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Long-lived nuclear spin order: theory and applications PDF

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Long-lived Nuclear Spin Order Theory and Applications 1 0 0 P F 2- 7 9 9 1 0 8 8 7 1 8 7 9 9/ 3 0 1 0. 1 oi: d g | or c. s s.r b u p s:// p htt n o 0 2 0 2 pril A 7 0 n o d e h s bli u P View Online New Developments in NMR Editor-in-chief: William S. Price, Western Sydney University, Australia 1 0 0 Series editors: P F 2- Bruce Balcom, University of New Brunswick, Canada 7 9 Istv´an Furo´, Industrial NMR Centre at KTH, Sweden 9 1 0 Masatsune Kainosho, Tokyo Metropolitan University, Japan 8 8 7 Maili Liu, Chinese Academy of Sciences, Wuhan, China 1 8 7 9 39/ Titles in the series: 0 1 0. 1: Contemporary Computer-Assisted Approaches to Molecular Structure 1 oi: Elucidation d g | 2: New Applications of NMR in Drug Discovery and Development or 3: Advances in Biological Solid-State NMR c. s.rs 4: Hyperpolarized Xenon-129 Magnetic Resonance: Concepts, b u Production, Techniques and Applications p s:// 5: Mobile NMR and MRI: Developments and Applications p htt 6: Gas Phase NMR n o 7: Magnetic Resonance Technology: Hardware and System 0 02 Component Design 2 pril 8: Biophysics and Biochemistry of Cartilage by NMR and MRI A 9: Diffusion NMR of Confined Systems: Fluid Transport in Porous Solids 7 0 and Heterogeneous Materials n d o 10: NMR in Glycoscience and Glycotechnology e h 11: Fast NMR Data Acquisition: Beyond the Fourier Transform s ubli 12: Cross-relaxation and Cross-correlation Parameters in NMR: Molecular P Approaches 13: Contrast Agents for MRI: Experimental Methods 14: NMR-based Metabolomics 15: Modern Methods in Solid-state NMR: A Practitioner’s Guide 16: Paramagnetism in Experimental Biomolecular NMR 17: Optimizing NMR Methods for Structure Elucidation: Characterizing Natural Products and Other Organic Compounds 18: Field-cycling NMR Relaxometry: Instrumentation, Model Theories and Applications 19: Hybrid MR-PET Imaging of the Brain: Systems, Methods and Applications View Online 20: NMR Methods for Characterization of Synthetic and Natural Polymers 21: In-cell NMR Spectroscopy: From Molecular Sciences to Cell Biology 22: Long-lived Nuclear Spin Order: Theory and Applications 1 0 0 P F 2- 7 9 9 1 0 8 8 7 1 8 7 9 9/ 3 0 1 0. 1 oi: d g | or c. s s.r b u p s:// p htt n o 0 2 0 2 pril A 7 0 n o d e h s bli u P How to obtain future titles on publication: Astandingorderplanisavailableforthisseries.Astandingorderwillbring delivery of each new volume immediately on publication. For further information please contact: BookSalesDepartment,RoyalSocietyofChemistry,ThomasGrahamHouse, Science Park, Milton Road, Cambridge, CB4 0WF, UK Telephone: þ44 (0)1223 420066, Fax: þ44 (0)1223 420247 Email: [email protected] Visit our website at www.rsc.org/books View Online 1 0 0 P F 2- 7 9 9 1 0 8 8 7 1 8 7 9 9/ 3 0 1 0. 1 oi: d g | or c. s s.r b u p s:// p htt n o 0 2 0 2 pril A 7 0 n o d e h s bli u P View Online Long-lived Nuclear Spin Order Theory and Applications 1 0 0 P F 2- 7 9 Edited by 9 1 0 8 8 17 Giuseppe Pileio 8 7 9 University of Southampton, UK 9/ 03 Email: [email protected] 1 0. 1 oi: d g | or c. s s.r b u p s:// p htt n o 0 2 0 2 pril A 7 0 n o d e h s bli u P View Online 1 0 0 P F 2- 7 9 9 1 0 8 8 7 1 8 NewDevelopmentsinNMRNo.22 7 9 9/ 3 0 PrintISBN:978-1-78801-568-4 1 0. PDFISBN:978-1-78801-997-2 1 oi: EPUBISBN:978-1-78801-998-9 org | d PErleincttrIoSnSiNc:IS2S0N44:-2205434X-2548 c. s bs.r AcataloguerecordforthisbookisavailablefromtheBritishLibrary u p s:// rTheRoyalSocietyofChemistry2020 p htt on Allrightsreserved 0 2 0 2 Apartfromfairdealingforthepurposesofresearchfornon-commercialpurposesorfor pril privatestudy,criticismorreview,aspermittedundertheCopyright,DesignsandPatents A Act1988andtheCopyrightandRelatedRightsRegulations2003,thispublicationmaynot 7 0 bereproduced,storedortransmitted,inanyformorbyanymeans,withouttheprior n o