NMR Crystallography

EMR HandbooksBased on the Encyclopedia of Magnetic Resonance (EMR), this monograph series focuses on hot topics andmajor developments in modern magnetic resonance and its many applications. Each volume in the serieswill have a specific focus in either general NMR or MRI, with coverage of applications in the key scientificdisciplines of physics, chemistry, biology or medicine. All the material published in this series, plus additionalcontent, will be available in the online version of EMR, although in a slightly different format.

Forthcoming EMR HandbooksMultidimensional NMR Methods for the Solution StateEdited by Gareth A. Morris and James W. EmsleyISBN 978-0-470-77075-7

Solid State NMR Studies of BiopolymersEdited by Ann E. McDermott and Tatyana PolenovaISBN 978-0-470-72122-3

Handbook of RF Coils for MRI and NMREdited by John T. Vaughan and John R. GriffithsISBN 978-0-470-77076-4

Ultrafast Echo-time ImagingEdited by Graeme M. Bydder, Felix W. Wehrli and Ian R. YoungISBN 978-0-470-68835-9

Encyclopedia of Magnetic ResonanceEdited by Robin K. Harris, Roderick E. Wasylishen, Edwin D. Becker, John R. Griffiths, Vivian S. Lee, Ian R.Young, Ann E. McDermott, Tatyana Polenova, James W. Emsley, George A. Gray, Gareth A. Morris, MelindaJ. Duer and Bernard C. Gerstein.

The Encyclopedia of Magnetic Resonance (EMR) is based on the original printed Encyclopedia of NuclearMagnetic Resonance, which was first published in 1996 with an update volume added in 2000. EMR waslaunched online in 2007 with all the material that had previously appeared in print. New updates have sincebeen and will be added on a regular basis throughout the year to keep the content up to date with currentdevelopments. Nuclear was dropped from the title to reflect the increasing prominence of MRI and othermedical applications. This allows the editors to expand beyond the traditional borders of NMR to MRI andMRS, as well as to EPR and other modalities. EMR covers all aspects of magnetic resonance, with articleson the fundamental principles, the techniques and their applications in all areas of physics, chemistry, biologyand medicine for both general NMR and MRI. Additionally, articles on the history of the subject are included.

For more information see: http://www.mrw.interscience.wiley.com/emr

NMR CrystallographyEditors

Robin K. HarrisUniversity of Durham, Durham, UK

Roderick E. WasylishenUniversity of Alberta, Edmonton, Alberta, Canada

Melinda J. DuerUniversity of Cambridge, Cambridge, UK

A John Wiley and Sons, Ltd., Publication

This edition first published 2009© 2009 John Wiley & Sons Ltd

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Library of Congress Cataloging-in-Publication Data

NMR crystallography / editors, Robin K. Harris, Roderick E. Wasylishen, Melinda J. Duer.p. cm.

Includes bibliographical references and index.ISBN 978-0-470-69961-4

1. Crystallography. 2. Nuclear magnetic resonance spectroscopy. I. Harris, RobinKingsley. II. Wasylishen, Roderick E. III. Duer, Melinda J.

QD906.7.N83N67 2009548—dc22

2009031427

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

ISBN-13: 978-0-470-69961-4

Set in 9.5/11.5 pt Times by Laserwords (Private) Limited, Chennai, IndiaPrinted and bound in Singapore by Markono Print Media Pte Ltd

Encyclopedia of Magnetic Resonance

Editorial Board

Editors-in-Chief

Robin K. HarrisUniversity of DurhamDurhamUK

Roderick E. WasylishenUniversity of AlbertaEdmonton, AlbertaCanada

Section EditorsSOLID-STATE NMR & PHYSICS

Melinda J. DuerUniversity of CambridgeCambridgeUK

Bernard C. GersteinAmes, IAUSA

SOLUTION-STATE NMR & CHEMISTRY

James W. EmsleyUniversity of SouthamptonSouthamptonUK

George A. GrayVarian Inc.Palo Alto, CAUSA

Gareth A. MorrisUniversity of ManchesterManchesterUK

BIOCHEMICAL NMR

Ann E. McDermottColumbia UniversityNew York, NYUSA

Tatyana PolenovaUniversity of DelawareNewark, DEUSA

MRI & MRS

John R. GriffithsCancer Research UK

Cambridge ResearchInstitute

CambridgeUK

Vivian S. LeeNYU Langone Medical

CenterNew York, NYUSA

Ian R. YoungImperial CollegeLondonUK

HISTORICAL PERSPECTIVES

Edwin D. BeckerNational Institutes of HealthBethesda, MDUSA

vi Encyclopedia of Magnetic Resonance

International Advisory Board

David M. Grant (Chairman)University of UtahSalt Lake City, UTUSA

Isao AndoTokyo Institute

of TechnologyTokyoJapan

Adriaan BaxNational Institutes of HealthBethesda, MDUSA

Chris BoeschUniversity BernBernSwitzerland

Paul A. BottomleyJohns Hopkins UniversityBaltimore, MDUSA

William G. BradleyUCSD Medical CenterSan Diego, CAUSA

Graeme M. BydderUCSD Medical CenterSan Diego, CAUSA

Paul T. CallaghanVictoria University

of WellingtonWellingtonNew Zealand

Richard R. ErnstEidgenossische Technische

Hochschule (ETH)ZurichSwitzerland

Ray FreemanUniversity of CambridgeCambridgeUK

Lucio FrydmanWeizmann Institute

of ScienceRehovotIsrael

Maurice GoldmanVillebon sur YvetteFrance

Harald GuntherUniversitat SiegenSiegenGermany

Herbert Y. KresselHarvard Medical SchoolBoston, MAUSA

C. Leon PartainVanderbilt University Medical

CenterNashville, TNUSA

Alexander PinesUniversity of California

at BerkeleyBerkeley, CAUSA

George K. RaddaUniversity of OxfordOxfordUK

Hans Wolfgang SpiessMax-Planck Institute

of Polymer ResearchMainzGermany

Charles P. SlichterUniversity of Illinois

at Urbana-ChampaignUrbana, ILUSA

John S. WaughMassachusetts Institute

of Technology (MIT)Cambridge, MAUSA

Bernd WrackmeyerUniversitat BayreuthBayreuthGermany

Kurt WuthrichThe Scripps Research

InstituteLa Jolla, CAUSAandETH ZurichZurichSwitzerland

Contents

Contributors ix

Series Preface xiii

Volume Preface xv

Part A: Introduction 1

1 Crystallography & NMR: an OverviewRobin K. Harris 3

2 Tensors in NMRS. Chandra Shekar, Alexej Jerschow 19

3 Computation of Magnetic Resonance Parameters for Crystalline Systems: PrinciplesJonathan R. Yates, Chris J. Pickard 29

4 Experimental Characterization of Nuclear Spin Interaction TensorsJeremy J. Titman 41

Part B: Chemical Shifts 51

5 Magnetic Shielding & Chemical Shifts: BasicsJulio C. Facelli, Anita M. Orendt 53

6 Symmetry Effects at the Local LevelMatthias Bechmann, Angelika Sebald 63

7 Chemical Shift Computations for Crystalline Molecular Systems: PracticeRobin K. Harris, Paul Hodgkinson, Chris J. Pickard, Jonathan R. Yates, Vadim Zorin 81

