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Solid State NMR
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Solid State NMR
Principles, Methods, and Applications
Klaus Müller
Marco Geppi
Figures edited by Beatrice Omiecienski
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Univ. degli Studi di Trento
Facoltà di Ingeneria
Via Mesiano 77
Facoltà di Ingeneria
38100 Trento
Italy
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Professor Marco Geppi
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Dipartimento di Chimica e Chimica
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vii
Contents
Foreword xiii
Preface xv
Foreword xvii
1
1.1
1.2
1.2.1
1.2.2
1.2.3
1.2.4
1.3
1.3.1
1.3.2
1.3.3
1.3.4
1.4
1.4.1
1.4.2
1.4.3
1.4.4
1.5
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
Introductory NMR Concepts 1
Historical Aspects 1
Basic Description of NMR Spectroscopy 5
Nuclear Spins and Nuclear Zeeman Effect 8
Spin Ensembles 11
Single Pulse Experiment, Bloch Equations, and Fourier
Transformation 17
Populations and Coherences 27
Liquid-state NMR Spectroscopy: Basic Concepts 29
Chemical Shift 29
Indirect Spin–Spin Coupling and Spin Decoupling 32
Nuclear Spin Relaxation 38
Nuclear Overhauser Effect 44
Liquid-state NMR Spectroscopy: Some Experiments 47
Relaxation Experiments 47
Insensitive Nuclei Enhanced by Polarization Transfer 53
2D NMR Spectroscopy 53
Chemical Exchange 57
Solid Materials and NMR Spectroscopy 63
References 69
Mathematical and Quantum-mechanical Tools 73
Definitions and Basic Concepts 73
Operators and Functions 73
Eigenvalue Equations 74
Eigenstates and Superposition States: Pure and Mixed Ensembles
Nuclear Spin and Angular Momentum 76
75
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Contents
2.2
2.2.1
2.2.2
2.2.3
2.3
2.3.1
2.3.2
2.3.3
2.3.3.1
2.3.3.2
2.3.3.3
2.3.4
2.4
2.4.1
2.4.2
Rotations and Frame Transformations 77
Active and Passive Transformations 78
Rotation Operators 78
Rotation Matrices and Euler Angles 79
Time-Independent Features: Energy Levels and Related Aspects 81
Time-Independent Schrödinger Equation and Spin Hamiltonians 81
Time-Independent Perturbation Theory 81
Matrix Representation of Operators and Density Matrix Theory 83
Isolated Nucleus with Spin 1/2 84
Isolated Nucleus with Spin 1 87
Pair of Coupled Nuclei with Spin 1/2 87
Spin Temperature 89
Dealing with Time Dependence 90
Time-Dependent Schrödinger and Liouville–von Neumann
Equations 90
Average Hamiltonian Theory 91
References 93
3
3.1
3.2
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.3.6
Nuclear Spin Interactions 95
Introduction 95
Interactions with External Magnetic Fields 97
Internal Interactions 100
Shielding or Chemical Shift Interaction 100
Knight Shift Interaction 105
Quadrupolar Interaction 106
Dipolar Coupling 112
Indirect Spin–Spin (J) Coupling 116
Paramagnetic Coupling 117
References 119
4
4.1
4.2
4.2.1
4.2.2
4.3
4.4
4.4.1
4.4.2
4.4.2.1
4.4.2.2
4.4.2.3
4.4.2.4
4.4.2.5
4.4.3
Broadline NMR Spectroscopy 121
Introductory Remarks 121
Finite Pulse Duration and Adiabatic Pulses 133
Finite Pulse Duration: Excitation Profile and Spectral Distortions 133
Adiabatic Pulses 138
Inhomogeneous and Homogeneous Line Broadening Mechanisms 141
Dilute Spin-1/2 Nuclei 142
Broadline NMR Spectra 142
Cross-polarization 149
Pulse Sequence and Hartmann–Hahn Conditions 149
CP Explained by AHT 151
CP Explained by the Thermodynamic Model 157
CP Dynamics 160
CP-related Techniques 167
Heteronuclear Spin Decoupling 169
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4.4.3.1
4.4.3.2
4.4.4
4.5
4.5.1
4.5.2
4.5.2.1
4.5.2.2
4.5.2.3
4.5.3
4.5.4
4.5.4.1
4.5.4.2
4.6
4.6.1
4.6.2
4.6.3
4.6.4
4.6.4.1
4.6.4.2
4.6.4.3
4.6.4.4
5
5.1
5.1.1
5.1.2
5.1.3
5.1.4
5.1.5
5.1.5.1
5.1.5.2
5.1.5.3
5.1.5.4
5.2
5.2.1
5.2.2
5.2.3
5.3
5.3.1
5.3.2
CW Heteronuclear Spin Decoupling Explained by AHT 171
Beyond CW: Off-resonance Effects and Pulse Decoupling Schemes 172
Echo Experiments 176
Abundant Spin-1/2 Nuclei 184
Broadline NMR Spectra 184
Spin Diffusion 187
Fick’s Equation of Diffusion 187
The Goldman–Shen Experiment 189
Influence of Spin Diffusion on Spin-Lattice Relaxation Times 191
Moment Analysis 192
Echo Experiments for Refocusing the Homonuclear Dipolar
Interaction 194
Solid Echo 194
Magic-sandwich Echo 197
Quadrupolar Nuclei 200
Broadline NMR Spectra 200
Selective and Non-selective RF Pulses 205
Cross-polarization 209
Echo and Sensitivity Enhancement Experiments 210
Quadrupolar Echo 210
Solomon and Hahn Echoes 211
Quadrupolar Carr–Purcell–Meiboom–Gill 218
Other Sensitivity Enhancement Techniques 219
References 224
1D High-resolution Solid-state NMR Spectroscopy 227
Dilute Spin-1/2 Nuclei 227
Sample Rotation 228
Spinning Sideband Suppression 236
Heteronuclear Spin Decoupling and Sample Spinning 244
Cross-polarization and Sample Spinning 257
