NMR Spectroscopy E-Book

Harald Günther

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 1085

Beschreibung

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and widely used techniques in chemical research for investigating structures and dynamics of molecules. Advanced methods can even be utilized for structure determinations of biopolymers, for example proteins or nucleic acids. NMR is also used in medicine for magnetic resonance imaging (MRI). The method is based on spectral lines of different atomic nuclei that are excited when a strong magnetic field and a radiofrequency transmitter are applied. The method is very sensitive to the features of molecular structure because also the neighboring atoms influence the signals from individual nuclei and this is important for determining the 3D-structure of molecules. This new edition of the popular classic has a clear style and a highly practical, mostly non-mathematical approach. Many examples are taken from organic and organometallic chemistry, making this book an invaluable guide to undergraduate and graduate students of organic chemistry, biochemistry, spectroscopy or physical chemistry, and to researchers using this well-established and extremely important technique. Problems and solutions are included.

Leseprobe

Table of Contents

Related Titles

Title Page

Copyright

Preface

Chapter 1: Introduction

1.1 Literature

1.2 Units and Constants

References

Part I Basic Principles and Applications

Chapter 2: The Physical Basis of the Nuclear Magnetic Resonance Experiment. Part I

2.1 The Quantum Mechanical Model for the Isolated Proton

2.2 Classical Description of the NMR Experiment

2.3 Experimental Verification of Quantized Angular Momentum and of the Resonance Equation

2.4 The NMR Experiment on Compact Matter and the Principle of the NMR Spectrometer

2.5 Magnetic Properties of Nuclei beyond the Proton

References

Chapter 3: The Proton Magnetic Resonance Spectra of Organic Molecules – Chemical Shift and Spin–Spin Coupling

3.1 The Chemical Shift

3.2 Spin–Spin Coupling

References

Chapter 4: General Experimental Aspects of Nuclear Magnetic Resonance Spectroscopy

4.1 Sample Preparation and Sample Tubes

4.2 Internal and External Standards; Solvent Effects

4.3 Tuning the Spectrometer

4.4 Increasing the Sensitivity

4.5 Measurement of Spectra at Different Temperatures

References

Textbooks

Review Articles

Chapter 5: Proton Chemical Shifts and Spin–Spin Coupling Constants as Functions of Structure

5.1 Origin of Proton Chemical Shifts

5.2 Proton–Proton Spin–Spin Coupling and Chemical Structure

References

Monograph

Review Articles

Chapter 6: The Analysis of High-Resolution Nuclear Magnetic Resonance Spectra

6.1 Notation for Spin Systems

6.2 Quantum Mechanical Formalism

6.3 The Hamilton Operator for High-Resolution Nuclear Magnetic Resonance Spectroscopy

6.4 Calculation of Individual Spin Systems

6.5 Calculation of the Parameters νi and Jij from the Experimental Spectrum

References

Textbooks

Review Articles

Chapter 7: The Influence of Molecular Symmetry and Chirality on Proton Magnetic Resonance Spectra

7.1 Spectral Types and Structural Isomerism

7.2 Influence of Chirality on the NMR Spectrum

7.3 Analysis of Degenerate Spin Systems by Means of 13C Satellites and H/D Substitution

References

Review Articles

Part II Advanced Methods and Applications

Chapter 8: The Physical Basis of the Nuclear Magnetic Resonance Experiment. Part II: Pulse and Fourier-Transform NMR