8 Chemical Shifts & Solid-state Molecular-level StructureAnita M. Orendt, Julio C. Facelli 99

9 Chemical Shift Anisotropy & Asymmetry: Relationships to Crystal StructureJames K. Harper 113

Part C: Coupling Interactions 125

10 Dipolar & Indirect Coupling: BasicsRoderick E. Wasylishen 127

11 Dipolar Recoupling: HeteronuclearChristopher P. Jaroniec 137

viii Contents

12 Dipolar Recoupling: HomonuclearRobert Tycko 163

13 Dipolar Coupling: Molecular-level MobilityDetlef Reichert, Kay Saalwachter 177

14 Spin Diffusion in Crystalline SolidsLyndon Emsley 195

15 Indirect Coupling & ConnectivityAnne Lesage 209

16 Nuclear Quadrupole Coupling: An Introduction & Crystallographic AspectsSharon E. Ashbrook, Stephen Wimperis 223

Part D: Crystal Structure Determination using NMR 243

17 Fundamental Principles of NMR CrystallographyFrancis Taulelle 245

18 Interplay between NMR & Single-crystal X-ray DiffractionDarren H. Brouwer 263

19 Combined Analysis of NMR & Powder Diffraction DataKenneth D.M. Harris, Mingcan Xu 275

20 Tensor InterplayDavid L. Bryce 289

Part E: Properties of the Crystalline State 303

21 Intermolecular Interactions & Structural MotifsLindsay S. Cahill, Gillian R. Goward 305

22 Hydrogen Bonding in Crystalline Organic SolidsSteven P. Brown 321

23 Inorganic Non-stoichiometric Crystalline Systems & Atomic OrderingMark E. Smith 341

24 Rotational & Translational DynamicsChristopher I. Ratcliffe 355

25 Intramolecular Motion in Crystalline Organic SolidsPaul Hodgkinson 375

26 Structural Phase TransitionsKenneth R. Jeffrey, Glenn H. Penner 387

Part F: Applications of NMR to Crystalline Solids 415

27 Structural BiologyDavid A. Middleton 417

28 Organic & Pharmaceutical ChemistryMarek J. Potrzebowski 435

29 Inorganic & Materials ChemistryRay Dupree 455

30 GeochemistryBrian L. Phillips 463

Index 487

Contributors

Sharon E. Ashbrook School of Chemistry and EaStCHEM, University of St Andrews, St AndrewsKY16 9ST, UKChapter 16: Nuclear Quadrupole Coupling: An Introduction &Crystallographic Aspects

Matthias Bechmann Department of Chemistry, University of York, Heslington YO10 5DD, UKChapter 6: Symmetry Effects at the Local Level

Darren H. Brouwer Department of Chemistry, Redeemer University College, Ancaster, OntarioL9K 1J4, CanadaChapter 18: Interplay between NMR & Single-crystal X-ray Diffraction

Steven P. Brown Department of Physics, University of Warwick, Coventry CV4 7AL, UKChapter 22: Hydrogen Bonding in Crystalline Organic Solids

David L. Bryce Department of Chemistry, University of Ottawa, Ottawa, Ontario K1N 6N5,CanadaChapter 20: Tensor Interplay

Lindsay S. Cahill Department of Physics, University of Warwick, Coventry CV4 7AL, UKChapter 21: Intermolecular Interactions & Structural Motifs

Ray Dupree Physics Department, University of Warwick, Coventry CV7 4AL, UKChapter 29: Inorganic & Materials Chemistry

Lyndon Emsley Centre de RMN a Tres Hauts Champs (CNRS / ENS-Lyon / UCB Lyon 1),Universite de Lyon, 69100 Villeurbanne, FranceChapter 14: Spin Diffusion in Crystalline Solids

Julio C. Facelli Department of Biomedical Informatics and Center for High PerformanceComputing, University of Utah, Salt Lake City, UT 84112-0190, USAChapter 5: Magnetic Shielding & Chemical Shifts: BasicsChapter 8: Chemical Shifts & Solid-state Molecular-level Structure

Gillian R. Goward Department of Chemistry, McMaster University, Hamilton, OntarioL8S 4M1, CanadaChapter 21: Intermolecular Interactions & Structural Motifs

x Contributors

James K. Harper Department of Chemistry, University of Utah, Salt Lake City, UT 84112, USAChapter 9: Chemical Shift Anisotropy & Asymmetry: Relationships toCrystal Structure

Kenneth D. M. Harris School of Chemistry, Cardiff University, Cardiff CF10 3AT, UKChapter 19: Combined Analysis of NMR & Powder Diffraction Data

Robin K. Harris Department of Chemistry, University of Durham, Durham DH1 3LE, UKChapter 1: Crystallography & NMR: an OverviewChapter 7: Chemical Shift Computations for Crystalline MolecularSystems: Practice

Paul Hodgkinson Department of Chemistry, University of Durham, Durham DH1 3LE, UKChapter 7: Chemical Shift Computations for Crystalline MolecularSystems: PracticeChapter 25: Intramolecular Motion in Crystalline Organic Solids

Christopher P. Jaroniec Department of Chemistry, Ohio State University, Columbus, OH 43210, USAChapter 11: Dipolar Recoupling: Heteronuclear

Kenneth R. Jeffrey Department of Chemistry, University of Guelph, Guelph, Ontario N1G 2W1,CanadaChapter 26: Structural Phase Transitions