Basic Pulse Experiments Under MAS Conditions 268
Pulse Sequences for the Measurement of Relaxation Times 269
Pulse Sequences for Spectral Editing: Distinguishing Components with
Different Dynamic Properties 270
Pulse Sequences for Spectral Editing: Distinguishing Rare Nuclei With
Different Chemical Bonds 271
Pulse Sequences for Quantitative Determinations: CP vs SPE 273
Abundant Spin-1/2 Nuclei 275
Sample Rotation 275
Multiple Pulse Experiments 275
Combined Pulse and Sample Rotation Experiments 282
Quadrupolar Nuclei 289
Sample Rotation 289
Integer Spin Nuclei 290
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Contents
5.3.3
5.3.3.1
5.3.3.2
5.3.3.3
5.3.4
Half-integer Spin Nuclei 291
CT Spectra 294
Double Angle Rotation 297
Satellite Transition Spectroscopy 300
Sensitivity Enhancement 301
References 305
6
6.1
6.1.1
6.1.2
6.1.3
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.2.5
6.2.6
6.2.7
6.2.8
6.3
6.3.1
6.3.2
6.3.3
6.3.4
6.3.5
6.3.6
6.3.7
6.4
6.4.1
6.4.2
6.4.3
6.4.3.1
6.4.3.2
6.4.3.3
6.4.3.4
6.4.3.5
6.4.3.6
6.4.4
6.5
6.5.1
6.5.2
6.6
6.6.1
2D Solid-State NMR Spectroscopy 309
Basic Concepts 311
Basic Structure of 2D Experiments 311
Need for Recoupling 313
Double (Multiple) Quantum Spectroscopy 316
Experiments Based on Chemical Shift Anisotropy 317
MAH, MAT, 5-π, and Related Experiments 318
STAG, S3 , SASS 321
VACSY 322
TOSS–ReverseTOSS and 2D-PASS 322
CSA Amplification Methods 324
Pulse Sequences Recoupling Chemical Shift Anisotropy 326
Pulse Sequences for Abundant Spin-1/2 Nuclei 326
Rotary Resonance (RR) 328
Experiments Based on Heteronuclear Dipolar Coupling 329
Heteronuclear Correlation Through Dipolar Interaction 330
Separated Local Field (SLF) 333
Rotary Resonance Recoupling (R3 ) 337
REDOR 337
REAPDOR and TRAPDOR 348
TEDOR 352
HARDSHIP 354
Experiments Based on Homonuclear Dipolar Coupling 355
WISE 355
Rotational Resonance (R2 ) 358
Broadband Homonuclear Dipolar Recoupling 360
DRAMA and MELODRAMA 362
RFDR and SEDRA 365
2Q-HORROR, MSD-HORROR, and DREAM 366
BABA 370
Symmetry-based Recoupling Schemes: C7 and POST-C7 370
Dipolar Truncation and High-order Recoupling Schemes 371
Homonuclear Correlation Through Dipolar Interaction 372
Experiments Based on J-coupling 375
Heteronuclear Correlation Through J-coupling 376
Homonuclear Correlation Through J-coupling 378
Experiments Based on Quadrupolar Interaction 380
Nutation 380
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6.6.2
6.6.3
6.6.4
DAH and DAS 381
MQMAS 384
STMAS 388
References 391
7
7.1
7.1.1
7.1.1.1
7.1.1.2
7.1.1.3
7.1.2
7.1.2.1
7.1.2.2
7.1.2.3
7.1.2.4
7.1.2.5
7.1.3
7.2
7.2.1
7.2.2
7.2.3
7.3
7.3.1
7.3.2
7.3.2.1
7.3.2.2
7.3.3
7.3.3.1
7.3.3.2
7.3.3.3
7.4
7.4.1
7.4.1.1
7.4.1.2
7.4.1.3
7.4.2
7.4.2.1
7.4.2.2
7.4.3
7.4.3.1
7.4.3.2
7.4.3.3
Molecular Dynamics by Solid-State NMR 397
Experimental Observables and Motional Timescales 399
Spectral Lineshapes 399
High-Resolution Spectra 400
Powder Spectra 401
Spectra Acquired by “Exchange” Experiments 403
Relaxation Times in Solids 404
Spin–Spin Relaxation Times 406
Spin–Lattice Relaxation Times of Abundant Nuclei 409
Spin–Lattice Relaxation Times of Rare Nuclei 410
Dipolar and Quadrupolar Spin–Lattice Relaxation Times 411
Theory of Relaxation 412
Absolute Frequency Regimes 416
Motional Models 419
Models for Lineshape Analysis 419
Spectral Densities 422
Dependence of Correlation Times on Temperature 423
Broadline Experiments 424
Acquisition of 1D Spectra 425
Measurement of Relaxation Times 426
Spin–Spin Relaxation Times, FID Analysis, and DQ Techniques
Spin–Lattice Relaxation Times 432
Other Techniques 435
Stationary Stimulated Echo 436
2D Exchange 436
Spin Alignment 437
High-Resolution Experiments 438
Acquisition of 1D and 2D Spectra 438
1D Chemical Exchange 438
Line Broadening from Interferences 439
Lineshapes from 2D Experiments 440
Measurement of Relaxation Times 440
Abundant Nuclei 440
Rare Nuclei 441
Other Techniques 442
2D Chemical Exchange 442
1D and 2D Exchange of Spinning Sidebands 442
CODEX 443
References 444
426
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Contents
8
8.1
8.1.1
8.1.2
8.1.3
8.1.4
8.1.5
8.1.6
8.1.7
8.1.8
8.2
8.2.1
8.2.2
8.2.3
8.2.4
8.2.4.1
8.2.4.2
8.2.4.3
8.2.5
8.2.6
8.2.6.1
8.2.6.2
8.3
8.3.1
8.3.2
8.3.2.1
8.3.2.2
8.3.2.3
8.3.2.4
8.3.3
8.3.3.1
8.3.3.2
8.3.3.3
8.4
8.4.1
8.4.2
8.4.3
8.4.4
8.4.5
8.4.6
Application of SSNMR to Selected Classes of Systems 447
Pharmaceuticals 447
Introduction 447
Polymorphs, Solvates, and Salts 449
Molecular Complexes and Cocrystals 454
NMR Crystallography 456
Molecular Dynamics 459
Disordered and Amorphous Forms 461
Identification of API Forms in Formulations 461
Miscibility and Interactions in Drug Formulations and Dispersions 463
Polymeric Materials 465
Introduction 465
Primary Structure 466
Secondary and Tertiary Structure 466
