Cross-relaxation and cross-correlation parameters in NMR: molecular approaches

336 Pages·2018·6.507 MB·English

by  Canet, Daniel

Cross-relaxation and Cross-correlation Parameters in NMR
Molecular Approaches
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New Developments in NMR
Editor-in-Chief:
William S. Price, University of Western Sydney, Australia
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75- Sharon Ashbrook, University of St Andrews, UK
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22 Bruce Balcom, University of New Brunswick, Canada
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82 Istv´an Furo´, Industrial NMR Centre at KTH, Sweden
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81 Masatsune Kainosho, Tokyo Metropolitan University, Japan
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9 Maili Liu, Chinese Academy of Sciences, Wuhan, China
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0. Titles in the Series:
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doi: 1: Contemporary Computer-Assisted Approaches to Molecular Structure
g | Elucidation
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c. 2: New Applications of NMR in Drug Discovery and Development
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s.r 3: Advances in Biological Solid-State NMR
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http:// Techniques and Applications
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17 6: Gas Phase NMR
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Oct 8: Biophysics and Biochemistry of Cartilage by NMR and MRI
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0 9: Diffusion NMR of Confined Systems: Fluid Transport in Porous Solids
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d o and Heterogeneous Materials
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12: Cross-relaxation and Cross-correlation Parameters in NMR:
Molecular Approaches
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Cross-relaxation and
Cross-correlation Parameters
1 in NMR
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5- Molecular Approaches
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or Universite de Lorraine, France
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75- Preface
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1 Sometimeago,IwasaskedbyProfessorWilliamS.Pricetobetheeditorofa
doi: book about cross-correlation in NMR. I found the idea fairly interesting, but
org | at first (and only at first), that it might appear as a sibylline and restricted
sc. subject.IansweredBillthatcross-correlationisevidentlyrelatedto(andpart
bs.r of)spinrelaxationbutthatspinrelaxationwaspersetoobroadasubject.By
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p://p contrast, it could be interesting to add cross-relaxation to the initial title of
htt the project. In fact, what are called cross-correlation relaxation rates can
n beconsideredaswellaspertainingtocross-relaxation.Theconceptofcross-
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17 relaxation wasintroduced asearlyas1953 byA.W.Overhauser, whohadto
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ob irradiating electronspins, nuclear spins would be enhancedby the transfer
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O of electron polarization. This idea was rapidly extended to cross-relaxation
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0 among nuclear spins with the tremendous applications known as the
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d o nuclear Overhauser effect (nOe), which generated a new era in nuclear
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sh magnetic resonance (NMR) accessing unprecedented information about
ubli molecular structure. Cross-relaxation rates depend on a single relaxation
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mechanism (generally the interaction between the magnetic moments
associated with the two considered spins). By contrast, cross-correlation
ratesdependontwodifferentmechanismsand,althoughactinginthesame
wayas cross-relaxation rates, may couplequantitiesthat are not necessarily
polarizations. Cross-correlation, discovered shortly after cross-relaxation,
wasconsideredforsometimeasascientificcuriosity.Itthenappearedthat
cross-correlation rates can provide invaluable dynamical and structural
information. Relevanttheoretical and experimental developments followed,
eventuallyleadingtoline-narrowingphenomenathatproveddecisiveforthe
NMR observation of larger and larger biomolecules.
This book is divided into four chapters. The first chapter, by nature
introductive, is an overview of nuclear spin relaxation with an emphasis on