8.1 The NMR Signal by Pulse Excitation

8.2 Relaxation Effects

8.3 Pulse Fourier-Transform (FT) NMR Spectroscopy

8.4 Experimental Aspects of Pulse Fourier-Transform Spectroscopy

8.5 Double Resonance Experiments

References

Textbooks

Review articles

Chapter 9: Two-Dimensional Nuclear Magnetic Resonance Spectroscopy

9.1 Principles of Two-Dimensional NMR Spectroscopy

9.2 The Spin Echo Experiment in Modern NMR Spectroscopy

9.3 Homonuclear Two-Dimensional Spin Echo Spectroscopy: Separation of the Parameters J and δ for Proton NMR Spectra

9.4 The COSY Experiment – Two-Dimensional 1H,1H Shift Correlations

9.5 The Product Operator Formalism

9.6 Phase Cycles

9.7 Gradient Enhanced Spectroscopy

9.8 Universal Building Blocks for Pulse Sequences

9.9 Homonuclear Shift Correlation by Double Quantum Selection of AX Systems – the 2D-INADEQUATE Experiment

9.10 Single-Scan 2D NMR

References

Textbooks and Monographs

Methods Oriented

Application Oriented

Review articles

Chapter 10: More 1D and 2D NMR Experiments: the Nuclear Overhauser Effect – Polarization Transfer – Spin Lock Experiments – 3D NMR

10.1 The Overhauser Effect

10.2 Polarization Transfer Experiments

10.3 Rotating Frame Experiments

10.4 Multidimensional NMR Experiments

References

Textbooks

Review articles

Chapter 11:Carbon-13 Nuclear Magnetic Resonance Spectroscopy

11.1 Historical Development and the Most Important Areas of Application

11.2 Experimental Aspects of Carbon-13 Nuclear Magnetic Resonance Spectroscopy

11.3 Carbon-13 Chemical Shifts

11.4 Carbon-13 Spin–Spin Coupling Constants

11.5 Carbon-13 Spin–Lattice Relaxation Rates

References

Textbooks and Monographs

Review articles

Chapter 12: Selected Heteronuclei

12.1 Semimetals and Non-metals with the Exception of Hydrogen and Carbon

12.2 Main Group Metals

12.3 Transition Metals

References

Textbooks

Monographs

General Review Articles

Selected Review Articles dealing with Individual Nuclei not cited Above

Chapter 13: Influence of Dynamic Effects on Nuclear Magnetic Resonance Spectra

13.1 Exchange of Protons between Positions with Different Larmor Frequencies

13.2 Internal Dynamics of Organic Molecules

13.3 Intermolecular Exchange Processes

13.4 Line Broadening by Fast Relaxing Neighboring Nuclei

References

Textbooks

Review Articles

Chapter 14: Nuclear Magnetic Resonance of Partially Oriented Molecules and Solid State NMR

14.1 Nuclear Magnetic Resonance of Partially Oriented Molecules

14.2 High-Resolution Solid State Nuclear Magnetic Resonance Spectroscopy

References

Textbooks

Review Articles

Chapter 15:Selected Topics of Nuclear Magnetic Resonance Spectroscopy

15.1 Isotope Effects in Nuclear Magnetic Resonance

15.2 Nuclear Magnetic Resonance Spectroscopy of Paramagnetic Materials

15.3 Chemically Induced Dynamic Nuclear Polarization (CIDNP)

15.4 Diffusion-Controlled Nuclear Magnetic Resonance Spectroscopy – DOSY

15.5 Unconventional Methods for Sensitivity Enhancement – Hyperpolarization

15.6 Nuclear Magnetic Resonance in Biochemistry and Medicine

References

Review Articles

Appendix

1 The “Ring Current Effect” of the Benzene Nucleus

2 Tables of Proton Resonance Frequencies and Substituent Effects S(δ)

3 Tables of 1H,1H Coupling Constants

4 Chemical Shifts and Substuent Effects S(δ) of 13C Resonances in Organic Compounds

5 The Hamiltonian Operator in Polar Coordinates

6 Intensity Distribution in A-multiplets Caused by n Neighbouring X-Nuclei with Spin I = 1 or I =

7 Commutable Operators

8 The Fz Operator

9 Equations for the Direct Analysis of AA′BB′ Spectra

10 Bloch Equations

11 Bloch Equations Modified for Chemical Exchange

12 Phase Behavior of Cross Peaks in 2D Nuclear Overhauser Spectroscopy (NOESY), Rotating-Frame Overhauser Spectroscopy (ROESY), Total Correlation Spectroscopy (TOCSY) and Chemical Exchange (EXSY) Experiments