Phase Properties 470
Polymorphism 470
Heterophasicity 470
Phase Transformations 474
Interfaces and Domain Dimensions 474
Molecular Dynamics 479
Motions in Glassy and Crystalline Phases 480
Motions in Rubbers and Melts 481
Inorganic and Organic–Inorganic Materials 485
Introduction 485
Inorganic Systems 486
Silicates 486
Zeolites 489
Aluminophosphates 491
Amorphous Materials: Cements, Geopolymers, and Glasses 493
Organic–Inorganic Materials 497
Organometallic Complexes 497
Metal–Organic Frameworks 500
Organically Modified Fillers and Polymer/Filler Composites 502
Liquid Crystals and Model Membranes 507
Introduction 507
Mesogens and Mesophases 507
SSNMR Techniques for Investigating Mesophases 511
Orientational Order 515
Phase Structure 519
Molecular Dynamics 523
References 525
Index 531
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xiii
Foreword
Klaus Müller studied Chemistry at the University of
Freiburg (1975–1981) and received his doctorate degree
in December 1985 with Prof. Kothe at the University of
Stuttgart and his postdoctoral lecture qualification in 1993.
From 1999 to 2009, he taught as a Professor at the Institute of
Physical Chemistry at the same university. As he committed
himself to the promotion of research and teaching with great
dedication, in these 10 years, he supervised 16 PhD theses, 4
postdocs, and several dissertations within his own research
group, as well as the German-French Double Diploma (a
study course in Chemistry). For the postgraduate course of lectures “Magnetic Resonance” (1998–2007), he was seen as a tower of strength.
Müller was both an expert and internationally sought-after cooperation partner
in the area of solid-state NMR, where he examined both bio-membranes and
host–guest compounds, ceramics, and materials of any kind. For his multiple, often
groundbreaking ideas, he was invariably an asset and motivation.
He accepted a Professorship at the University of Trento on 1 January 2009. At this
particular time, he was already writing this textbook. From the very beginning, I
was permitted to produce the figures for this project and could therefore continually
follow the developments. He had the gift to awaken a very special curiosity and his
enthusiasm for this project captured me too.
As Klaus Müller – incomprehensibly for all of us – totally unexpectedly passed
away on 1 April 2011 at the age of only 55 years, he left behind his manuscript. From
the initial, unimaginable idea to complete this book, as already so much time and
energy had been put into these pages, a time-consuming task developed. It took me
a long time to find an adequate coauthor.
Therefore I extend my very special thanks to Dr. Marco Geppi, who met the challenge and intensely inspected the existing manuscript. He brought a lot of time and
effort in creating the missing chapters and completed this book in the spirit of Klaus
Müller.
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Foreword
We also want to thank Silvia Gross as well as Philipp, Oliver, and Giulia Müller
for allowing both of us to be contributors and Wiley-VCH as publisher the rights to
continue Klaus Müller’s work and to finish the book.
Stuttgart 2020
Beatrice Omiecienski
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xv
Preface
Writing this book was one of the most difficult (and long) tasks of my professional
life, and writing this preface is probably even more difficult than the rest of the book.
This book was conceived and partially written by Klaus Müller, a very good friend
of mine, several years ago. It was his project. I was told after he passed away that he
used to put a special love in teaching, and I could clearly find such a love in the parts
of the book he developed. A few years after Klaus departure, Silvia told me about
this book and asked me if I was willing to complete it. I could not refuse, for Silvia
and the little Giulia, and especially for Klaus. And I couldn’t for myself, too.
Klaus and I always told each other, “We have to do something together.” We were
sharing research subjects, approaches to research, views, and values. In addition,
it was a pleasure to stay together. After he moved to Trento, and especially during
WWMR 2010 in Florence, we drafted together common projects involving GIDRM
and, in particular, the small Italian solid-state NMR community. However, none of
our projects had the time to start, and we never effectively did anything together
before his passing on 1 April 2011. This was a few days after a phone call during
which we agreed on the title of his talk to a workshop supposedly in Pisa a couple of
months later.
Completing his book, transforming it in our book, was an unexpected chance to
do something, and something very important, together for the first time.