permissioninwritingofTheRoyalSocietyofChemistryorthecopyrightowner,orinthe d e caseofreproductioninaccordancewiththetermsoflicencesissuedbytheCopyright h blis LicensingAgencyintheUK,orinaccordancewiththetermsofthelicencesissuedbythe Pu appropriateReproductionRightsOrganizationoutsidetheUK.Enquiriesconcerning reproductionoutsidethetermsstatedhereshouldbesenttoTheRoyalSocietyof Chemistryattheaddressprintedonthispage. Whilstthismaterialhasbeenproducedwithallduecare,TheRoyalSocietyofChemistry cannotbeheldresponsibleorliableforitsaccuracyandcompleteness,norforany consequencesarisingfromanyerrorsortheuseoftheinformationcontainedinthis publication.Thepublicationofadvertisementsdoesnotconstituteanyendorsementby TheRoyalSocietyofChemistryorAuthorsofanyproductsadvertised.Theviewsand opinionsadvancedbycontributorsdonotnecessarilyreflectthoseofTheRoyalSocietyof Chemistrywhichshallnotbeliableforanyresultinglossordamagearisingasaresultof relianceuponthismaterial. TheRoyalSocietyofChemistryisacharity,registeredinEnglandandWales, Number207890,andacompanyincorporatedinEnglandbyRoyalCharter (RegisteredNo.RC000524),registeredoffice:BurlingtonHouse,Piccadilly, LondonW1J0BA,UK,Telephone:þ44(0)2074378656. Forfurtherinformationseeourwebsiteatwww.rsc.org PrintedintheUnitedKingdombyCPIGroup(UK)Ltd,Croydon,CR04YY,UK 7 0 0 P F 2- Preface 7 9 9 1 0 8 8 7 1 8 7 9 9/ 3 0 1 0. Itwasthebeginningof2005andIwaslookingforaresearchgrouptospend 1 oi: sixmonthswithasapartofmyPhDprogramme.IendedupjoiningLevitt’s d g | group in Southampton with the clear aim to learn about spin dynamics in c.or great depth. That was indeed the right place. At that time Malcolm and s s.r group members were quite excited about their recent demonstrations of b s://pu tuhneaneximistoeunscleyobfelnieuvceldeatrosbpeinashtaatredslwimhiotsteolnifuectilmeaeresxpcienesdteadteTs’1l–ifeutpimtoe.thThene p htt veryfirsttwopapersonthephenomenonhadjustbeenpublishedandIwas n 0 o assigned the task to carry the research forward. I liked the idea very much; 2 0 mainly because the topic embraces a good amount of spin dynamics in the 2 pril derivationofnewanalyticalequationstodescribetherelaxationofsuchspin A states or the development of new pulse sequences, the use of synthetic 7 n 0 chemistry to design molecules supporting those states and a good level of o d thinking and imagination to exploit these findings into some useful appli- e sh cations.Itisnownearly15yearslaterandIamstillinvestigatingthefieldas bli u part of the activities of my own research group. Meanwhile, the potentiality P of the subject was rapidly embraced by a number of colleagues worldwide and a good number of research papers has been published as a result. InthisbookIinvitedsuchcolleaguestosharetheresultsoftheirresearch efforts but todo so inalanguage that is atan introductory level so that the bookcanserveasastartingpointofunderstandingforresearcherswhomay become fascinated by the subject in the future. The book brings together 23 chapters written by experts from all over the world who are actively working onthesubject.Thebookisdividedintofourpartsthat encompass themajortheoriesbehindthephenomenon,themethodologydevelopedso far, the range of proposed applications and some generalisations of the originalidea.InPart1,afteropeningwithageneraloverviewofthetopic,we lay down a symmetry-based theory for the existence of singlet order in a NewDevelopmentsinNMRNo.22 Long-livedNuclearSpinOrder:TheoryandApplications EditedbyGiuseppePileio rTheRoyalSocietyofChemistry2020 PublishedbytheRoyalSocietyofChemistry,www.rsc.org vii View Online viii Preface given spin-system and the analytical equations that describe the relaxation ofsuchspinorderunderseveralrelaxationmechanisms.InPart2wediscuss theNMRpulsesequencesdevelopedtoaccessandmanipulatesingletorder, starting with the synthetic chemistry rules to produce molecules that supportsuchanorder.Part3isdedicatedtotheexploitationofsingleorder 7 00 in a number of fields, including investigations of drug affinity, quantum P F computing or the study of porous media. Part 4 discusses other forms of 2- 97 long-lived spin order such as long-lived coherences or long-lived spin order 9 01 in more complex spin systems. 