13 The International System (SI) of Units (MKSA System)

References

Solutions for Exercises

Glossary

Index

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The Author

Prof. em. Dr. Harald Günther

Fakultät IV, OC II

Universität Siegen

D-57068 Siegen

Germany

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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

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Hardcover ISBN: 978-3-527-33004-1

Softcover ISBN: 978-3-527-33000-3

Preface

When the first German edition of this textbook appeared in 1973, nuclear magnetic resonance was already a well established physical method in chemical research. In the years that followed, however, we witnessed unprecedented new developments of this technique with three outstanding advancements: the introduction of cryomagnets and the inventions of Fourier transform and multidimensional NMR. Further editions of this book covered these new aspects but the unbroken vitality of NMR required now a thorough revision of the last edition that was published in English in 1995.

The present text follows the original concept that tried to fill the reader with enthusiasm for applying NMR methods to solve chemical problems. Since this was not without success, the author kept this policy but has now considerably expanded the scope of this introduction. Furthermore, he took pains to eliminate errors contained in the last edition. After an Introduction, the first seven Chapters that concentrate on proton NMR are now united in Part I: Basic Principles and Applications. They are amended with new developments as, for example, the nucleus independent chemical shifts (NICS) and include the analysis of spin systems. They cover as before the basic theory of NMR and the material important for NMR beginners as well as for users primarily interested in the relations between NMR parameters and chemical structure. More emphasis was led on Fourier transform and high-field NMR and 2D experiments were introduced. Part II: Advanced Methods and Applications starts in Chapter 8 with a more detailed treatment of the physical background of NMR and of the pulse Fourier transform method. Chapters 9 and 10 are devoted to the introduction of advanced techniques like two-dimensional and nuclear Overhauser experiments. Chapter 11 deals with carbon-13 NMR and presents the heteronuclear 2D experiments. It also includes NMR results for fullerenes. A separate Chapter 13 then gives an overview of dynamic NMR.

The largest changes are the addition of the new Chapter 12 on NMR of selected heteronuclei, including transition metals. Chapter 14 on partially oriented molecules and solid state NMR has been complemented by a section on residual dipolar couplings, and Chapter 15 that contains—aside from the earlier accounts on NMR of paramagnetic materials and chemically induced nuclear polarization (CIDNP)—the description of special techniques like sensitivity enhancement by the use of para-hydrogen (PHIP), by optical pumping and by dynamic nuclear polarization (DNP). Moreover, experiments based on diffusion processes as well as diffusion-ordered spectroscopy (DOSY) are described and a final section gives an introductory overview of NMR in biochemistry and medicine.

In treating the material presented care was taken to keep the inclusion of the physical and mathematical background at an acceptable limit, especially since excellent physics-oriented textbooks are available. The book has then certainly a “chemical touch”, as a reviewer of a former edition put it, but this is just what the author intended. In the same way the description of technical aspects of the NMR spectrometer and of its operation were confined to an introductory level, again, because monographs and textbooks that treat these topics in more detail are at hand.

A few changes compared to the earlier editions and points where the text differs from conventions used in other NMR books must be mentioned. The low-energy orientation of the nuclear magnetic moment was now changed to be that parallel to the positive z-axis of the Cartesian coordinate system and to the direction of the external field B0, that is with the α-state as the ground state. To avoid a negative Hamiltonian, the reverse order, which has no consequences on the appearance of the spectrum, was kept in Chapter 5 when treating the analysis of spin systems. Throughout the text the left-hand-rule is used to describe the action of magnetic fields B on nuclear spins and in the coherence level diagrams the receiver is set at +1.