Now, after the huge effort done to understand, develop, integrate, and complete
this book, I am very happy to see our names together, knowing that I did my best to
honor and remember him and to value his work. I hope that Silvia and Beatrice will
also be happy for the completion of this work, although it took much longer than
they probably expected.
I also hope that Klaus will forgive me for the many parts of the book that possibly
came out different from his initial idea or from how he could have realized them.
But I am sure that he would be happy that finally we were able to do “something
together.”
Pisa 2020
Marco Geppi
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xvi
Preface
Marco Geppi obtained his degree in Chemistry in 1991 at the University of Pisa,
Italy, working on 2 H NMR studies of molecular dynamics in liquid crystals, and his
PhD in Chemistry in 1997 at the Scuola Normale of Pisa, working on solid-state
NMR of polymeric materials, with professors C.A. Veracini and F. Ciardelli as
supervisors. Part of his PhD research was carried out at the University of Durham,
United Kingdom, under the supervision of Prof. R.K. Harris. In 2001 he became a
researcher and, in 2014, associate professor in Physical Chemistry at the Department of Chemistry and Industrial Chemistry of the University of Pisa, where he is
now leader of the solid-state NMR spectroscopy group and laboratory, and teacher
of Physical Chemistry, Spectroscopy, and solid-state NMR. In 2015 he was awarded
the GIDRM/GIRM gold medal. Since 2017 he has been president of the Italian
Discussion Group on Magnetic Resonances (GIDRM). His research interests mainly
concern the application of NMR techniques to a variety of solid materials, including
polymers, biopolymers, pharmaceuticals, inorganics, organic–inorganic hybrids
and composites, and soft matter (e.g. liquid crystals, gels, model membranes).
He is also involved in the development of experimental and data analysis NMR
techniques, as well as of NMR softwares, mainly devoted to studies on nuclear
spin relaxation and molecular dynamics. He has been scientific manager of several
contracts with chemical industries and of Italian and international scientific
projects. He has coauthored over 140 research articles on NMR spectroscopy.
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xvii
Introduction
Beyond the horizon of the place we lived when we were young
In a world of magnets and miracles
Our thoughts strayed constantly and without boundary
….
Running before times took our dreams away
Leaving the myriad small creatures trying to tie us to the ground
To a life consumed by slow decay
(High Hopes – Pink Floyd)
Discovered by physicists and widely applied in chemistry, Nuclear Magnetic Resonance (NMR) is a phenomenon that nowadays finds a crucial importance in most
fields of natural science (chemistry, biology, physics, pharmacy, agriculture, materials, earth, and environmental science) as well as in medicine and engineering.
Common basic principles concerning the spin of atomic nuclei and its interaction
with radio waves originated three main, equally important, experimental techniques, which through the years became more and more specialized: solution-state
NMR spectroscopy, solid-state NMR spectroscopy (to which this book is devoted),
and magnetic resonance imaging. The latter finds its main field of application in
medicine, where it is nowadays of extraordinary importance. Solution-state and
solid-state NMR spectroscopies obviously differ on the physical state of the sample
under investigation. Although they are both strikingly important in the same fields,
they have different applications and can be complementary. Solution-state NMR
spectroscopy is generally unrivalled in the determination of unknown chemical
structures, representing a vital tool for chemists, although its applications are not
restricted to this field. The role of solid-state NMR spectroscopy is beyond determining chemical structures of insoluble samples: it also provides precious and detailed
information on conformations, molecular packing, intermolecular interactions,
polymorphism, structural order/disorder, molecular dynamics, and average phase
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Introduction
domain dimensions, i.e. on “microscopic” properties that are crucial in defining
the macroscopic behavior of a material. Moreover, it shows virtually no limits on
the type of anisotropic phase to be investigated, which can either be crystalline or
amorphous, solid or soft. For these reasons, solid-state NMR spectroscopy is one of
the most powerful and versatile techniques for the characterization of materials.
As a physicochemist, my main interest in NMR in general, and solid-state NMR
spectroscopy in particular, stems from its natural position between theory and
experiments as these continuously superimpose and apply in NMR and throughout
this book. However, as it was for Klaus, my approach to NMR spectroscopy is mostly
experimental. In this book the theoretical description of the concepts is always
directed to a better understanding of the techniques, their applications, and, finally,
the interpretation of the experimental results.
Solid-state NMR spectroscopy is a field too large and varied to be exhaustively
covered in a single book. Here we aimed at giving the essential tools to graduate
and PhD students and to novice researchers in the field. Moreover, we wanted to
present the possible applications of solid-state NMR spectroscopy to researchers of
other fields, who could find them useful to exploit this technique for their studies.
The book is permeated by the concepts of anisotropy of the internal nuclear interactions and of peculiar linebroadening mechanisms and relaxation behavior occurring in solids and, more in general, in anisotropic phases, also including soft matter.
On one hand, these concepts are treated in contrast to solution-state NMR, determining why and how in comparison solid-state NMR is theoretically and experimentally
more complex, but, potentially, a richer source of information. On the other hand,
the implications of such concepts on both low- and high-resolution solid-state NMR
experiments and on their applications are dealt with in detail. Furthermore, we presented and described many useful pulse sequences (both 1D and 2D), and we tackled
the crucial aspect of molecular dynamics, in attempts to describe their influence on
nuclear properties and to provide a complete survey of the NMR techniques that
allow their close investigation. Several subjects, which are certainly very important
in the current research, could not be treated here, concerning theoretical aspects (e.g.
Floquet theory), techniques (e.g. Dynamic Nuclear Polarization, DNP), and applications (e.g. structural biology studies), for which the reader should refer to more
specialized books or scientific literature.
