few army surplus electronic components, a rather strong magnet, and a block of wax!

In his Nobel Prize address, Purcell was moved to a poetic description of his feeling of wonder, cited above. He went on to describe how

in the winter of our first experiments… looking on snow with new eyes. There the snow lay around my doorstep – great heaps of protons quietly precessing in the Earth’s magnetic field. To see the world for a moment as something rich and strange is the private reward of many a discovery.

In the years since then, NMR has become an incredible physical tool for investigating matter. Its range is staggering, encompassing such diverse areas as brains, bones, cells, ceramics, inorganic chemistry, chocolate, liquid crystals, laser-polarized gases, protein folding, surfaces, superconductors, zeolites, blood flow, quantum geometric phases, drug development, polymers, natural products, electrophoresis, geology, colloids, catalysis, food processing, metals, gyroscopic navigation, cement, paint, wood, quantum exchange, phase transitions, ionic conductors, membranes, plants, micelles, grains, antiferromagnets, soil, quantum dots, explosives detection, coal, quantum computing, cement, rubber, glasses, oil wells and Antarctic ice.

Two brief examples may suffice here to show the range and power of NMR.

The first example is taken from functional NMR imaging. As explained in Section 12.6, it is possible to use the radio-frequency (r.f.) signals from the nuclei to build up a detailed picture of the three-dimensional structure of an object. The grey image given in Plate 1 shows this method applied to a human head, revealing the lobes of the brain inside the skull. The red and yellow flashes superimposed on the picture reveal differences in the NMR signals when the subject is performing some mental task, in this case processing the memory of a face that has just been removed from view. NMR can map out such mental processes because the brain activity changes slightly the local oxygenation and flow of the blood, which affects the precession of the protons in that region of the brain.

The second example illustrates the determination of biomolecular structures by NMR. Plate 2 shows the structure of a protein molecule in solution, determined by a combination of multidimensional NMR techniques, including the COSY and NOESY experiments described in Chapter 16 and 20. The structure is colour coded to reveal the mobility of different parts of the molecule, as determined by NMR relaxation experiments.

In this book, I want to provide the basic theoretical and conceptual equipment for understanding these amazing experiments. At the same time, I want to reinforce Purcell’s beautiful vision: the heaps of snow, concealing innumerable nuclear magnets, in constant precessional motion. The years since 1945 have shown us that Purcell was right. Matter really is like that. My aim in this book is to communicate the rigorous theory of NMR, which is necessary for really understanding NMR experiments, but without losing sight of Purcell’s heaps of precessing protons.

Part 1

Nuclear Magnetism

1 Matter

2 Magnetism

3 NMR Spectroscopy

1

Matter

1.1 Atoms and Nuclei

Matter is made of atoms. Atoms are made up of electrons and nuclei. Each atomic nucleus has four important physical properties: mass, electric charge, magnetism and spin.

The mass of bulk matter is largely due to the mass of the nuclei. A large number of other physical properties, such as heat capacity and viscosity, are strongly dependent on the nuclear mass.

The electric charge of atomic nuclei is supremely important. Atoms and molecules are bound together by strong electrostatic interactions between the positively charged nuclei and the negatively charged electrons. The chemical properties of each element are determined by the electric charge on the atomic nuclei.

The other two properties, nuclear magnetism and nuclear spin, are much less evident. The magnetism of a nucleus implies that it interacts with magnetic fields, like a small bar magnet. However, nuclear magnetism is very weak and is of little consequence for atomic or molecular structure. The bulk magnetism of some materials, such as iron, is due to the electrons, not to the nuclei.

The spin of the nucleus is even less tangible. The spin of a nucleus indicates that, very loosely speaking, the atomic nucleus behaves as if it is spinning around, rotating in space like a tiny planet.

Nuclear magnetism and nuclear spin have almost no effect on the normal chemical and physical behaviour of substances. Nevertheless, these two properties provide scientists with a wonderful tool for spying on the microscopic and internal structure of objects without disturbing them.

Magnetic nuclei interact with magnetic fields. These magnetic fields may come from the molecular environment, e.g. the surrounding electrons, or from other nuclear spins in the same molecule. Magnetic fields may also originate from sources outside the sample, such as an external apparatus. This book tells a small part of a long, complicated, and rather unlikely story: How the extremely weak magnetic interactions of atomic nuclei with the molecular environment on one hand, and with the spectrometer apparatus on the other hand, give access to detailed molecular information which is inaccessible by any other current method.

1.2 Spin

The concept of spin is difficult. It was forced upon scientists by the experimental evidence.1 Spin is a highly abstract concept, which may never be entirely ‘grasped’ beyond knowing how to manipulate the quantum mechanical equations.

Nevertheless, it is worth trying. NMR involves detailed manipulations of nuclear spins. The field has developed to a high level of sophistication, in part because of the possibility of thinking ‘physically’ and ‘geometrically’ about spins without being entirely wrong. Geometrical arguments can never tell the whole truth, because the human mind is probably incapable of grasping the entire content of quantum mechanics. Nevertheless, it is possible to acquire a feel for spin beyond a purely technical proficiency in the equations. In this book, I will try to communicate how I think one should think about nuclear spins, as well as presenting the technical mathematics.

1.2.1 Classical angular momentum

A rotating object possesses a quantity called angular momentum. This may be visualized as a vector pointing along the axis about which the object rotates; your right hand may be used to figure out which way the arrow points. If your thumb points along the rotation axis, then the right-hand fingers ‘wrap around’ in the direction of the rotation:

Figure 1.1 Macroscopic angular momentum.

1.2.2 Quantum angular momentum

In quantum mechanics, angular momentum is quantized. Consider, for example, a diatomic molecule:

Figure 1.2 A rotating molecule, its energy levels, and the Zeeman effect.

As described in many texts (see Further Reading), and discussed further in Chapter 7, a rotating diatomic molecule possesses a set of stable rotational states, in which the total angular momentum has one of the values