During the preparation of the present edition, the author received numerous support and encouragement that is gratefully acknowledged. Prof. H. Ihmels provided continued access to computer equipment as did Dra P. Olivares Guerrero and Dr. T. Paululat critically reviewed Chapter 4. Special advice was given by Prof. B. Wrackmeyer and Drs. J. Keeler and J. Schraml and valuable help in acquiring literature came from Dr. N. Schlörer. Material for three figures was kindly contributed by Profs. R.K. Harris and H. Rüterjans and Dr. W. Baumann. As acknowledged in former editions, my coworkers supplied a great number of the figures and to those already mentioned there I have to thank Drs. R. Aydin, T. Fox, W. Frankmölle, S. Jost, S. Oepen, P. Schmitt, and J.R. Wesener for new material. I am also most grateful to Profs. R.R. Ernst and K. Wüthrich for supplying their photographs and to the Physics Departments of Harvard University and The University of Illinois at Urbana Champaign for the photographs of E.M. Purcell and P.C. Lauterbur. Additional photographic material was kindly provided by Bruker Biospin and Siemens AG. Thanks are also due to the people engaged in the production process of the book and to the publisher for their cooperation. Last but not least I wish to thank my wife for continuously assisting with patience and advice my efforts to finish this project.

Siegen, June 2013

H. Günther

Chapter 1

Introduction

Of the important spectroscopic aids that are at the disposal of the chemist for use in structure elucidation, nuclear magnetic resonance (NMR) spectroscopy is one of the major tools. When, in December 1945 and in January 1946, two groups of physicists in the United States working independently – Edward M. Purcell, Howard C. Torrey, and Richard V. Pound at Harvard University on the US east coast and Felix Bloch, William W. Hansen, and Martin Packard at Stanford University in California – first succeeded in observing the phenomenon of NMR in solids and liquids they set the starting point for the unforeseen development of a new branch of science. The impact of their discovery was soon recognized and Bloch and Purcell received the Nobel Prize in Physics in 1952 (Figures 1.1 and 1.2).

Figure 1.1 The founding fathers of nuclear magnetic resonance: Felix Bloch (1905–1983) (a) (Reprinted with permission from Reference [1]. Copyright 1985 International Society of Magnetic Resonance.) and Edward M. Purcell (1912–1997) (b). Courtesy of Physics Department, Harvard University.

Figure 1.2 The first proton NMR signal from a water sample as seen on the screen of an oscilloscope by Bloch, Hansen, and Packard at Stanford University, California, USA, in January 1946 (Reprinted with permission from [2]. Copyright 1946 by the American Physical Society).

At the beginning of the 1950s, the phenomenon was called upon for the first time in the solution of a chemical problem. Since then its importance has steadily increased – a situation highlighted by three additional Nobel Prizes: in 1991 to Richard R. Ernst from the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland, for his outstanding contributions to the development of experimental NMR techniques, in 2002 to Kurt Wüthrich from the same institution for his contributions to structural biology, and in 2003 to Paul C. Lauterbur from the University of Illinois at Urbana-Champaign, and Sir Peter Mansfield, University of Nottingham, UK, for the invention of NMR imaging, known today as magnetic resonance imaging (MRI).

The physical foundation of NMR spectroscopy lies in the magnetic properties of atomic nuclei. The interaction of the nuclear magnetic moment with an external magnetic field, B0, leads, according to the rules of quantum mechanics, to a nuclear energy level diagram, because the magnetic energy of the nucleus is restricted to certain discrete values Ei, the so-called eigenvalues. Associated with the eigenvalues are the eigenstates, which are the only states in which an elementary particle can exist. They are also called stationary states. Through a radiofrequency (RF) transmitter, transitions between these states can be stimulated. The absorption of energy is then detected in an RF receiver and recorded as a spectral line, the so-called resonance signal (Figure 1.3).

Figure 1.3 Formation of an NMR signal.