Alexej Jerschow Department of Chemistry, New York University, New York, NY 10003, USAChapter 2: Tensors in NMR

Anne Lesage Laboratoire de Chimie, Ecole Normale Superieure de Lyon, 69364 Lyon 07,FranceChapter 15: Indirect Coupling & Connectivity

David A. Middleton School of Biological Sciences, University of Liverpool, Liverpool L69 7ZB,UKChapter 27: Structural Biology

Anita M. Orendt Center for High Performance Computing, University of Utah, Salt Lake City,UT 84112-0190, USAChapter 5: Magnetic Shielding & Chemical Shifts: BasicsChapter 8: Chemical Shifts & Solid-state Molecular-level Structure

Glenn H. Penner Department of Chemistry, University of Guelph, Guelph, Ontario N1G 2W1,CanadaChapter 26: Structural Phase Transitions

Brian L. Phillips Department of Geosciences, Stony Brook University, Stony Brook, NY 11794-2100, USAChapter 30: Geochemistry

Contributors xi

Chris J. Pickard School of Physics & Astronomy, University of St. Andrews, St. Andrews KY169SS, UKChapter 3: Computation of Magnetic Resonance Parameters forCrystalline Systems: PrinciplesChapter 7: Chemical Shift Computations for Crystalline MolecularSystems: Practice

Marek J. Potrzebowski Center of Molecular and Macromolecular Studies, Polish Academy ofSciences, 90-362 Łodz, PolandChapter 28: Organic & Pharmaceutical Chemistry

Christopher I. Ratcliffe Steacie Institute for Molecular Sciences, National Research Council Canada,Ottawa, Ontario K1A 0R6, CanadaChapter 24: Rotational & Translational Dynamics

Detlef Reichert Institut fur Physik, Martin-Luther-Universitat Halle-Wittenberg, D-06108Halle, GermanyChapter 13: Dipolar Coupling: Molecular-level Mobility

Kay Saalwachter Institut fur Physik, Martin-Luther-Universitat Halle-Wittenberg, D-06108Halle, GermanyChapter 13: Dipolar Coupling: Molecular-level Mobility

Angelika Sebald Department of Chemistry, University of York, Heslington YO10 5DD, UKChapter 6: Symmetry Effects at the Local Level

S. Chandra Shekar Department of Chemistry, New York University, New York, NY 10003, USAChapter 2: Tensors in NMR

Mark E. Smith Department of Physics, University of Warwick, Coventry CV4 7AL, UKChapter 23: Inorganic Non-stoichiometric Crystalline Systems & AtomicOrdering

Francis Taulelle Lavoisier Institute, University of Versailles-Saint-Quentin-en-Yvelines, 78035Versailles, FranceChapter 17: Fundamental Principles of NMR Crystallography

Jeremy J. Titman School of Chemistry, University of Nottingham, Nottingham NG7 2RD, UKChapter 4: Experimental Characterization of Nuclear Spin InteractionTensors

Robert Tycko Laboratory of Chemical Physics, National Institute of Diabetes and Digestiveand Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520, USAChapter 12: Dipolar Recoupling: Homonuclear

Roderick E. Wasylishen Department of Chemistry, Gunning/Lemieux Chemistry Centre, University ofAlberta, Edmonton, Alberta T6G 2G2, CanadaChapter 10: Dipolar & Indirect Coupling: Basics

xii Contributors

Stephen Wimperis Department of Chemistry and WestCHEM, University of Glasgow, GlasgowG12 8QQ, UKChapter 16: Nuclear Quadrupole Coupling: An Introduction &Crystallographic Aspects

Mingcan Xu School of Chemistry, Cardiff University, Cardiff CF10 3AT, UKChapter 19: Combined Analysis of NMR & Powder Diffraction Data

Jonathan R. Yates TCM Group, Cavendish Laboratory, University of Cambridge, CambridgeCB3 OHE, UKChapter 3: Computation of Magnetic Resonance Parameters forCrystalline Systems: PrinciplesChapter 7: Chemical Shift Computations for Crystalline MolecularSystems: Practice

Vadim Zorin Department of Chemistry, University of Durham, Durham DH1 3LE, UKChapter 7: Chemical Shift Computations for Crystalline MolecularSystems: Practice

Series Preface

The Encyclopedia of Nuclear Magnetic Resonancewas published in eight volumes in 1996, in part tocelebrate the fiftieth anniversary of the first publica-tions in NMR in January 1946. Volume 1 containsan historical overview and ca. 200 short personalarticles by prominent NMR practitioners, while theremaining seven volumes comprised ca. 500 articleson a wide variety of topics in NMR (including MRI).Two “spin-off” volumes incorporating the articles onMRI and MRS (together with some new ones) werepublished in 2000 and a ninth volume was broughtout in 2002. In 2006, the decision was taken to pub-lish all the articles electronically (i.e. on the WorldWide Web) and this was carried out in 2007. Sincethen, new articles have been placed on the web everythree months and a number of the original articleshave been updated. This process is continuing. Theoverall title has been changed to the Encyclopedia ofMagnetic Resonance to allow for future articles onEPR and to accommodate the sensitivities of medicalapplications.

The existence of this large number of articles, writ-ten by experts in various fields, is enabling a new

concept to be implemented, namely the publicationof a series of printed handbooks on specific areasof NMR and MRI. The chapters of each of thesehandbooks will comprise a carefully chosen selec-tion of Encyclopedia articles relevant to the area inquestion. In consultation with the Editorial Board,the handbooks are coherently planned in advance byspecially selected editors. New articles are writtenand existing articles are updated to give appropriatecomplete coverage of the total area. The handbooksare intended to be of value and interest to researchstudents, postdoctoral fellows, and other researcherslearning about the topic in question and undertak-ing relevant experiments, whether in academia orindustry.