NewDevelopmentsinNMRNo.12
Cross-relaxationandCross-correlationParametersinNMR:MolecularApproaches
EditedbyDanielCanet
rTheRoyalSocietyofChemistry2018
PublishedbytheRoyalSocietyofChemistry,www.rsc.org
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vi Preface
cross-relaxation and cross-correlation. The next two chapters are devoted to
cross-relaxation and cross-correlation in small or medium-size molecules,
chapter two in homonuclear systems and chapter three in heteronuclear
systems. The final chapter (Chapter 4) deals with the important impact of
5 cross-relaxationandcross-correlationinbiologicalsystems.Wehopetohave
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5- growing topic. Many examples illustrate its considerable possibilities. In
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24 addition, the reader will find different theoretical approaches (leading
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26 nevertheless to the same results), corresponding to the sensitivity of each
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17 author; this should be helpful for fully understanding the rich literature on
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97 this subject.
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03 Chapter 1 Introduction to Nuclear Spin Cross-relaxation and
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doi: Daniel Canet
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c. 1.1 A Survey of Nuclear Spin Relaxation Mechanisms
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bs.r and the Concept of Spectral Densities 2
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01 1.1.3 Chemical Shift Anisotropy (CSA) 8
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1.2.3 Product-operators for a Two Spin 1/2 System
and Relevant Spin States 16
1.2.4 The Density-matrix and the
Density-operator 20
1.3 Evolution Equations 23
1.3.1 The Interaction Representation 23
1.3.2 Solving the Density-operator
Evolution Equation within the
Bloch–Wangsness–Redfield Theory 24
1.3.3 EvolutionEquationsofQuantitiesAssociated
with Product-operators 26
NewDevelopmentsinNMRNo.12
Cross-relaxationandCross-correlationParametersinNMR:MolecularApproaches
EditedbyDanielCanet
rTheRoyalSocietyofChemistry2018
PublishedbytheRoyalSocietyofChemistry,www.rsc.org
vii
View Online
viii Contents
1.4 Spin Relaxation in a Single Spin 1/2 System 28
1.4.1 Relaxation by Random Fields 28
1.4.2 Relaxation by Chemical Shift Anisotropy
(CSA) 29
07 1.5 Spin Relaxation in a Two Spin 1/2 System Involving
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78 Auto-relaxation Rates Including the Dipolar
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c.or 1.6.1 TheNuclearOverhauserEffect(nOe)andthe
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on 1.7 Multi-spin Systems. Occurrence of Dipolar–Dipolar
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Small Molecules and in Soft Matter 61
Kavita Dorai
2.1 Introduction 61
2.2 One-dimensional Cross-relaxation Experiments in
Homonuclear Systems 62
2.2.1 Steady-state Nuclear Overhauser
Enhancement 62
2.2.2 Transient NOE Experiments 63
2.2.3 2D Cross-relaxation Experiments in
Homonuclear Systems 71
2.2.4 Distance Measurements from NOE
Experiments 77
2.2.5 Selected Examples of the Usefulness of
Cross-relaxation 80
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Contents ix
2.3 Experiments to Measure Cross-correlated
Relaxation Rates 94
2.3.1 Experimental Observation of Longitudinal
Cross-correlations 94
07 2.3.2 Experimental Observation of Transverse
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2.5.5 Motional Information from
Cross-correlation Rates 145
2.6 Conclusions 148
Acknowledgements 149
References 149
Chapter 3 Heteronuclear Cross-relaxation 166
Bernard Ancian
3.1 Introduction and Basic Concepts 166
3.2 The Heteronuclear Overhauser Effect (HOE) 170
3.3 HOE’s Measurements and the Information they
Provide 174
3.4 2D Heteronuclear Overhauser Spectroscopy
(HOESY) 179
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x Contents
3.5 The 1D HOESY Experiment 187
3.6 An Improved HOESY Experiment: The P.HOESY
Sequence 188
3.7 Inverse HOESY Experiments 190
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4.2 Theory 241
4.2.1 The Homogeneous Master Equation 241
4.2.2 Frame Transformations of Liouvillian
Superoperators 243
4.2.3 Average Liouvillian Theory: Discrete
Averaging 244
4.2.4 ApplicationofDiscreteALT:Measurementof
CSA/DD CCCR Rates 246
4.2.5 Average Liouvillian Theory: Continuous
Averaging 246
4.2.6 Application of Continuous ALT:
Measurement of CSA/DD CCCR Rates 248
4.2.7 Note on the Secular Approximation 249
4.3 Measurements of Cross-relaxation at the
Steady-state Effects 249