In this way a spectrum can be generated for a molecule containing atoms whose nuclei have non-zero magnetic moments. Among these nuclei are the proton, 1H, the fluorine nucleus, 19F, the nitrogen isotopes, 14N and 15N, and many others of chemical interest. However, the carbon nucleus, 12C, that is so important in organic chemistry has, like all other nuclei with even mass and even atomic number, no magnetic moment. Therefore, NMR studies with carbon are limited to the stable isotope 13C, which has a natural abundance of only 1.1%.

To illustrate a NMR spectrum and its essential characteristics, the proton NMR spectrum of ethyl formate is reproduced in Figure 1.4. The spectrum was measured in a magnetic field of 1.4 T with a frequency ν of 60 MHz. In addition to the resonance signals observed at different frequencies, it shows a step curve produced by an electronic integrator. The heights of the steps are proportional to the areas under the corresponding spectral lines.

Figure 1.41H NMR spectrum of ethyl formate.

The following points should be noted:

1. Different resonance signals or groups of resonance signals are found for the protons. These arise because the protons reside in different chemical environments. The resonance signals are separated by a so-called chemical shift.

2. The area under a resonance signals is proportional to the number of protons that give rise to the signals. It can be measured by integration.

3. Not all proton resonances are simple (i.e., singlets). For some, characteristic splitting patterns are followed, forming triplets or quartets. This splitting is the result of spin–spin coupling – a magnetic interaction between different nuclei.

Empirically determined correlations between the spectral parameters, chemical shift and spin–spin coupling, on the one hand, and the structure of chemical compounds on the other hand form the basis for the application of proton and, in general, NMR to the structure determinations of unknown samples. In this respect the nuclear magnetic moment has proved itself to be a very sensitive probe with which one can gather extensive information. Thus, the chemical shift characterizes the chemical environment of the nucleus that is responsible for a signal. Integration of the spectrum allows one to draw conclusions concerning the relative numbers of nuclei present. Spin–spin coupling makes it possible to define the positional relationship between the nuclei since the magnitude of this interaction – the coupling constant J – depends upon the number and type of bonds separating them. The multiplicity of the resonance signals and the intensity distribution within the multiplet are, moreover, in simple cases, as illustrated by the ethyl group of ethyl formate, clearly dependent upon the number of nuclei on the neighboring group.

Numerous additional applications of NMR have been developed. One of general importance is based on the observation that the NMR spectra of many compounds are temperature dependent and apparently sensitive to dynamic processes. Such a case is found with dimethylformamide, the spectrum of which shows a doublet for the resonance of the methyl protons at 40oC while at 160oC a singlet is observed (Figure 1.5).

Figure 1.5 Temperature dependence of the 1H NMR spectrum of N,N-dimethylformamide.

The cause of this different behavior at the two temperatures is the high barrier to rotation about the carbonyl carbon–nitrogen bond (88 kJ mol−1), which possesses partial double bond character as illustrated by the resonance form (a). The two methyl groups therefore have a relatively long life-time in different chemical environments, cis or trans to the carbonyl oxygen, and this leads to separate resonances. At higher temperatures the rate of internal rotation is increased and frequent interconversion of methyl groups between chemically different positions results, so that we are obviously no longer able to distinguish between them.

It follows that, for several molecules, the line shape of NMR signals is dependent upon dynamic processes and the rates of such processes can be studied with the aid of NMR spectroscopy. What is even more significant is that one can study fast reversible reactions that cannot be followed by means of classical kinetic methods. Thus, the progress achieved in the fields of fluxional molecules, like bullvalene, and in other areas, such as conformational analysis, would have been unimaginable without NMR spectroscopy.

NMR spectroscopy is also used successfully to study reaction mechanisms in all branches of chemistry. In these experiments, magnetic isotopes of hydrogen, carbon, or nitrogen (2H, 13C, 15N) and many others can be used in labeling experiments that are devised to follow the fate of a particular atom during the reaction of interest. Labeling with radioactive carbon, 14C, can be replaced today in many cases by labeling experiments with the stable but NMR active carbon isotope 13C. Only where the highest sensitivity is indispensable does the use of the radiocarbon method still prevail.