Robin K. HarrisUniversity of Durham, Durham, UK

Roderick E. WasylishenUniversity of Alberta, Edmonton, Alberta, Canada

November 2009

Volume Preface

Since the earliest days of NMR, it has been rec-ognized that the technique can provide informationon matters concerning the disposition of atoms inthe unit cells of crystals. Thus, the distance bet-ween protons in the water molecules of gypsum,CaSO4 · 2H2O, was determined by Pake and reportedas 1.58 A in 1948. However, the term NMR crystal-lography has only recently come into common us-age, and even now causes raised eyebrows withinsome parts of the diffraction community. On the otherhand, the power of solid-state NMR to give crystallo-graphic information has considerably increased sincethe CPMAS suite of techniques was introduced in1976. In the first years of the 21st century, the abil-ity of NMR to provide information to support andfacilitate the analysis of single-crystal and powderdiffraction patterns has become widely accepted. In-deed, NMR can now be used to refine diffractionresults and, in favorable cases, to solve crystal struc-tures with minimal (or even no) diffraction data. Theincreasing ability to relate chemical shifts (includingthe tensor components) to the crystallographic loca-tion of relevant atoms in the unit cell via computa-tional methods has added significantly to the practiceof NMR crystallography. Of course, NMR will neverreplace diffraction techniques in the determinationof atomic positions in crystal structures, but diffrac-tion experts will increasingly welcome NMR as anally in their structural analyses. Indeed, it may bethat in future crystal structures will be determined bysimultaneously fitting diffraction patterns and NMRspectra.

However, NMR can also supply information oncrystal structures which is inaccessible or very dif-ficult to obtain by diffraction methods. Prominentamong such investigations is the determination ofdynamics at the molecular level in crystalline ma-terials. There are many NMR methods for studyingsuch motion, including relaxation measurements aswell as spectral features, and they cover a vast range

of motional rates. NMR can frequently distinguishbetween static and dynamic disorders.

Thus NMR crystallography can and should be con-sidered as both complementary and supplementaryto diffraction crystallography. At the time of writ-ing there are few reviews and no books on NMRcrystallography. It therefore seems to be timely toproduce this handbook. The chapters herein, thoughtaken from articles in the electronic version of theEncyclopedia of Magnetic Resonance, were commis-sioned specifically with this handbook in mind. Theeditors have attempted to produce a coherent set ofchapters covering most aspects of NMR crystallog-raphy in a reasonably uniform way. Of course, sinceeach chapter has its specific authors (expert in thetopics in question) there will undoubtedly be somesmall degree of overlap between them and possi-bly a few lacunae. However, the handbook shouldbe of value not only to students and practitionersof solid-state NMR but also to the wider crystallo-graphic community.

Some care has been taken to achieve consistencyof symbols and notation, but there remain a few vari-ations between chapters (for example, in the symbolsused for dipolar coupling constants).

Finally, it may be noted that single-crystal NMRwork, though feasible, is relatively unusual, so moststudies involve microcrystalline/polycrystalline sam-ples. Little information is sacrificed by this usage.Heterogeneous systems containing crystalline compo-nents are also amenable to study. Moreover, structuralinformation at the molecular level (including geomet-rical data) can be obtained by NMR from amorphousand glassy materials, again with little loss. Althoughthat situation is hinted at in various parts of the hand-book, it is not specifically covered, though matterssuch as defect and other nonstoichiometric structuresare discussed.

The handbook is organized into six parts. Thefirst contains an overview and some chapters on

xvi Volume Preface

fundamental NMR topics. Next comes a part con-centrating on chemical shifts, followed by one oncoupling interactions. Part D contains chapters de-scribing how NMR results relate to fundamentalcrystallography concepts and to diffraction meth-ods. The fifth part concerns specific aspects ofstructure, such as hydrogen bonding, and also haschapters on questions of molecular-level mobilityand phase transitions. Finally, the four chapters inthe last part give applications of NMR crystallogra-phy to structural biology, organic and pharmaceuti-cal chemistry, inorganic and materials chemistry, andgeochemistry.

As mentioned above, the articles are also to befound, with minimal differences but changed format,in the online Encyclopedia of Magnetic Resonance,which is at:

http://www.mrw.interscience.wiley.com/emr.The online versions also contain brief autobi-ographies of the article authors, a list of relatedEncyclopedia articles, and, in a number of cases,acknowledgements by the authors. They also havecross-references to Encyclopedia articles which

are not part of this handbook. Additionally, articleabstracts and key words can be found online.

We are grateful to all the authors involved in thishandbook for their agreements to write the onlinearticles which preceded the handbook, for their experttexts and for their cooperation in reaching this stage.We also thank the people at Wiley and at Laserwordsfor all their hard work in bringing the handbook tothe point of publication.

We offer this handbook in the hope that it will notonly provide valuable information for a wide rangeof scientists but that it will also stimulate furtheradvances in NMR crystallography.

Robin K. HarrisUniversity of Durham, Durham, UK

Roderick E. WasylishenUniversity of Alberta, Edmonton, Alberta, Canada

Melinda J. DuerUniversity of Cambridge, Cambridge, UK

November 2009

PART A

Introduction

Chapter 1Crystallography & NMR: an Overview

Robin K. HarrisDepartment of Chemistry, University of Durham, Durham DH1 3LE, UK

1.1 Introduction 31.2 Limitations of Diffraction

Techniques 51.3 NMR and its Crystallographic

Significance 71.4 Required Information 81.5 Concluding Remarks 16

References 17

1.1 INTRODUCTION

Although there is no problem defining nuclear mag-netic resonance (NMR), different people interpret theterm crystallography differently. In particular, expertsin diffraction studies of crystals frequently use theterm as though it is synonymous with structural in-formation obtained by diffraction methods. However,historically, crystals were studied and classified bytheir morphology alone. It became recognized, forexample, that different habits can result from thesame underlying symmetry.

The term crystallography is derived from theGreek words crystallon, meaning cold drop/frozendrop, and graphein, meaning “write”. It refers to theexperimental science of determining the arrangementof atoms in solids, specifically for what are nowcalled crystalline solids. In older usage, it is simply

NMR Crystallography Edited by Robin K. Harris,Roderick E. Wasylishen and Melinda J. Duer © 2009John Wiley & Sons, Ltd. ISBN: 978-0-470-69961-4

the scientific study of crystals. The use of the words“atoms in solids” implies that amorphous solids maybe included in “crystallography”, but this is con-tentious and such systems will not, in general, bedealt with here. Moreover, the original usage of theword (dating from eighteenth century Latin “crys-tallographiæ” and French “cristallographie”) referredto the external shape of crystals (morphology) ratherthan the internal structure, and this is still includedin the normal meaning. Dictionaries define “crystal-lography” in various ways. Some include both inter-nal arrangement and external morphology of crystals.Others discuss the properties of crystals and/or theirclassification. One of the simplest definitions statesmerely “the study of crystal form and structure”.1

Most dictionaries (as opposed to encyclopedias) donot mention diffraction in the definition.

Of course, studies of morphology alone tend toobscure the varied nature of the internal arrange-ments. A student first meeting crystallographic con-cepts may be lead to believe in crystalline perfec-tion, i.e., the existence of perfect three-dimensionaltranslational symmetry of a unit cell with fixed con-tents, belonging to a well-defined space group. Re-ality shows a greater variety of possibilities withinthe general idea of “crystallinity”, questions of non-stoichiometric systems, disorder, defects, incommen-surate cases, and molecular-level mobility all com-plicating the general situation. Moreover, the surfacestructure of crystals deviates from that of their bulkcontents; surface structures are extremely important,since they govern interactions with the surroundingmedium, as in all types of composite materials.

4 Introduction

These facts clearly indicate the width of usageand applicability of the terms crystallography andcrystal structure. As a result, many tools must bebrought to fully understand both the macroscopicnature and atomic-level structure of crystallinematerials. Over the last century, diffraction ex-periments have emerged as the primary way ofdetermining the disposition of atoms in unit cellsof crystals. When a new compound is synthesizedand obtained in crystalline form, it is usually ofhigh priority to determine its solid-state structureby means of single-crystal diffraction studies.Indeed, this is also frequently the key way ofobtaining the molecular structure definitively fororganic and organometallic compounds, thoughsolution-state NMR is equally powerful for suchdeterminations. Indeed, synthetic chemists areoften not interested in crystallographic detailsother than the molecular structure. Single-crystaldiffraction work is accepted as the “gold standard”for providing molecular structure (and the structureof network systems) for crystalline systems. It willundoubtedly remain so.

However, NMR has much to offer the crys-tallographer because it can both supplement andcomplement the diffraction results. The term NMRcrystallography has come into common use in thelast decade, though some diffraction experts decryit.a Historically, NMR has given crystallographicinformation since the earliest days of the technique.It was recognized, for example, that dipolar interac-tions could yield direct information on internucleardistances. This can be achieved easily when there areisolated pairs of protons in a crystal. In 1948 Pake2

reported the line-pair separations of the water protonresonances for a single crystal of calcium sulfatedihydrate (gypsum), CaSO4 · 2H2O, as a function ofthe crystal orientation in B0 (Figure 1.1). Thence, hederived the internuclear distance between the protonsin the hydrate water molecules as 1.58 A. Thiswas at a time (1948) when detecting hydrogenatoms by X-ray diffraction was problematic (as itremained for many years – and even today this

aOne referee objected to the term NMR crystallography in the title ofa submitted paper as follows:

• Since the authors are dealing with powders rather than crystals, theuse of the term crystallography is inappropriate.

• Crystallography specifically applies to diffraction of electromag-netic radiation.

Neither comment appears apposite!

2

1

0

−1

Spl

ittin

g (m

T)

π/2 πh

Figure 1.1. Proton line-pair separations for a single crys-tal of gypsum as a function of the angle, η, between the[100] direction and the applied magnetic field. (Reproducedfrom Ref. 2. © American institute of Physics, 1948.)

can cause difficulties in some cases). Pake alsoillustrated the lineshape for the proton spectrum ofa polycrystalline sample of gypsum, which is of thetype now well known as a Pake doublet, allowinginternuclear distance information to be obtainedeven in the absence of a single crystal. An articlea year later3 illustrates the experimental powderpattern for ClH2C–CH2Cl (Figure 1.2), togetherwith a simulated Pake doublet (though this casedoes not really have isolated proton spin pairs). Thesame paper states the following in the introduction:“The development of experimental methods forobserving nuclear magnetism has provided a meansof investigating certain aspects of molecular andcrystal structure” (italicization inserted here).

Today, NMR methods (and consequently the na-ture of results) have advanced enormously so thatit is now feasible to solve crystal structures forpolycrystalline samples, in favorable cases, by NMRmeans, given only the unit cell parameters and spacegroup from diffraction work,4 and to obtain struc-tural information about crystalline proteins.5 Whileno one would suggest that NMR will ever replacediffraction work, it can and does address crystal-lographic matters that diffraction methods strugglewith. The complementarity of the two techniques isbased on the fact that diffraction methods rely on thepresence of long-range order, whereas NMR spectrareflect the local environment of the nucleus understudy. This means that a combination of the twotechniques is especially powerful (see Chapters 18and 19). For instance, NMR can give structural in-formation on imperfect crystalline situations (suchas are mentioned above) and on crystal surfaces –all cases for which diffraction methods struggle togive definitive data. Indeed, the NMR techniquesare not limited to crystalline materials; hence, infor-mation on molecular-level structure and local envi-ronment can be obtained for amorphous solids (and

Crystallography & NMR: an Overview 5

CH2Cl – CH2Cl 90° K

−10 −5 0 5 10Gauss

H0–H∗→

Figure 1.2. The proton magnetic resonance absorptionline and its derivative for solid 1,2-dichloroethane at 90 K.The solid lines in both parts of the figure (the lower partbeing in derivative mode) represent experimental data. Inthe upper part of the figure, the open circles in the lefthalf are theoretical values computed for a proton separationof 1.70 A and the points in the right half are for 1.72 A.The dashed curve is the theoretical lineshape for a crystalpowder with a proton separation of 1.70 A and in whichmagnetic interactions are confined to pairs of nuclei. Theupper diagram illustrates the well-known “Pake doublet”.(Reproduced from Ref. 3. © American institute of Physics,1948.)

for heterogeneous systems) for which diffraction islargely inapplicable. Such systems provide importantapplications of NMR, but the present article is limitedto crystalline materials (except for one case).

NMR work on single crystals is feasible (andyields detailed crystallographic information).6

However, rather large crystals and special probesare required; hence, single-crystal NMR is notcommon (though more use is perhaps justified).Polycrystalline samples are normally studied, usuallyusing magic-angle spinning. Fortunately, given the

range of specialist pulse sequences available forderiving specific pieces of information, the loss ofinformation incurred by not using single crystals is,in general, rather small. The remainder of this articlewill only involve polycrystalline systems.