8 78 Before inviting you to read this work, I would like to thank all of the 1 78 authors who contributed to this book, which is clearly the result of a 9 9/ collective effort rather than my personal one. My most special thanks go to 3 0 1 MalcolmLevitt,whointroducedmetothetopicand,asinhisstyle,gaveme 0. oi:1 the possibility to navigate the field without boundaries while being there d with all his invaluable knowledge and expertise to guide me through. I am g | or also indebted to a number of friends who worked together with me on the sc. subject whileinMalcolm’sgroup:JiriBocan,LyndaBrown, Richard Brown, bs.r Marina Carravetta, Maria Concistr`e, Jean-Nicholas Dumez, Stuart Elliott, u p s:// P¨ar Håkansson, Joseph Hill-Cousin, Ole Johannessen, Alex Pop, Gabriele http Stevanato and Michael Tayler as well as to a number of dedicated students n andresearcherswhoworkorhaveworkedontheseideasasmembersofmy o 20 research group: Francesco Giustiniano, Andrew Hall, Giulia Melchiorre, 0 pril 2 AliFkiinMalloyy,siIadami, SvyelwryiathOasntrkofwuslktao, SthuendReoeypalRaStohcoieretyaonfdCMhoenmiqisuteryTaonudreltlh.e A 7 editor-in-chiefofthisseries,Prof.William S.Price,forproposingthatIedit 0 on this very first book on the subject of long-lived nuclear spin order. d e h s bli Giuseppe Pileio u P Southampton, UK 9 0 0 P F 2- Contents 7 9 9 1 0 8 8 7 1 8 7 9 39/ Part 1 – Singlet Order and Its Properties 0 1 0. 1 Chapter 1 Long-lived States in Nuclear Magnetic Resonance: An oi: d Overview 3 g | or Malcolm H. Levitt c. s s.r b 1.1 Introduction 3 u p s:// 1.2 What Are Long-lived States? 7 p htt 1.2.1 Disconnected Eigenstates 7 on 1.2.2 Disconnected State Manifolds 9 0 02 1.3 Symmetry Theory of Long-lived States 12 2 pril 1.3.1 The Coherent Hamiltonian and Its A Symmetry 13 7 0 n 1.3.2 The Fluctuating Hamiltonian and Its o d Symmetry 15 e h blis 1.3.3 The Symmetric Approximate Hamiltonian 15 u P 1.3.4 The Number of Long-lived States 20 1.3.5 Long-lived State Operators 21 1.4 Long-lived State NMR 23 1.4.1 Excitation 23 1.4.2 Filtering 25 1.4.3 Evolution 25 1.4.4 Read-out 26 1.4.5 Detection 26 Acknowledgements 26 References 26 NewDevelopmentsinNMRNo.22 Long-livedNuclearSpinOrder:TheoryandApplications EditedbyGiuseppePileio rTheRoyalSocietyofChemistry2020 PublishedbytheRoyalSocietyofChemistry,www.rsc.org ix View Online x Contents Chapter 2 Symmetry and Long-lived Spin Order 33 Gabriele Stevanato 2.1 Introduction 33 2.1.1 The Concept of Symmetry 33 9 0 0 2.1.2 The Definition of Group 34 P F 2- 2.1.3 The Group Formed by the Permutation of 7 99 Three Elements 35 1 0 8 2.1.4 Representation of Groups, Homomorphism 8 7 1 and Isomorphism 36 8 7 9/9 2.1.5 Reducible and Irreducible Representations 37 3 0 2.1.6 The Vanishing Integral Rule 38 1 0. 1 2.2 Symmetry Conditions for the Existence of oi: d Long-lived Spin Orders 39 g | or 2.2.1 Spin Eigenstates 39 c. s 2.2.2 Spin Relaxation 40 s.r ub 2.2.3 Symmetry Classification of Nuclear Spin p s:// Operators 41 p htt 2.2.4 Spin System Definition 44 n o 2.2.5 Symmetry of the Nuclear Spin 0 2 0 Hamiltonian 44 2 pril 2.3 Number of Expected Long-lived Orders 51 A 7 2.3.1 Approximations 51 0 n 2.3.2 Number of LLS and Analytical Expression o ed in the Idealized Case 53 h s bli 2.3.3 Example for a Two-spin System 54 u P 2.3.4 Example for a Three-spin System 55 2.4 LLS Accessibility via Coherent/Incoherent Mechanisms 56 2.4.1 Example 1 56 2.4.2 Example 2 57 2.4.3 Example 3 59 2.4.4 Example 4 60 2.5 Conclusions 61 References 61 Chapter 3 Relaxation Theory of Long-lived Spin Order 64 Giuseppe Pileio 3.1 Introduction 64 3.2 Longitudinal and Singlet Order 65 3.3 A Model for Nuclear Spin Relaxation 67 3.4 Relaxation Decay Rates 70

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