The various aspects of the application of NMR to problems of inorganic, organic, and physical chemistry are supplemented by a remarkable variety of experimental techniques that lend a special position to NMR spectroscopy in comparison with other spectroscopic methods. In addition to the versatile physics of the NMR experiment, the large number of magnetic nuclei that are of significance to chemistry also contributes to this situation.

In the fields of organic chemistry and biochemistry, 13C NMR plays a major role, but NMR investigations of 19F, 15N, and 31P nuclei also yield valuable information. As is demonstrated in Figure 1.6 with the 13C and 15N NMR spectra of purine anion, the chemical shifts of these nuclei are sensitive to the chemical structure. With additional information from proton NMR, each position in the molecule is labeled with a reporter that provides data about bonding, structure, and reactivity.

Figure 1.6 Carbon-13 (13C) and nitrogen-15 (15N) NMR spectra of the purine anion.

For inorganic chemistry numerous metal nuclei are of interest and have become available for NMR experiments due to the rapid development of experimental techniques (Figure 1.7). Since nearly all elements of the Periodic Table contain a stable isotope with a magnetic moment, a large area is accessible for NMR investigations, even if the natural abundance of many of these isotopes is rather small.

Figure 1.7 Nuclear magnetic resonance signals of metal nuclei.

Another innovation of general importance is high-resolution NMR spectroscopy of solids, which opened up new areas of structural research in inorganic and organic chemistry. Fast sample rotation and magnetization transfer from sensitive to insensitive nuclei – methods known as magic-angle spinning (MAS) and cross polarization (CP) – provide the basis for the measurement of chemical shifts and the study of dynamic processes even in solids.

All these topics have been accompanied by an improvement of existing, and the invention of completely new, measuring techniques. Three major events characterize this development:

1. Introduction of cryomagnets with high magnetic fields, B0, that are provided by a superconducting coil;

2. replacement of the continuous wave (CW) method by the pulse Fourier transform (PFT) method;

3. introduction of the concept of two-dimensional (2D) NMR.

These achievements have revolutionized practically all branches of NMR spectroscopy, for liquids as well as for solids:

because the energy difference, Δ

E

, between the ground and excited state of NMR spectroscopy as well as the chemical shift are field dependent, the increase in

B

0

has strongly improved

sensitivity

and

spectral dispersion;

while the older CW method used monochromatic signal excitation and the time needed to record a spectrum signal by signal was 250 or 500 s, the PFT method provides polychromatic signal excitation and the whole spectrum is measured in 1 s. The receiver signal is then analyzed mathematically by a Fourier transformation;

two

- and later

multidimensional NMR

became possible because special techniques of impulse spectroscopy allow the recording of NMR spectra with two or more independent frequency dimensions.

A 2D spectrum, for example, is characterized by two frequency axes, F1 and F2, and the signals appear as frequency pairs (f1, f2). In some experiments, the frequency axis F2 only contains chemical shifts, while F1 only contains spin–spin coupling constants. Both parameters are, therefore, separated by the 2D NMR experiment. For practical purposes spectra with chemical shift data on both frequency axes are the most important because they allow a so-called shift correlation between resonance frequencies of different nuclei and in this way a spectral assignment. One distinguishes homo- and heteronuclear shift correlations because F1 and F2 can contain frequencies of the same nuclides, for example, of protons, or of different nuclides, for example, of protons in F1 and of carbon-13 in F2.

A homonuclear two-dimensional shift correlation, a so-called COSY spectrum (correlated spectroscopy), is shown in Figure 1.8 for the protons of ethyl formate. The new and important aspect is the observation of cross peaks that appear in addition to the normal spectrum recorded on the diagonal. Cross peaks have coordinates F1 ≠ F2 and indicate spin–spin coupling between the respective nuclei, here those of the CH2 and CH3 group. Diagonal signals have the coordinates F1 = F2 and reproduce the 1D spectrum. The so-called contour diagram shown in Figure 1.8b gives a particularly clear demonstration of the characteristic cross peak positions.