One of the simplest uses of solid-state NMRin crystallography is to distinguish between habit(samples giving identical MAS spectra) and polymor-phism (spectra being different) (see Chapter 28).7

Polymorphism is ubiquitous throughout chemistryand its study is essential to many solid-state appli-cations, especially in the pharmaceutical industry.Distinctions between polymorphs by NMR aregenerally clear-cut and are rendered particularlystraightforward by taking advantage of the multi-nuclear nature of NMR. For example, 13C spectramay reveal differences between samples that arenot apparent from 15N studies. The distinctionsenable studies of phase transitions to be made byNMR (see Chapter 26). Another simple use ofsolid-state NMR is in detecting isomorphism. Thus,Figure 1.3 shows8 that four samples of finas-teride (see I) solvates are isomorphous while theremaining (acetic acid) one has a different structure.This example also demonstrates the superb directchemical information given by NMR, i.e., thesignals definitively determine the solvent moleculesinvolved, in contrast to diffraction that, because ofsolvent molecule mobility in the solvates, can onlyshow a volume of electron density of indiscriminatenature.

2

3N

5

101

67

89

OH

H

1914

1312

11

15

16

17

18

HA B

H3C

H3C 20 NH

22 CH3

25 CH3

O

C D

23

24

H3C

Finasteride, I

1.2 LIMITATIONS OF DIFFRACTIONTECHNIQUES

Although it is stressed that the superb ability ofdiffraction techniques to obtain structural information

6 Introduction

70 60 50 40 30 20 10

dC (ppm)

C6 C15 C19C18

C11

C16C7C8

C12

C10C13C9C22C14C17C5

C23,C24& C25

CH

3

CH

CH

3

CH

3CO

+CH

2

CH

2

CH

2O

CH

3

CH

2O

Figure 1.3. Carbon-13 CPMAS spectra of five solvates of finasteride (I). Top to bottom: acetic acid solvate; ethyl acetatehydrate solvate; THF hydrate solvate; isopropanol hydrate solvate; and dioxane hydrate solvate. Assignments are indicatedfor the solvent peaks. (Reproduced with permission from Ref. 8. © 2007, John Wiley & Sons Ltd.)

for crystalline materials (most importantly, the posi-tions of atoms in the unit cell) is and will remainunsurpassed, there are certain inherent difficultieswith obtaining some facets of crystallographic in-formation from single-crystal diffraction experiments.These can be summarized as follows:

• For the best results, single crystals are required,which should be of the order of 0.001 mm3 orgreater (though with synchrotron radiation muchsmaller crystals can be effectively studied).

• The crystals need to be as perfect as possible, i.e.,without substantial defects – though special tech-niques can cope with some imperfections (such astwinning).

• Disorder, either spatial or temporal, causes uncer-tainties.

• For X-ray diffraction (though not neutrondiffraction), distinctions between atoms ofdifferent elements with similar atomic numbersare sometimes difficult to make (especially inisoelectronic cases).

• Historically, hydrogen atoms have been difficultto locate with accuracy, especially in the presenceof heavy atoms.

• The crystal studied may not be representativeof the bulk sample (though powder diffractionexperiments can be used to clarify this matter).

• Amorphous solids cannot be adequately exam-ined.

Advances in technology are rendering some ofthese difficulties less restrictive. In addition, in recentyears, the power of powder diffraction techniques hasbeen greatly increased so that it is feasible in manycases to obtain detailed crystal structures by thismeans.9 This is particularly valuable, for example, forsamples of small crystals embedded in an amorphousmatrix, as is the case for many ceramic systems.Other advances in X-ray diffraction procedures allowelectron distributions to be modeled in detail, andthe location of hydrogen atoms is much improved.However, the fact remains that X rays locate electrondensity, not nuclei, though neutron diffraction doesdepend on the positions of atomic nuclei.

Crystallography & NMR: an Overview 7

There are two major areas in which complementaryinformation is desirable:

1. Molecular-level mobility: Most X-ray diffractionmeasurements that result in structure determina-tions now take place at 120 K. However, evenat this temperature, there is significant mobilityover the timescale of a typical diffraction exper-iment (generally ca. 4–6 h). Analysis of diffrac-tion patterns can take some account of this (espe-cially for vibrational motion) by using ellipsoidsbased on atomic displacement factors, though forX-ray measurements these actually depict elec-tron density distributions. Site exchange (tem-poral disorder) by rapid jump motions can beaccounted for by the use of fractional popula-tions if the sites are distinguishable. However,when equivalent sites are involved, as with 120◦

rotations of tertiary butyl groups, the exchangecannot be easily detected by diffraction methods.Moreover, obtaining information on the kineticsof molecular-level motion is extremely difficultby diffraction techniques. In this context, mostvibrations occur at a sufficiently high frequencythat their effects on both diffraction patterns andNMR spectra can be ignored.

2. Purely spatial (i.e., static) disorder raises a differ-ent problem, in that, in principle, the structure isnot properly spatially repetitive; hence, it is notpossible in strict theory to define a space groupexcept on an average basis. In such cases, theanalysis of diffraction patterns results in struc-tures with fractional occupations. Differentlyordered domains are difficult to investigate.

1.3 NMR AND ITS CRYSTALLOGRAPHICSIGNIFICANCE

The relationship of NMR to crystallography is a com-plex one (see Chapter 17). NMR parameters can pro-vide substantial crystallographic information in bothdirect and indirect ways. Such information derivesfrom the various NMR measurables (see Chapters 2and 4), namely, the following:

• Isotropic chemical shifts (see Chapters 5 and 8):Traditionally, these have been used in the solutionstate to give direct information on molecular-levelchemical structure. They can be used in simi-lar manner for crystalline solids.10 They can also

define the number of nuclei in different environ-ments for relevant nuclei in the crystal structure.This will determine the crystallographic asym-metric unit. In favorable circumstances, molecularsymmetry and even space group information areobtained. In addition, chemical shifts often pro-vide knowledge about intermolecular interactions,for example, the location of hydrogen bonds.

• Full information on chemical shift tensors: Theanisotropy and asymmetry of the tensor relatedirectly to the detailed electronic environmentof the atom concerned and hence correlate withthe information obtainable from X-ray diffraction(see Chapter 9).

• Dipolar coupling (see Chapter 10): Thisspin–spin interaction gives interatomic distanceinformation directly and provides a verypowerful method of studying crystal structure.However, molecular-level motion can stronglyaffect the observed dipolar coupling constants(see Chapter 13) so that care needs to betaken in interpretation. When MAS is used,recoupling pulse sequences are frequentlynecessary to obtain dipolar coupling constants(see Chapters 11 and 12).

• Isotropic indirect spin–spin couplingb (seeChapters 10 and 15): This parameter gives in-formation largely on conformational matters andis especially powerful for studies of molecularstructure within crystals. However, its utility forsolids has hitherto been muted because splittingpatterns are often obscured by the linewidthsin solids, particularly for (H,H) and long-range(C,H) coupling. On the other hand, couplinginvolving heavier atoms can be informative.Moreover, sophisticated measurements canreveal coupling across hydrogen bonds,11 givingintermolecular relationships in crystals (seeChapter 22).

• Quadrupolar coupling: This interaction dependson electric field gradients (EFGs) at the nuclei,which in turn depend sensitively on the local en-vironment. The anisotropy and asymmetry of thecoupling provide additional information related tothe site symmetry of the relevant nuclei in crys-talline materials (see Chapter 16).

• Relaxation times: Three such processes are ofparticular importance for obtaining informationon molecular-level motion (see Chapters 13, 24

bIn principle, indirect coupling is a tensor property, but its anisotropyand asymmetry have so far proved to be of limited use.

8 Introduction

and 25). These are (a) spin-lattice (otherwiseknown as longitudinal) relaxation, with character-istic time designated T1; (b) spin-lattice relaxationin the rotating frame, designated time T1ρ ; and (c)spin–spin (otherwise known as transverse) relax-ation, with time T2. They have characteristic mo-tional dependencies at rates of tens to hundreds ofmegahertz, tens of kilohertz, and low frequencies,respectively. The related phenomenon of spin dif-fusion also carries information about the solidstate (see Chapter 14).

Other articles will explore these parameters in con-siderable detail. In this one, examples will be quotedto give the flavor of “NMR crystallography”. Thederived information can facilitate the complete struc-ture determination from single-crystal or powderdiffraction patterns. In many cases, the knowledgeobtained is additional to that found from diffrac-tion work. Applications of NMR crystallography havebeen made to structural biology (see Chapter 27),geochemistry (see Chapter 30), organic and pharma-ceutical chemistry (see Chapter 28), and inorganicand materials chemistry (see Chapter 29).

1.4 REQUIRED INFORMATION

So what constitutes crystallographic information?

1.4.1 Molecular-Level Information

As mentioned above, one key aspect is theatomic bonding (connectivity) pattern, formingthe molecules or networks. The long history ofsolution-state NMR in this context, predating mosthigh-resolution solid-state NMR, indicated the poten-tial of the technique for solids. That potential is nowincreasingly being fulfilled, especially by the use ofisotropic chemical shifts. One aspect of importancelies in the fact that solid-state structures may notbe identical to those in solution. A relatively earlyNMR example of this phenomenon was provided12

by Pt(PPh3)2(P(mesityl) = CPh2) (II). Phosphorus-31CPMAS spectra of the solid showed unambiguously(from chemical shifts) that this compound has anη1-coordinated (see IIa) phosphaalkene ligand, indisagreement with the η2 case (see IIb) indicatedby NMR for the solution state. The CPMAS workconfirmed single-crystal diffraction results, thus

giving an example of solid-state NMR acting as abridge between solution-state NMR and diffractiontechniques.

Pt P

Mesityl

C

Ph

PhPh3P

Ph3P

Pt

Ph3P

Ph3P

P

C

Mesityl

Ph2

IIa IIb

CPMAS NMR provides an easier route to molec-ular structure in solids than diffraction because thelink between isotropic chemical shifts and bondingenvironments is direct and specific to each atom.The correlations between shifts and bonding havebeen exhaustively worked out over five decades fromsolution-state NMR data. Indeed, solution-state NMRis usually the preferred route to obtain molecularstructure. Solid-state molecular-level structure deter-mination can make use of the shift/structure correla-tions, but due regard has to be paid to specificallysolid-state shift effects.

Indirect coupling can also play an important rolein determining bonding patterns in crystalline solids(see Chapter 15), though, in contrast to solution-statework, this has mostly not involved (H,H) or (C,H)coupling. An early example of such usage was thedetermination13 of the connectivity in the zeoliteZSM-39 via 29Si COSY experiments (Figure 1.4).Recent pulse sequence developments14 have extendedthe scope for such determinations via J coupling.Combinations of NMR experiments are sometimesnecessary to provide full topological information oncrystal structures.15 Dipolar coupling can also be ofassistance in determining molecular structure in crys-talline materials, though it has to be remembered that,because it occurs through space, it does not, per se,distinguish between connectivity and intermolecularproximity.

Of course, there is more to molecular structure thanconnectivity. In particular, conformations of flexi-ble chains are of importance – and these can beexpected to differ between solution and crystallinestates since conformational flexibility is normally in-hibited in most solids. Solid-state NMR chemicalshifts provide direct conformational information, asillustrated by the case of form II of oxybuprocaine

Crystallography & NMR: an Overview 9

−106 −108 −110 −112 −114 −116 −118 −120 −122 −124

dSi (ppm)

T1

T1T2

T2T3

T2

T3

Figure 1.4. A two-dimensional homonuclear Si,Si connectivity plot for the zeolite ZSM-39, showing the connectivity(via oxygen) between the four different silicon sites. (Reprinted with permission from Ref. 13. © 1989 American ChemicalSociety.)

hydrochloride (III).16 The 13C CPMAS spectrum ofthis compound (Figure 1.5) shows the existence ofsignals at unusual shifts for an ethyl group, 4–7 ppmto low frequency of those for the solution state.These are consistent with the expected positions fora gauche–gauche conformation (influenced by thewell-known “γ -gauche shielding effect”).

H2N

O

ONH+

10

O

98

7

34

5

2

1

6

11

12

13

14

15

16

17

Cl−

Oxybuprocaine hydrochloride, III

dC (ppm)020406080100120140160180

(a)

(b)

Figure 1.5. Carbon-13 CPMAS spectra of oxybuprocainehydrochloride (III) form I (b) and form II (a), with arrowsindicating the unusual positions for an ethyl group in thelatter.

Dipolar coupling, being through space, can alsogive information on conformations – in principlemore directly than “scalar” coupling can. Thus, Terao

10 Introduction

and coworkers17 were able to determine the com-plete molecular structure of glycylisoleucine (IV),involving six dihedral angles, via selective dipolarrecoupling experiments. Chemical shifts and dipolarcoupling constants are being increasingly used to de-termine the secondary structure of crystalline (andamorphous) proteins.18

CH

CH2CH3H3C

H2NCH2CO.NHCHCO2H

Glycylisoleucine, IV

A second key aspect of crystallography concernsintermolecular interactions and the intermolecular en-vironment. Here also, NMR has a strong role to play(see Chapter 21). One common stabilizing influencefor crystal structures is the existence of intermolecu-lar hydrogen bonding. The presence of such bondingand its location can frequently be attested by thechemical shift of a relevant nucleus (see Chapter 22).Thus, for form III of cortisone acetate (V), whichhas three molecules in the asymmetric unit, isotropic13C chemical shifts (assigned via measurements ofthe anisotropies and asymmetries) show19 that twosuch molecules have hydrogen bonds involving thecarbonyl group at position C3, while the third bondsthrough the carbonyl group at position C22. Inter-molecular hydrogen bonding (NH–N) has also beendetected by establishing the existence of indirectspin–spin (JNN) coupling.20

O

O

O

OH

O

O

19

12

3 54

109

8

76

1112

13

14

18

1716

15

2021 22

23

Cortisone acetate, V

Additional information on atomic environmentscan come from the use of the tensorial natureof shielding (see Chapter 9). For example,experimental measurements of the anisotropy

−1.0 −0.5 0.0

s/(−sp)

(a)

(b)

(c)

(d)

(e)

Figure 1.6. Schematic solid-state 199Hg spectra for staticsamples, illustrating the effects of changes in mercury coor-dination from linear HgX2 (top) to trigonal HgX3 (bottom).(Reproduced with permission from Ref. 21. © 1997, Else-vier Science B.V.)

Crystallography & NMR: an Overview 11

and asymmetry of 199Hg chemical shifts allowthe coordination of mercury in its crystallinecompounds to be deduced from simple theoreticalconsiderations.21 Thus, Figure 1.6 shows the varia-tion of bandshape expected as the local environmentvaries between linear HgX2 and trigonal HgX3. Thecompound [Hg(S-2,3,5,6-Me4C6H)3]− illustratesthis point: the measured values of the anisotropyand asymmetry of the 199Hg chemical shift tensorindicate that the compound contains a distortedHgS3 environment.

The multidimensional capability of NMR conveysconsiderable advantages and can reveal intermolec-ular effects. This is well seen for the simple caseof methanol.22 Two-dimensional spectra involvingchemical shift anisotropy and spin diffusion for13C-enriched samples detect (Figure 1.7) differencesin orientation between neighboring moleculesbecause the spin-exchange process results in changesin the direction of the chemical shift principal axes.

Moreover, there is a clear distinction between theα and β forms of methanol, which is not readilyapparent in the one-dimensional spectra. Theshape of the band for the β form in Figure 1.7(c)is simulated with the assumption that there is a12◦ angle between C–O bond vectors in adjacentmolecules. The simulated spectrum for the α formutilizes the crystal structure of Torrie et al.23 Itmay be noted that the spectrum of the glassysample shows rather random relative orientations ofmolecules in this case.c

Isotropic chemical shifts give immediate informa-tion about host–guest systems, including solvates.This includes recognition of the nature of the guestmolecules (which may not be immediately appar-ent from diffraction patterns if the guests are highly

cWhile amorphous systems can scarcely come under the heading of“crystallography” and are not otherwise dealt with in this article, thisexample is included here to emphasize that NMR is not limited tocrystalline systems.

b form168 K

a form133 K

Glass103 K

80 40 0ppm

80 40 0ppm(a) (b) (c)

8040

080

400

8040

0

Figure 1.7. Carbon-13 spectra of static samples for three forms of methanol: (a) one-dimensional spectra; (b) experimentalEXSY spectra (involving spin diffusion during the mixing time); and (c) simulated spectra.

12 Introduction

mobile8). The relative positions of guest and host canalso be addressed by studying the mutual effects onchemical shifts. In the case of incommensurate sys-tems, which require considerations of n-dimensional(n> 3) “superspace” for diffraction analysis, NMRcan again provide immediate information on the guestmolecules and on the host molecules separately.

Dipolar coupling is, in principle, a prime sourceof intermolecular environment information (seeChapter 10). For cases of hydrogen bonding, goodresults can be obtained. For instance, for l-tyrosinehydrochloride an intermolecular C–O–H distanceof 2.47 ± 0.07 A was obtained by NMR,24 whichmay be compared with the value 2.521 A reportedfrom neutron diffraction experiments. A trulyintermolecular distance of <3 A between aromaticprotons has been found from double-quantumMAS work on a benzoxazine dimer.25 N,C dipolarcouplings have been used26 to show the proximityof the α-helix of one molecule of a 56-amino acidprotein to the N terminus of another molecule.Distances between carbon atoms in differentfibrils of amyloid peptides have been explored byNMR.27 However, in general, there are considerabledifficulties in quantifying intermolecular internuclear

distances via measurements of dipolar couplingbecause multiple interactions frequently complicatethe evaluations, even in the case of selective isotopicenrichment. This means that diffraction-derivedstructures are usually required to understand theNMR results.

A third key element of crystallography, which isimperfectly addressed by diffraction techniques, ismolecular-level mobility. NMR has many approachesto this problem (see Chapters 24 and 25), but a cou-ple of examples will suffice at this point. In urea- andthiourea-inclusion compounds, the guest moleculesare highly mobile, though in restricted ways. For theparticular case of fluorocyclohexane as a guest, ringinversion is not greatly hindered by the channels, andvariable-temperature 19F spectra reveal28 a classic co-alescence phenomenon (Figure 1.8), from which theactivation thermodynamic parameters can be derived.

Mobility information can come from quadrupolarspectra as well as those of spin-1/2 nuclides. Thus,molecular-level mobility can, in some circumstances,affect the linewidths of isotropic STMAS spectra butnot isotropic MQMAS spectra29 (Figure 1.9). Deu-terium bandshapes of static samples are powerfulindicators of mobility. For instance, they have beenused30 to accurately describe the nature of the motion

−130 −140 −150 −160 −170 −180 −190 −200 −210 −220

Temperature (K)

300

278

268

258

247

237

217

177

dF (ppm)

Figure 1.8. Experimental 19F MAS spectra (with proton decoupling) of the fluorocyclohexane/thiourea inclusion com-pound for various temperatures, showing the coalescence of the axial and equatorial signals resulting from ring inversion.