This book consists of eight chapters. Chapter 1 is both a summary of the main
concepts at the basis of solution-state NMR and an introduction to the world of
solid-state NMR. In Chapter 2, the main mathematical and quantum-mechanical
tools necessary to understand the following subjects are briefly treated. Chapter
3 contains the formal description of the main external and internal nuclear spin
interactions and their effects on nuclear energy spin levels. Chapters 4 and 5 are
devoted to one-dimensional static and Magic Angle Spinning (MAS) approaches,
respectively: in each chapter the main concepts are dealt with from both theoretical
and experimental standpoints and a description of the most important experimental
techniques is present, following a division among dilute spin 1/2, abundant spin 1/2,
and quadrupolar nuclei. Chapter 6 treats two-dimensional solid-state NMR spectroscopy, providing a description of the main concepts and the main experiments,
divided by type of exploited interaction: chemical shift, hetero- and homonuclear
dipolar, indirect spin–spin, and quadrupolar. Chapter 7 is entirely dedicated to
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Introduction
molecular dynamics: theoretical and experimental aspects of the many NMR
quantities useful in this field are discussed, highlighting in particular the different
motional timescales involved and the procedures to extract motional parameters.
Finally, Chapter 8 deals with the application of solid-state NMR to several important classes of materials: pharmaceuticals, polymers, inorganics, organo metallic
complexes and organic–inorganic hybrids and composites, and soft matter.
Many people have to be acknowledged for their contributions to this book. First
of all, Beatrice Omiecienski, who was the only person who took part in all the
phases of this work, representing, both ideally and in practice, the best possible
bridge between Klaus and me. Without her extraordinary and tireless commitment
throughout these years, and without her fierce determination in doing everything
she could to complete Klaus’s original project, this book would not exist. She
constantly applied her skills and patience, supporting both Klaus and me in many
aspects and, in particular, by editing, revising, and adapting all the many figures of
this book.
I owe my special friend Alan Kenwright for the rest of my life for his dedication to
greatly improve both the scientific content and English language of the whole book.
I am deeply grateful to Lucia Calucci, Silvia Borsacchi, Elisa Carignani,
Francesca Martini, and Federica Balzano, who provided extensive and crucial
contributions as well as precious suggestions to several parts of the book. Francesca
Nardelli, Noemi Landi, and Elena Maurina are also acknowledged for their
help in proof corrections.
I’m in debt with Giovanni Granucci, Giulia Mollica, and Giacomo Parigi, for
their help and suggestions on selected subjects, for which my trust in them was much
bigger than in myself.
I must acknowledge the authors of earlier and very important books on NMR and,
in particular, solid-state NMR, which are listed in the following as further readings.
I also want to thank my many graduate students, who through the years have
been giving me the stimulus and strength to learn more: I wish they could realize
how important for me was and is every small piece of knowledge transferred to each
of them.
In the end, I thank from the bottom of my heart my research group and my
family, who suffered in several ways the consequences of my commitment to this
book and supported me for several years.
Marco Geppi
Further Readings
General Text on NMR
Freeman, R. (1997). Spin Choreography. Oxford: Spektrum Academic Publishers.
Günther, H. (2013). NMR Spectroscopy. Weinheim: Wiley.
Keeler, J. (2010). Understanding NMR Spectroscopy. Chichester: Wiley.
Levitt, M.H. (2008). Spin Dynamics. Chichester: Wiley.
Slichter, C.P. (1990). Principles of Magnetic Resonance. Berlin: Springer-Verlag.
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Introduction
Texts on Solid-State NMR
Apperley, D.C., Harris, R.K., and Hodgkinson, P. (2012). Solid-State NMR: Basic
Principles & Practice. New York: Momentum Press.
Duer, M.J. (2002). Solid-State NMR Spectroscopy: Principles and Applications.
Oxford: Blackwell Science.
Haeberlen, U. (1976). High Resolution NMR in Solids. Selective Averaging. New
York: Academic Press.
MacKenzie, K.J.D. and Smith, M.E. (2002). Multinuclear Solid-State NMR of
Inorganic Materials. Oxford: Pergamon.
McBrierty, V.J. and Packer, K.J. (1993). Nuclear Magnetic Resonance in Solid
Polymers. Cambridge: Cambridge University Press.
Mehring, M. (1983). Principles of High Resolution NMR in Solids. Berlin:
Springer-Verlag.
Saito, H., Ando, I., and Naito, A. (2006). Solid State NMR Spectroscopy for
Biopolymers: Principles and Applications. Dordrecht: Springer.
Schmidt-Rohr, K. and Spiess, H.W. (1994). Multidimensional Solid-State NMR and
Polymers. London: Academic Press.
Stejskal, E.O. and Memory, J.D. (1994). High Resolution NMR in the Solid State.
Oxford: Oxford University Press.
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1
Introductory NMR Concepts
1.1 Historical Aspects
Several reviews discussing the historic evolution of nuclear magnetic resonance
(NMR) spectroscopy have been published (see, for instance, Emsley and Feeney
(1995)), but the most comprehensive analysis can be found in various articles of the
“Encyclopedia of Nuclear Magnetic Resonance,” edited by Wiley (see, for instance,
Becker and Fisk (2007)). Here, we only highlight a very short outline of the most
important developments, with a particular focus on the field of solid-state NMR
(SSNMR).
The discovery of NMR can be attributed to Isidor I. Rabi (Nobel Prize in physics
in 1944) and coworkers, who performed in 1938 the very first NMR experiment
on a molecular beam of LiCl (Rabi et al. 1938). However, the first successful NMR
experiments on solids and liquids were reported in early 1946 by two independent
research groups at Stanford (Bloch, Hansen, Packard) and Harvard (Purcell, Torrey,
Pound). Actually, the Harvard group led by Edward M. Purcell at MIT submitted a
letter about their discovery to Physical Review on 24 December 1945, more than one
month before the submission by the Stanford group to the same journal. However, it
was established that the two researches were conducted independently and, for this
reason, the 1952 Nobel Prize in Physics was awarded jointly to Bloch and Purcell.
In particular, the group at Harvard discovered the phenomenon by studying solid
paraffin in their very first experiment, and therefore, we can really say that solids
were studied since the beginning of NMR.
The different behaviors between liquids and solids, as well as the anisotropic character of the nuclear interactions, were soon discovered by Bloembergen, Purcell, and
Pound working on a CaF2 crystal (Purcell et al. 1946). This was later explained in
more detail by Purcell’s doctoral student, George Pake, who, through his studies on
di-hydrated CaSO4 crystals, first found the resonance signal that was a doublet and
the typical pattern, now carrying his name, given by the homonuclear dipolar coupling between the two water protons in the case of single-crystal and powder samples, respectively. In the very first years of its life, NMR was mostly applied to solids
and its study was rooted firmly in the physics community, for instance, to investigate
molecular motions as a function of temperature from changes in a lineshape.
Solid State NMR: Principles, Methods, and Applications, First Edition. Klaus Müller and Marco Geppi.
© 2021 WILEY-VCH GmbH. Published 2021 by WILEY-VCH GmbH.
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1 Introductory NMR Concepts
In 1950, Proctor and Yu (1950a, 1950b) fortuitously discovered chemical shift,
i.e. how the local chemical environment surrounding a nucleus influences the
frequency at which it resonates, by looking at the 14 N spectrum of NH4 NO3 in
water, and spin–spin indirect coupling, observing the 121 Sb resonance of NaSbF6
in solution. Implications in NMR spectra became apparent, and most of the efforts
moved to the study of liquids, characterized by much narrower lines. In the 1950s,
tremendous strides were made in the development of the instrumentation. In 1952,
the first high-resolution commercial spectrometer, working at a proton Larmor frequency of 30 MHz, was introduced by Varian and sold to Exxon in Baytown, TX, and
at the end of the 1950s, a 60 MHz spectrometer was available. Great improvements
have been made in the stability and homogeneity of the magnetic fields following
the introduction of field stabilizers, shim coils, and sample spinning. Moreover,
principal advances progressed the development of experiments (e.g. Carr–Purcell
spin echoes, 13 C spectra at natural abundance) and theory (e.g. Bloch equations,
effect of exchange on spectra, nuclear Overhauser effect (NOE), relaxation in the
rotating frame, Solomon equations, Redfield theory of relaxation, spin temperature
theory, Karplus theory for the dependence of three-bond J coupling on a dihedral
angle, dependence of 1 H chemical shift on hydrogen bond strength). In 1958,
Andrew observed that the broad 23 Na line in NaCl single crystals, arising from
dipolar interactions, could be significantly narrowed by spinning the sample sufficiently fast. Moreover, he showed a dependence of the linewidth under spinning
on |0.5(3cos2 𝛽 − 1)|, with 𝛽 the angle between the axis of rotation and the external
magnetic field. Indeed, for 𝛽 = 54∘ 44′ , the dipolar interaction effect on the linewidth
was predicted to vanish as demonstrated experimentally in 1959 by Andrew himself
(Andrew et al. 1959) and by Lowe (1959). As Andrew writes, “When we reported
our first sample rotation results at the AMPERE Congress in Pisa in 1960, Professor
Gorter of Leiden found the removal of the dipolar broadening of the NMR lines
quite remarkable and referred to it as ‘magic,’ so we called the technique ‘magic
angle spinning’ after that.” (Andrew 2007). The 1950s also saw a substantial passage
of NMR from the hands of physicists to those of chemists, since the pioneering
developments started to be successfully exploited in applications of NMR, mostly
as a novel tool for chemical structure determination, especially thanks to the
development of correlation charts between chemical shift and molecular functional
groups and of the first theories trying to explain these correlations.
In the 1960s, spectrometers were further developed with the introduction of
field-frequency lock (1961), superconducting magnets (1962), and time averaging (1963). Hartmann and Hahn (1962) suggested a method (and developed
the corresponding theory) for transferring polarization between two different
nuclear species (cross-polarization [CP]), which would reveal its extraordinary
importance for the study of rare nuclei in solids only about 15 years later. Powles
and Mansfield (1962) devised a simple two-pulse “solid echo” technique, able to
refocus the quadrupolar and (to a good extent) the dipolar interaction in solids.
Moreover, Goldburg and Lee (1963) showed how line narrowing in solids could
be achieved not only by sample spinning as shown by Andrew a few years before
but also by rotating radio-frequency (RF) fields, still at the magic angle. Stejskal
and Tanner (1965) introduced pulsed field gradients (PFG), opening entirely new
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1.1 Historical Aspects
perspectives for diffusion measurements. A few years later (1968), Waugh, Huber,
and Haeberlen developed the WAHUHA pulse sequence, showing that it was able
to remove homonuclear dipolar coupling by using a non-symmetrized combination
of Hamiltonian states (Waugh et al. 1968), and at the same time, Waugh and
Haeberlen also proposed the average Hamiltonian theory (AHT) (Haeberlen and
Waugh 1968). All this considered, the biggest breakthrough of that decade was
represented by the development of Fourier transform (FT) and pulsed methods: the
first results, obtained by Ernst and Anderson at Varian Associates, were presented
at the Experimental NMR Conference in Pittsburgh in 1965 and published in 1966
in the journal “Review of Scientific Instruments” (Ernst and Anderson 1966) after
the same paper had been rejected twice by the Journal of Chemical Physics for
being not sufficiently original. FT applied to NMR (FT NMR as we know it today),
the main reason for the Nobel Prize in Chemistry awarded to Richard Ernst in
1991, quickly encountered widespread success due to the development, in the
same years, of computers and software. In 1965, a new algorithm was developed at
Bell Laboratories able to perform a FT of 4096 data points in approximately only
20 minutes!
During the 1970s, there was a huge increase in magnetic field strengths, and a 1 H
Larmor frequency of 600 MHz was reached in 1977 in a non-superconducting magnet developed at Carnegie Mellon University. In 1973, the first paper concerning
the use of NMR to obtain images by exploiting magnetic field gradients was published by Lauterbur (1973), who expanded the one-dimensional technique already
proposed by Herman Carr in his PhD thesis more than 20 years before. In 2003,
Lauterbur was awarded, together with Mansfield (who further contributed to the
development of magnetic resonance imaging [MRI] soon after), the Nobel Prize in
Medicine.1 Another significant development made in the 1970s was the introduction of bidimensional techniques. Ernst developed an idea of Jeener, presented at
an Ampère summer school in 1971 (and never transformed into a published paper),
and published his first results in 1975. Due to the almost simultaneous development
of MRI, the very first paper dealing with 2D techniques concerned their applications to imaging rather than spectroscopy (Kumar et al. 1975), but spectroscopic
applications followed soon (Müller et al. 1975). On the solid’s front, first Mansfield,
Rhim, Elleman, and Vaughan (Mansfield 1970; Rhim et al. 1973) and then Burum
and Rhim (1979) improved the WAHUHA pulse sequence developing the MREV-8
and BR-24 pulse sequences for homonuclear dipolar decoupling. Moreover, separated local field (SLF) techniques, separately measuring correlated 13 C chemical
shifts and dipolar interactions and representing a basis for the development of 2D
techniques in solids, were first introduced by Waugh and coworkers in 1976 (Hester
et al. 1976). All in all, the 1970s can claim the birth of “high-resolution SSNMR”: this
can be considered coincident with the first experiments where the previously developed magic angle spinning (MAS), CP (based on the Hartmann–Hahn method), and
1 This Nobel Prize was strongly protested by Raymond Vahan Damadian, who in 1971 had
discovered that tumoral and normal tissues have different T 1 /T 2 proton relaxation properties and
had claimed that he proposed the idea of an MR body scanner. The echoes of the debate on
whether Damadian would have deserved to share the 2003 Nobel Prize are still present in the
scientific community.
3
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1 Introductory NMR Concepts
heteronuclear dipolar decoupling techniques were combined together by Schaefer
and Stejskal to obtain resolved spectra of rare nuclei, the first of which was the 13 C
spectrum of poly(methyl methacrylate) (Schaefer and Stejskal 1976). Nevertheless,
a fundamental contribution was made by Pines et al. a few years previously by successfully combining CP and decoupling techniques to obtain high-resolution static
13 C spectra of some organic solids, such as adamantane (Pines et al. 1972). Following Schaefer and Stejskal, MAS was also combined with homonuclear decoupling
techniques to give the so-called combined rotation and multiple pulse spectroscopy
(CRAMPS) experiment to obtain high-resolution spectra of abundant nuclei (Gerstein et al. 1977).
The 1980s were characterized by the rapid development of NMR in several
fields and especially in the study of the tridimensional structure of biological
macromolecules by solution-state NMR, for which the Nobel Prize in Chemistry
was awarded to Kurt Wüthrich in 2002. Moreover, NMR started to be used as a
diagnostic tool in medicine. The first apparatuses for fast field-cycling relaxation
measurements in both liquids and solids were developed (Kimmich 1980; Noack
1986). Levitt and Freeman (1981) made significant improvements in the field of
broadband decoupling, for instance, devising composite 180∘ inversion pulses and
the MLEV cycle. Two-dimensional exchange techniques for studying structure and
dynamics were introduced in the group of Spiess in 1986 (Schmidt et al. 1986). In
the same year, the parahydrogen-enhanced methods for increasing NMR sensitivity
were suggested for the first time (Bowers and Weitekamp 1986). At the end of that
decade, both dynamic angle spinning (DAS) and double rotation (DOR) techniques
were developed in Pines’ group: they provided a solution for the line narrowing of
the central transition of half-integer quadrupolar nuclei, which cannot be achieved
by MAS alone (Samoson et al. 1988; Llor and Virlet 1988; Chmelka et al. 1989;
Mueller et al. 1990). In the same years, Gullion and Schaefer (1989) devised the
rotational echo double resonance (REDOR) technique for the direct measurement
of heteronuclear dipolar coupling between isolated pairs of labeled nuclei. At the
end of the 1980s, all the major companies were manufacturing spectrometers based
on superconducting magnets up to 600 MHz.
The field strength had a further step upward in the first half of the next decade,
with the first 800 MHz spectrometers commercialized in 1995. In the same year,
the unilateral NMR scanner MOUSE (an acronym for mobile universal surface
explorer) was built in Aachen (Eidmann et al. 1996). Still, in 1995, Frydman et al.