Figure 1.8 Two-dimensional 1H,1H COSY spectrum of ethyl formate with the axes F1 and F2 with diagonal and cross peaks (the latter are marked with an asterisk, *); (a) stacked plot and (b) contour plot. The splitting due to spin-spin coupling is hidden in the line width.

COSY spectroscopy is important for the analysis of complex spectra with intensive signal overlap, where coupled nuclei can no longer be recognized on the basis of simple multiplet structures. Other 2D NMR spectra show cross peaks resulting from non-scalar interactions between nuclei that are close in space or that participate in a chemical exchange process. In this way information about atomic distances or the mechanism of intramolecular dynamic processes becomes available. Two-dimensional NMR thus paved the way to successful investigation of the structures of complex molecules like natural products and biopolymers such as proteins or nucleic acids. In many cases even the complete three-dimensional structure could be derived solely on the basis of NMR data.

In summary, this short overview may convince the reader that NMR spectroscopy is an indispensable tool for all branches of chemistry. In addition, the method has its place in other sciences such as physics, biology, and even medicine, where in addition to the NMR imaging techniques the measurement of NMR spectra in vivo yields new information about body fluids or chemical processes in living tissue.

1.1 Literature

Numerous textbooks and monographs deal with NMR, ranging from physics to chemistry and biology to medicine. A complete biography is, therefore, beyond the limits of our introduction.

For the present textbook, we have adopted the following procedure: after each chapter we provide first a list with the original citations for material used in the text. Then, where required, selected textbooks or monographs are recommended for further reading, followed by a list of review articles on topics treated in the particular chapter. The following review series are frequently cited throughout the book:

Webb, G.A. (ed) Annual Reports on NMR Spectroscopy, Elsevier, Amsterdam.

Harris, R.K. and Grant, D.M. (eds) (1996) Encyclopedia of Nuclear Magnetic Resonance, John Wiley & Sons, Ltd, Chichester.

Diehl, P., Fluck, E., Kosfeld, R., Günther, H., and Seelig, J. (eds) NMR - Basic Principles and Progress, Springer-Verlag, Berlin.

Bodenhausen, G., Gadian, D.G., Meier, B.H., and Morris, G.A. (eds) Progress in Nuclear Magnetic Resonance Spectroscopy, Pergamon Press, Oxford.

To conclude this section, three classic books should also be listed:

1. Abragam, A. (1961) The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 599 pp.

2. Ernst, R.R, Bodenhausen, G., and Wokaun, A. (1987) Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 610 pp.

3. Pople, J.A., Schneider, W.G., and Bernstein, H.J. (1959) High-Resolution Nuclear Magnetic Resonance, McGraw-Hill Book Co., Inc., New York, 501 pp.

The first two books are physics-oriented and the last one was the first monograph with the emphasis on chemistry.

1.2 Units and Constants

The Système International (SI), based on the meter, kilogram, second, and ampere, is now accepted for all units of physicochemical quantities. Accordingly, SI units have generally been used in the present text. In chemistry, however, the old centimeter, gram, second (CGS) system is still in use and, of course, older textbooks and research papers employed this system. It seems, therefore, necessary to point out some of the main changes that occur when SI units are used:

1. For the magnetic field we use the symbol B, the magnetic induction field or magnetic flux density, a vector with magnitude B. The former use of H is incorrect, since this symbolizes the magnetic field intensity. The SI unit for the magnetic induction field is the tesla (T = kg s−2 A−1), which is 104 times the electromagnetic unit, the gauss (G). Nevertheless, the simple expressions “magnetic field” or “field strength” are still in use when B is discussed.