(Frydman and Harwood 1995; Medek et al. 1995) introduced the multiple quantum
magic angle spinning (MQMAS) technique, which suddenly revealed a huge
improvement, with respect to DOR and DAS, in providing high-resolution NMR
spectra of or achieving the line narrowing of the central transition of half-integer
quadrupolar nuclei. Density functional theory (DFT) techniques started to be used
for the computation of chemical shifts, and in this regard, a great improvement
for the study of solids was provided by the development of gauge-including
projector-augmented wave (GIPAW) methods in 2001 (Pickard and Mauri 2001).
In the twenty-first century, the use of SSNMR became much more widespread:
the number of SSNMR-related publications increased by more than three times
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1.2 Basic Description of NMR Spectroscopy
from the last decade of the twentieth century to the first of the twenty-first century,
passing from about 1000 publications/year on average to about 3500, further
raised to about 4400 per year in the second decade of the twenty-first century.
Along with further increases in magnetic field strengths (nowadays reaching a
proton Larmor frequency of 1.2 GHz), several new techniques were developed or
“rediscovered” for the study of solids. The group of Samoson obtained significant
improvements in MAS frequencies and advanced the CryoMAS probe for standard
CP-based experiments in structural biology (Samoson et al. 2005). At the moment
of writing, a MAS frequency of 110–111 kHz has been reached on commercial
MAS probes using rotors with a diameter of 0.70–0.75 mm, while CryoMAS probes
with different designs have also been developed in Southampton and Bethesda
laboratories and are also commercialized. Hyperpolarization methods, in particular
parahydrogen-induced polarization (PHIP) and dynamic nuclear polarization
(DNP), although very well-known since the 1980s and the 1950s, respectively,
recently demonstrated an extraordinary revival. This resulted in the development
of commercial DNP-NMR spectrometers: the potentially wide application of DNP
for obtaining NMR spectra with a signal-to-noise ratio increased by some orders
of magnitude, even in solids, is nowadays clearly recognized and feasible (Rankin
et al. 2019). Moreover, microcoils, already applied in MRI and solution-state NMR,
have also recently found usefulness in solids, and a brilliant new technique has
been developed by Sakellariou, based on spinning the microcoil, put within the
MAS rotor, and on inductive coupling (Sakellariou et al. 2007).
1.2 Basic Description of NMR Spectroscopy
NMR and electron paramagnetic resonance (EPR) spectroscopies probe the states
of inherent magnetic properties of the materials under investigation. Such magnetic
resonance methods differ from optical spectroscopy, as the samples interact with the
magnetic component of the electromagnetic radiation, while in the latter case, the
electric field component is involved. Moreover, resonance spectroscopies examine
transitions between spin states in a static magnetic field, required to lift their degeneracy. In particular, since the energy differences between nuclear spin states are very
small, NMR spectroscopy is located at the low-frequency end (i.e. the RF range) of
the electromagnetic spectrum (Figure 1.1). For this reason, saturation effects, relaxation, and related phenomena play important roles in NMR spectroscopy, while they
are of minor importance for spectroscopies at higher frequencies.
In addition to the static magnetic field, an oscillatory magnetic field, arising from
the RF pulsed irradiation, induces transitions between the spin states from which
the NMR signal is derived. The basic NMR spectrometer consists of (i) a strong
external magnetic field, (ii) an RF source, (iii) a probe that goes inside the external magnetic field and includes a coil which surrounds the sample, with the axis
defining the direction of the oscillatory magnetic field perpendicular to the external
field direction, used for both RF irradiation of the sample and detection of the signal, (iv) a receiver unit, and (v) a computer. As will be outlined later, the detected
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1 Introductory NMR Concepts
Visible
log(ν / Hz)
RadioMicrofrequency wave Infrared
6
8
10
12
Ultraviolet
X-rays γ-rays
14
16
NMR Rotation, Vibration Electronic
EPR
ν (MHz)
13C
31P
100
18
20
Nuclear
1H
200 300 400 500 600
δ (ppm)
Aliphatic
Acetylenic
Olefinic
Aromatic
Aldehydic
6
0 2 4 6 8 10
4 kHz
Scalar
coupling
~10 Hz
Figure 1.1 The electromagnetic spectrum and expansion of the NMR radio-frequency
range to show typical frequencies for different isotopes and for 1 H nuclei in different
chemical environments.
time-dependent signal is converted to the NMR spectrum, which contains the relevant information about the sample under investigation.
One basic requirement for NMR spectroscopy is a sample with a certain amount
of nuclei (typically 1018 –1020 ) with non-zero nuclear spin I. The periodic chart
in Figure 1.2 demonstrates that for the majority of chemical elements one or
more isotopes are found, in their most stable nuclear spin configuration2 , with
non-null nuclear spin. The respective spin quantum number can assume integer or
half-integer values depending on the number of protons and neutrons forming the
nucleus (Table 1.1). Quadrupolar nuclei possess a spin quantum number I greater
than 1/2 and are characterized by a nonspherical, oblate or prolate, nuclear charge
distribution with positive or negative nuclear quadrupole moment Q, respectively
(Figure 1.3). Interaction with the electric field from nearby electrons gives rise to
the so-called quadrupolar interaction, which plays a prominent role in SSNMR
spectroscopy and for spin relaxation.
2 Each isotope can give rise to different nuclear spin configurations, which correspond to different
combinations of the spins of neutrons and protons and, consequently, to different spin quantum
numbers. The different configurations are characterized by huge energy separations (tens of keV,
10–11 orders of magnitude larger than those involved in NMR), and the transitions among them
are studied by the Mössbauer spectroscopy, making use of γ-rays. Considering that only the
fundamental configuration is populated in normal conditions, in this book, we will use the short
expression “spin quantum number of an isotope” referring to the spin quantum number of its
fundamental configuration.