2. The SI unit for energy is the joule (J = kg m2 s−2), and this replaces the calorie. Accordingly, activation energies are now given in kJ mol−1, entropies in J K−1 mol−1 (4.184 times the numerical values in kcal mol−1 or cal K−1 mol−1, respectively).

3. The SI system uses rationalized equations. In these, the factors 2π or 4π appear where expected on geometrical grounds, that is, if the equation refers to situations where circular or spherical symmetry is involved.

4. The permeability of free space, μ0, often appears explicitly in SI equations.

Table 1.1 lists the constants that may be used for the physical relations given in the different chapters. In relevant situations we shall indicate which system is used.

Table 1.1 Constants for use in this booka,b.

References

1. Andrew, E.R. (1985) Bull. Magn. Reson., 7, 81.

2. Bloch, F., Hansen, W.W., and Packard, M. (1946) Phys. Rev., 70, 474.

3. Gerthsen, C., and Kneser, H.O. (1971) Physik, 11th ed., Springer, Berlin, p. 545.

Part I

Basic Principles and Applications

Chapter 2

The Physical Basis of the Nuclear Magnetic Resonance Experiment. Part I

Today's nuclear magnetic resonance (NMR) spectroscopy is characterized by Fourier transform (FT) spectroscopy and the use of superconducting magnets, so-called cryomagnets, with high magnetic fields. This chapter gives an elementary presentation of the method as applied to the proton, along with reference to the historical development of the technique. This presentation should suffice for the empirical and chemically routine application of the method, and as preparation for the material in Chapters 3–7. Chapter 8 gives a more detailed treatment of the physical principles.

2.1 The Quantum Mechanical Model for the Isolated Proton

The magnetic properties of atomic nuclei form the basis of NMR spectroscopy. We know from nuclear physics that several nuclei, among them the proton, possess angular momentum, P, that in turn is responsible for the fact that these nuclei also exhibit a magnetic moment, μ. These two quantities are related through the expression:

2.1

where γ (in rad T−1 s−1), the magnetogyric ratio, is a constant characteristic of the particular nucleus. It can be positive or negative depending on the sense of nuclear rotation.

According to quantum theory, angular momentum and nuclear magnetic moment are quantized, a fact that cannot be explained by arguments based on classical physics. The allowed values or eigenvalues of the maximum component of the angular momentum in the z-direction of an arbitrarily chosen Cartesian coordinate system are measured in units of (h/2π) and are defined by the relation:

2.2

with mI as the magnetic quantum number that characterizes the corresponding stationary or eigenstates of the nucleus. According to the quantum condition:

2.3

the magnetic quantum numbers are related to the spin quantum number, I, of the respective nucleus; I can have half-integer or integer values up to (e.g., krypton-83, 83Kr) or 3 (as for boron-10, 10B), respectively. The total number of possible eigenstates or energy levels is equal to 2I + 1.

The proton (1H) has a spin quantum number and, consequently, can exist in only two eigenstates, also called spin states and characterized by the magnetic quantum numbers and . With Eq. (2.1) we find for the z-component of its magnetic moment:

2.4

or:

2.5

The proton can therefore be pictured as a magnetic dipole – just called spin – that can exist in two different states.

In quantum mechanics, an atomic system is described by means of wave functions that are solutions of the well-known Schrödinger equation. For the purpose of the following discussion we introduce eigenfunctions α and β corresponding to the two eigenstates of the proton with and , respectively. In Chapter 6 we shall describe in more detail the properties of these functions, since through them the energy of a spin system in a magnetic field can be determined. Here, they serve simply to label the two spin states.

The α and β states for the nuclei of spin quantum number have the same energy, that is, they are degenerate. Only in a static magnetic field B0 is this degeneracy lifted as a result of the interaction of the nuclear magnetic moment μ with B0 and both states have different energy (). The potential energy of a magnetic dipole in the field directed along the positive -axis of a Cartesian coordinate system is given by: