摘要:

4369 4377 4387 4397 4407 4417 4427 4439 445 1 4457 447 1 4475 4487 4495 450 1 4509 Con tents A New Form of the High-temperature Isopiestic Technique and its Applica- tion to Mercury-Bismuth, Mercury-Cadmium, Mercury-Gallium, Mercury- Indium and Mercury-Tin Binary Amalgams Z-C. Wang, X-H. Zhang, Y-Z. He and Y-H. Bao The Derivation of Chemical-diffusion Coefficients of Oxygen in UO,,, over the range 180-300 "C. Spectroscopic Procedure and Preliminary Results T. R. Griffiths, H. V. St. Aubyn Hubbard, G. C. Allen and P. A. Tempest Pho tophysics at Solid Surfaces. Evidence of Dimer Formation and Polarization of Monomer and Excimer Fluorescences of Pyrene in the Adsorbed State on Silica-gel Surfaces T. Fujii, E. Shimizu and S. Suzuki Ordering in Monodispersed Polymer Latices induced by a Temperature Gradient K.Furusawa, N. Tobori and S. Hachisu X-Ray Diffraction Study of Molten Eutectic LiF-NaF-KF Mixture K. Igarashi, Y. Okamoto, J. Mochinaga and H. Ohno Viscosity Measurements of Some Tetra butylammonium, Copper( I), Silver( I) and Thallium( 1) Salts in Acetonitrile-Pyridine Mixtures at 15, 25 and 35 "C D. S. Gill and B. Singh The Ethane- 1,2-diol-Water Solvent System. The Dependence of the Dis- sociation Constant of Picric Acid on the Temperature and Composition of the Solvent Mixture Silver(1) Complexation with Tertiary Amines in Toluene M. Soledade Santos, E. F. G. Barbosa and M. Spiro Enhanced Oxygen Evolution through Electrochemical Water Oxidation mediated by Polynuclear Complexes embedded in a Polymer Film G. J. Yao, A. Kira and M. Kaneko Nature of Acid Sites in SAP05 Molecular Sieves.Part 1.-Effects of the Concentration of Incorporated Silicon C. Halik, J. A. Lercher and H. Mayer Hemimicelle Formation of Cationic Surfactants at the Silica Gel-Water Interface T. Gu, Y. Gao and L. He Nuclear Magnetic Resonance Relaxation in Micelles. Deuterium Relaxation at Three Field Strengths of Three Positions on the Alkyl Chain of Sodium Dodecyl Sulphate Studies of the Temperature Dependence of Retention in Supercritical Fluid Chromatography K. D. Bartle, A. A. Clifford, J. P. Kithinji and G. F. Shilstone Hydrogen and Muonium Atom Adducts of Trimethylsilyl Derivatives of Ethyne The Radical Cation of Formaldehyde in a Freon Matrix. An Electron Spin Resonance Study Phase Transition of the Water confined in Porous Glass studied by the Spin- probe Method H.Yoshioka G. C. Franchini, A. Marchetti, L. Tassi and G. Tosi 0. Soderman, G. Carlstrom, U. Olsson and T. C. Wong C. J. Rhodes and M. C. R. Symons C. J. Rhodes and M. C. R. Symons4369 4377 4387 4397 4407 4417 4427 4439 445 1 4457 447 1 4475 4487 4495 450 1 4509 Con tents A New Form of the High-temperature Isopiestic Technique and its Applica- tion to Mercury-Bismuth, Mercury-Cadmium, Mercury-Gallium, Mercury- Indium and Mercury-Tin Binary Amalgams Z-C. Wang, X-H. Zhang, Y-Z. He and Y-H. Bao The Derivation of Chemical-diffusion Coefficients of Oxygen in UO,,, over the range 180-300 "C. Spectroscopic Procedure and Preliminary Results T. R. Griffiths, H. V. St. Aubyn Hubbard, G. C. Allen and P. A. Tempest Pho tophysics at Solid Surfaces.Evidence of Dimer Formation and Polarization of Monomer and Excimer Fluorescences of Pyrene in the Adsorbed State on Silica-gel Surfaces T. Fujii, E. Shimizu and S. Suzuki Ordering in Monodispersed Polymer Latices induced by a Temperature Gradient K. Furusawa, N. Tobori and S. Hachisu X-Ray Diffraction Study of Molten Eutectic LiF-NaF-KF Mixture K. Igarashi, Y. Okamoto, J. Mochinaga and H. Ohno Viscosity Measurements of Some Tetra butylammonium, Copper( I), Silver( I) and Thallium( 1) Salts in Acetonitrile-Pyridine Mixtures at 15, 25 and 35 "C D. S. Gill and B. Singh The Ethane- 1,2-diol-Water Solvent System. The Dependence of the Dis- sociation Constant of Picric Acid on the Temperature and Composition of the Solvent Mixture Silver(1) Complexation with Tertiary Amines in Toluene M.Soledade Santos, E. F. G. Barbosa and M. Spiro Enhanced Oxygen Evolution through Electrochemical Water Oxidation mediated by Polynuclear Complexes embedded in a Polymer Film G. J. Yao, A. Kira and M. Kaneko Nature of Acid Sites in SAP05 Molecular Sieves. Part 1.-Effects of the Concentration of Incorporated Silicon C. Halik, J. A. Lercher and H. Mayer Hemimicelle Formation of Cationic Surfactants at the Silica Gel-Water Interface T. Gu, Y. Gao and L. He Nuclear Magnetic Resonance Relaxation in Micelles. Deuterium Relaxation at Three Field Strengths of Three Positions on the Alkyl Chain of Sodium Dodecyl Sulphate Studies of the Temperature Dependence of Retention in Supercritical Fluid Chromatography K. D. Bartle, A. A. Clifford, J. P. Kithinji and G. F. Shilstone Hydrogen and Muonium Atom Adducts of Trimethylsilyl Derivatives of Ethyne The Radical Cation of Formaldehyde in a Freon Matrix. An Electron Spin Resonance Study Phase Transition of the Water confined in Porous Glass studied by the Spin- probe Method H. Yoshioka G. C. Franchini, A. Marchetti, L. Tassi and G. Tosi 0. Soderman, G. Carlstrom, U. Olsson and T. C. Wong C. J. Rhodes and M. C. R. Symons C. J. Rhodes and M. C. R. Symons

ISSN:0300-9599    

DOI:10.1039/F198884FX041

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

NOMENCLATURE AND SYMBOLISM Units and Symbols. The Symbols Committee of The Royal Society, of which The Royal Society of Chemistry is a participating member, has produced a set of recommendations in a pamphlet 'Quantities, Units, and Symbols' (1 975) (copies of this pamphlet and further details can be obtained from the Manager, Journals, The Royal Society of Chemistry, Burlington House, London W1V OBN). These recommendations are applied by The Royal Society of Cemistry in all its publications. Their basis is the 'Systeme International d'Unit6s' (9). A more detailed treatment of units and symbols with specific application to chemistry is given in the IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (Pergamon, Oxford, 1979). Nomenclature. For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers.In order to encourage authors to use IUPAC nomenclature rules when drafting papers, attention is drawn to the following publications in which both the rules themselves and guidance on their use are given: Nomenclature of Organic Chemistry, Sections A, B, C, D, E, F, and H (Pergamon, Oxford, 1979 edn). Nomenclature of Inorganic Chemistry (Butterworths, London, 1971 , now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). Compendium of Chemical Terminology: IUPAC Recommendations (Blackwells, Oxford, 1987).A complete listing of all IUPAC nomenclature publications appears in the January issues of J. Chem. SOC., Faraday Transactions. It is recommended that where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society's editorial staff. (xiv)NOMENCLATURE AND SYMBOLISM Units and Symbols. The Symbols Committee of The Royal Society, of which The Royal Society of Chemistry is a participating member, has produced a set of recommendations in a pamphlet 'Quantities, Units, and Symbols' (1 975) (copies of this pamphlet and further details can be obtained from the Manager, Journals, The Royal Society of Chemistry, Burlington House, London W1V OBN). These recommendations are applied by The Royal Society of Cemistry in all its publications.Their basis is the 'Systeme International d'Unit6s' (9). A more detailed treatment of units and symbols with specific application to chemistry is given in the IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (Pergamon, Oxford, 1979). Nomenclature. For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers. In order to encourage authors to use IUPAC nomenclature rules when drafting papers, attention is drawn to the following publications in which both the rules themselves and guidance on their use are given: Nomenclature of Organic Chemistry, Sections A, B, C, D, E, F, and H (Pergamon, Oxford, 1979 edn). Nomenclature of Inorganic Chemistry (Butterworths, London, 1971 , now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). Compendium of Chemical Terminology: IUPAC Recommendations (Blackwells, Oxford, 1987). A complete listing of all IUPAC nomenclature publications appears in the January issues of J. Chem. SOC., Faraday Transactions. It is recommended that where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society's editorial staff. (xiv)

ISSN:0300-9599    

DOI:10.1039/F198884BX043

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

Carbon-13 NMR Spectroscopy High-Resolution Methods and Applications in Organic Chemistry and Biochemistry Third, completely revised edition by E. Breitmaier and W. Voelter 1987. XVI, 515 pages with 129 figures and 158 tables. Hardcover. f 88.00. ISBN 3-527-26466-3 Carbon-13 NMR Spectral Data A Living COM-Microfiche Collection of Reference Material Fourth edition by W. Bremser, L. Ernst, W. Fachinger, R. Gerhards, A. Hardt and P. M. E. Lewis 1987. 58108 spectra of 48357 compounds on 235 micro- fiches with a 35-page introductory text. For new customers: Complete set: 3 ring binders containing 11 pages of housing frames. f 1467.00. ISBN 3-527-26198-2 For previous subscribers: 1 ring binder containing 4 addi- tional pages of housing frames. f 880.00. ISBN 3-527-25899-X Biomedical Magnetic Resonance Imaging Prlnciples, Methodology and Applications edited by F.W. Wehrli, D. Shaw and J. B. Kneeland 1988. XVIII, 601 pages with 313 figures and 30 tables. Hardcover. f 69.00. ISBN 3-527-26701 -8 Series: Methods in Stereochemical Analysis Stereochemical Applications of NMR Studies in Rigid Bicyclic Systems Volume 1: by A. P. Marchand 1982. XI, 231 pages with 4 figures and numerous tables. Hardcover. f 103.00. ISBN 3-527-25976-7 Volume 2 Carbon-Carbon and Carbon-Proton NMR Couplings Applications to Organic Stereochemistry and Conformational Analysis by J. L. Marshall 1983. VIII, 241 pages with 9 figures and numerous tables. Hardcover. f 64.00. ISBN 3-527-25977-5 Volume 3 Stereochemistry and Reactivity of Systems Containing n Electrons edited by W.H. Watson 1983. XIV, 439 pages. Hardcover. f 59.00. ISBN 3-527-261 15-X To order please contact your bookseller or VCH Publishers (UK) Ltd.. 8 Wellington Court. Wellington S t , GB-Cambridge CB1 1HW VCH Verlagsgesellschaft. P 0. Box 1011 61, D-6940 Wemheim VCH Verlags-AG. Hardstrasse 10, P.O. Box, CH-4020 Basel . VCH Publishers. Sulte 909.220 East 23rd Street, New York, NY 10010-4606, USA Volume 4 Applications of Dynamic NMR Spectroscopy to Organic Chemistry by M. Oki 1985. XII, 423 pages with 8 figures and 109 tables. Hardcover. f 77.00. ISBN 3-527-26166-4 Volume 6 Applications of NMR Spectroscopy to Problems in Stereochemistry and Conformational Analysis edited by Y. Takeuchi and A. P. Marchand 1986. IX. 221 pages with 52 figures. Hardcover. f 49.75. ISBN 3-527-26145-1 Volume 7 High-Resolution NMR Spectroscopy of Synthetic Polymers in Bulk edited by R.A. Komoroski 1986. XI. 379 pages with 47 figures. Hardcover. f 68.00. ISBN 3-527-26464-7 Volume 8 Phosphorus-31 NMR Spectroscopy in Stereochemical Analysis Organic Compounds and Metal Complexes edited by J. G. Verkade and L. D. Quin 1987. XVI, 717 pages with 74 figures. Hardcover. f 95.00. ISBN 3-527-26465-5 Volume 5 Lanthanide Shift Reagents in Stereo- chemical Analysis edited by T. C. Morrill 1987. XIII, 193 pages with 43 figures and 17 tables. Hardcover. f 42.25. ISBN 3-527-26167-2 Volume 9 Two- Dimensional NMR Spectroscopy Applications for Chemists and Biochemists edited by W. A. Croasmun and R. M. K. Carlson 1987. XVIII, 51 1 pages with 192 figures and 32 tables.Hardcover. f 78.95. ISBN 3-527-26528-7 Sterling prices subject to change without noticeNuclear Magnetic Resonance Vol 17 Specialist Periodical Report Senior Reporter: 0 A Webb, UniverSi2g ofSumq ISBN: 0 85186 402 3 Hardcover 546pp Rice: jZl10.00 ($239.00) Nuclear Magnetic Resonance Volume 17 provides a review of the literature published between June 1986 and May 1987. Brief Contents: Theoretical and Physical Aspects of Nuclear Shielding * Applications of Nuclear Shielding Theoretical Aspects of Spin-Spin Couplings Nuclear Spin Relaxation in Liquids Solid Sate NMR Mutiple Pulse NMR Natural Macromolecules Synthetic Macromolecules Conformational Analysis * Nuclear Magnetic Resonance of Living Systems Oriented Molecules Heterogeneous Systems Nuclear Magnetic Resonance Volume 17 contains a foreword by the senior reporter and a detailed contents list.Each chapter includes extensive references. ROYAL CHEMISTRY Information Services To order or for further information please contact: Alison Hibberd, Sales and Promotion Dept., Royal Soclety of Chemistry, The University, Nottlngham NG7 2RD, UK. Telephone (0602) 5074 1 1. Telex: 37488ISSN 0300-9238 JCFTAR 84(11) 3649-4201 (1 988) 3649 3673 369 1 3713 373 1 3747 376 1 3777 3785 3803 382 1 3857 JOURNAL OF THE CHEMICAL SOCIETY Faraday Transactions I Physical Chemistry in Condensed Phases Professor Robin Harris of Durham University was invited to contribute a keynote paper on the general theme of Nuclear Magnetic Resonance Spectroscopy in Solids. He was supported by a group of research workers who submitted original papers on cognate subjects.All these papers have now been refereed, and are collected at the beginning of the present issue. CO N T E NTS Perspectives in High-resolution Solid-state Nuclear Magnetic Resonance, with Emphasis on Combined Rotation and Multiple-pulse Spectroscopy R. K. Harris, P. Jackson, L. H. Merwin, B. J. Say and G. Hagele Carbon- 1 3 Chemical-shift Tensors in Single-crystal Methoxybenzenes C. M. Carter, J. C. Facelli, D. W. Alderman, D. M. Grant, N. K. Dalley and B. E. Wilson Enhancement of the Effect of Small Anisotropies in Magic-angle Spinning Nuclear Magnetic Resonance D. P. Raleigh, A. C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Griffin Spectral Spin Diffusion in Polycrystalline Solids under Magic-angle Spinning A.Kubo and C. A. McDowell The Nuclear Magnetic Resonance of 12'Xe trapped in Clathrates and some other Solids J. A. Ripmeester, C. I. Ratcliffe and J. S. Tse Quadrupole Nutation Nuclear Magnetic Resonance in Solids R. Janssen and W. S. Veeman Deuterium Quadrupole-echo Studies of Molecular Motion in a Biphenyl+- Cyclodextrin Clathrate Highly Resolved Solid-state Proton Magnetic Resonance Studies of Zeolites H. Pfeifer Nuclear Magnetic Resonance Study of Pt-Rh Bimetallic Clusters 2. Wang, J-P. Ansermet, C. P. Slichter and J. H. Sinfelt Peptide Backbone Conformation by Solid-state Nuclear Magnetic Resonance Spectroscopy Some New Developments in Solid-state Nuclear Magnetic Resonance Spectro- scopic Studies of Lipids and Biological Membranes, including the Effects of Cholesterol in Model and Natural Systems J.Forbes, J. Bowers, X. Shan, L. Moran, E. Oldfield and M. A. Moscarello 'H Nuclear Magnetic Resonance and Spin-Lattice Relaxation in Solid, High- density Polyethylene A. D. Ronemus, R. R. Vold and R. L. Vold P. L. Stewart, R. Tycko and S. J. Opella K. J. Packer, I. J. F. Poplett and M. J. Taylor 3865 3877 3885 Mixtures of Benzene and Chloroform near a Silica with Grafted Poly(ethy1ene oxide) Chains H. B. Ouada, H. Hommel A. P. Legrand, H. Balard and E. Papirer Viscosity of Solutions of NaI and CaCl, in Water-Ethanol and of NaI in Water-tetrahydro furan Mixtures B. Nowicka, A. Kacperska, J. Barczynska, A. Bald and S. Taniewska-Osinska Application of Kirkwood-Buff Theory to Enthalpies of Transfer and Expansibilities of Solutes in Binary Solvent Mixtures K.E. Newman 120-2389 1 3905 3917 3927 394 1 395 1 396 1 3973 3983 399 1 4013 4023 403 3 4043 4049 406 1 4073 4087 4097 4105 41 15 4125 4137 Con tents A Study of the Surface Chemistry of Anion-exchange Resins using X-Ray Photoelectron Spectroscopy G. C. Allen, N. R. Holmes, B. J. Lee and R. R. Harries Studies of Architecture of Moo,-TiO, Catalysts T. Machej, B. Doumain, B. Yasse and B. Delmon The Influence of Crown Ethers on Cation Migration Processes. Part 6.-The 174-Naphthoquinone Radical Anion N. J. Flint and B. J. Tabner Diffusion of H+ and OH- in Porous Solids J. J. Lewnard, E. E. Petersen and C. J. Radke Electrochromism of a Conducting Polypyrrole-Phosphotungstate Composite Electrode T. Shimidzu, A.Ohtani, M. Aiba and K. Honda Surface Solubilization B-Y. Zhu, X. Zhao and T. Gu An Electron Spin Resonance Study of Charge-carrier Stabilization in ZnO A. R. Gonzalez-Efipe and J. Soria Spectrophotometric Study of the Pseudotetrahedral Bromocomplexes of Cobalt(r1) in Hexamethylphosphoramide Solution M. Pilarczyk, W. Gryzb- kowski and L. Klinszporn A Theoretical Study of the Kinetics of Deoxyhaemoglobin S Aggregation R. P. Hazoume and N. M. Hounkonnou Heat Capacity and Corresponding States in Alkan- 1 -01-n-Alkane Systems L. Andreoli-Ball, D. Patterson, M. Costas and M. Caceres-Alonso Ionic Solvation. Part 4.--Copper(r) Solvation. Disproportionation and Halide- complex Formation in Propylene Carbonate A. Lewandowski The Kinetics of Cathodic Generation of R,N(Hg,) C.M. Ryan, V. SvetliW and E. Kariv-Miller Determination of Diffusion Coefficients and Effective Charge Numbers of Lignosulphonate. Influence of Ionic Strength and the Valency of t.he Counter- ion A-K. Kontturi Diffusion Coefficients and Effective Charge Numbers of Lignosulphonate. Influence of Temperature A-K. Kontturi Characterisation of Crystalline UO, oxidised in 1 Torr of Oxygen at 25,225 and 300 "C. Part 1.-X-Ray Photoelectron Spectroscopy G. C. Allen, P. A. Tempest and J. W. Tyler Characterisation of Crystalline UO, oxidised in 1 Torr of Oxygen at 25, 225 and 300 "C. Part 2.-X-Ray Diffraction and Scanning Electron Microscopy G. C. Allen, P. A. Tempest and J. W. Tyler Excess Heat Capacities and Excess Volumes of n-Alkane Mixtures D. Apam- Martinez and A.Trejo Calorimetric Study of Non-ionic Surfactants. Enthalpies and Heat-capacity Changes for Micelle Formation in Water of C,E, and Triton X-100 and Micelle Size of C,E, B. Andersson and G. Olofsson Reduction-Agglomeration Model for Metal Dispersion in Platinum-exchanged NaX Zeolite D. Exner, N. Jaeger, A. Kleine and G. Schulz-Ekloff Radiation Damage in Organic Phosphates. Crystal Structure of 3-0-Dip- henoxyphosphoryl- 172-U-isopropylidene 5-O-Trityl-a-~-ribofuranose and an Electron Spin Resonance Study of the X-Irradiated Single Crystal T. Berclaz, G. Bernardinelli, A. CClalyan-Berthier and M. Geoffroy Mechanism of Deuterium Addition and Exchange of Propene over Silica- supported Gold and Silver Catalysts The Excess Surface Tensions of Simple Binary Mixtures Acidic Properties of Molybdenum Oxide highly dispersed on Titania Miyata, T.Mukai, T. Ono and Y. Kubokawa s. Naito and M. Tanimoto J. S. Rowlinson H.Con tents 4145 4 157 4 16 1 4 169 Coupling of Free Energies in the Formation of Intermediates during the Catalytic Decomposition of H,O, Kinetics of a-Hydroxyl Elimination from [(H20)),CuiiCH2C(CH,),0H]+ in Aqueous Solution. A Pulse-radiolysis Study H. Cohen and D. Meyerstein Crystal-like Structures of Deionized Polystyrene Spheres at Interfaces with Quartz, Air, n-Hexane, Polystyrene and Poly(methy1 methacrylate) T. Okubo Kerr Constants and Dielectric Polarisations of Amides and Thioamides in Water and Dioxane Solutions M. J. Aroney, K. M. Dowling, E. Patsalides, R. K. Pierens and S. W. Filipczuk Photocatalytic Oxidation of Iodide Ions by Titanium Dioxide P. R. Harvey and R. Rudham Adsorption of Methylene Blue from Aqueous Solutions by ZSM-5-Type Zeolites and Related Silica Polymorphs M. L. Kremer 4181 419 1 G. P. Handreck and T. D. SmithCon tents 4145 4 157 4 16 1 4 169 Coupling of Free Energies in the Formation of Intermediates during the Catalytic Decomposition of H,O, Kinetics of a-Hydroxyl Elimination from [(H20)),CuiiCH2C(CH,),0H]+ in Aqueous Solution. A Pulse-radiolysis Study H. Cohen and D. Meyerstein Crystal-like Structures of Deionized Polystyrene Spheres at Interfaces with Quartz, Air, n-Hexane, Polystyrene and Poly(methy1 methacrylate) T. Okubo Kerr Constants and Dielectric Polarisations of Amides and Thioamides in Water and Dioxane Solutions M. J. Aroney, K. M. Dowling, E. Patsalides, R. K. Pierens and S. W. Filipczuk Photocatalytic Oxidation of Iodide Ions by Titanium Dioxide P. R. Harvey and R. Rudham Adsorption of Methylene Blue from Aqueous Solutions by ZSM-5-Type Zeolites and Related Silica Polymorphs M. L. Kremer 4181 419 1 G. P. Handreck and T. D. Smith

ISSN:0300-9599    

DOI:10.1039/F198884FP155

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

JOURNAL OF THE CHEMICAL SOCIETY 1775 1779 1789 1793 1803 1809 1825 1837 1847 1855 1867 7/2 157 7/22 13 Faraday Transactions II, Issue1 I I 1988 Molecular and Chemical Physics For the benefit of readers of Faraday Transactions I, the contents list of Faraday Transactions 11, Issue 11, is reproduced below. Polarisability Anisotropies of C-H, C-C, C-Cl and C-Br Bonds G. W. Allen, R. S. Armstrong, M. J. Aroney, R. K. Pierens and A. J. Williams Simulation of Preferential Cation Solvation in Aqueous Ammonia B. M. Rode and Y. Tanabe Ab Initio Study of the Hydration of the Glycine Zwitterion S. U. Kokpol, P. B. Doungdee, S. V. Hannongbua and B. M. Rode Effect of the Intermolecular Interactions on the Anisotropic Rotational Motions of Molecules. 'H, ,H and 14N Nuclear Magnetic Resonance Relaxation Study of the Acetonitrile-Chloroform Liquid System T.Tokuhiro Transient Species produced by Flash Photolysis of Acid Solutions of Methylene Blue G. J. Smith and M. G. Casarotto Quenching of Singlet and Triplet States of p-N,N-Dimethylaminobenzonitrile by Tertiary Amines. Intramolecular Charge-transfer State and Excited-state Three-electron Bond Y. Wang Combining Transition-state Theory with Quasiclassical Trajectory Calcu- lations. Part 5.-Canonical Calculations on the Reaction : F + H,(u = 0) -+ HF(u') + H R. J. Frost and I. W. M. Smith Combining Transition-state Theory with Quasiclassical Trajectory Calcu- lations. Part 6.-Microcanonical Calculations on the Reaction : F + H,(v = 0) -+ HF(u') + H Ab Initio HeF' ('E, 'rI) Interaction Potentials and Calculations of the Mobility of F+(3P) and F-(lS) in Helium P.W. Harland, R. G. A. R. Maclagan and R. W. Simpson Brownian Motion of Two Interacting Particles through Logarithmic and Lennard-Jones Potentials A. Morita Concentration-modulated Absorption Spectroscopy. Lifetime Measurements of the ,E State of Cr3+ in a Ruby Crystal B. Czarnik-Matusewicz, R. Griffiths, P. F. Jones, W. J. Jones, W. Malawaarachchi and G. Smith R. J. Frost and I. W. M. Smith The following papers were accepted for publication in Faraday Transactions I during August 1988. The Orthobaric Surface Tensions of the Three Binary Mixtures formed by Krypton, Ethane and Ethene B. S. Almeida, V. A. M. Soares, I. A. McLure and J. C. G. Calado FTIR Studies of Copper-containing Y Zeolites. Dehydration, Reduction and the Adsorption of Ammonia J.Howard and J. M. Nicol 8/00056E Distribution of the Oxidation Power of Surface Oxygen Species. The (0Contents Kinetics of CO Oxidation on Chromium Sesquioxide M. Kobayashi, T. Kanno and K. Makino Reactivation of Zeolite and Oxide Catalysts Using Nitrous Oxide G. J. Hutchings, H. Comnios, R. G. Copperthwaite, L. I. Van Rensburg, R. Hunter and T. Themistocleous A Study of the Exchange Sites Per Unit Area of External Surface of External Surface of Zeolite Al-ZSM-5 T. D. Smith and G. P. Handreck Reversible Volume Change of Microparticles Under Electric Field R. Kishi and Y. Osaka Solutions of Organic Solutes. Part 4.-Structure and the Effect of Solute Concentration on the Volume J. V. Leyendekkers Reactions of the Hydroxyl Free Radical with Copper@-Amino Acid Complexes in Aqueous Solution G.A. A. Johnson, N. T. Nazhat and R. A. Saadalla-Nazhat Fourier-transform I.R. Study of the Adsorption and of Reactions of Acetaldehyde on Dispersed Silica W. Hill, H. Miessner and G. Ohlmann New Aspects of the Oxidation-Reduction Mechanism of the As- corbic-Dehydroascorbic Acid System on the DME J. J. Ruiz, M. Dominguez, J. M. Rodriquez-Mellando and A. Aldaz Formate Oxidation Induced by Trivalent Copper Produced in Fenton- like Reactions H. C. Sutton An Investigation of Iron-containing Catalysts Prepared at Low Tem- peratures and Active for Carbon Monoxide Hydrogenation F. J. Berry and M. R. Smith Carbon Monoxide and Carbon Dioxide Adsorption on Cerium Oxide Studied by FTIR. Formation of Carbonate Species on Dehydroxylated CeO, at Room Temperature T.Onishi, L. Can, Y. Sakata, T. Arai, K. Domen and K-I. Maruya Measurements of Activity Coefficients, Mass-transfer Coefficients and Diffusion Coefficients in Multicomponent Liquid Mixtures by Reversed- flow Gas Chromatography Study of the Conformational Equilibrium Between Rotational Isomers Using Ultrasonic Relaxation and Raman Spectroscopy. Part 3.- 1-Bromo-2-chloroethane The State of Water in Non-ionic Surfactant Solutions and Lyotropic Phases. An Oxygen- 17 Magnetic Relaxation Study G. Carlstrom and B. Halle An A.C. Impedance Study of Poly(pyrrole)/PVC Composites A. Waller, A. S. Hampton and R. G. Compton A simultaneous A.C. Impedance ESR Study of Electrochemical Doping in Polypyrrole A. M.Waller and R. G. Compton A Diaphragm Cell for High- temperature Diffusion Measurements. Tracer Diffusion Coefficients for Water to 363 K A. J. Easteal, W. E. Price and L. A. Woolf P. Agathonos and G. Karaiskakis S. Koda, H. Matsui and H. Nomura 8/01459K 8/01 5 19H 8/01 533C 8/0 1622D 8/0 1 66 1 E 8/0 1672K 8 1016f39E 8/01 789A 8/01972J 8/01 990H 8/02 1 86D 8/02225 1 I 8/02264J 8/02295J 8/02298D 8/02326C (ii)Contents 8J02475H 8/02557F Activation Energies of the Reduction of Bulk and Supported Vanadium Pentoxide H. Bosch and P. J. Sinot Spectroscopic Studies of Silver(o) Centres Formed Radiolytically in Water-Ethanol Solvents at 4 and 77 K A. D. Stevens and M. C. R. Symons Supported Palladium Catalyst Prepared from Amorphous Palladium- Zirconium : Structural Properties and Catalytic Behaviour in the Hydrogenation of Carbon Dioxide A.Baiker and D. Gasser Infrared Spectroscopic Stuids on the Aggregation of Polyoxyethylene Surfactants in Hydrocarbon Solvents W. F. Packynko, J. Yarwood and G. J. T. Tiddy 8/02646G 8/02411 A (iii)Cumulative Author Index 1988 Abdel-Kader, M. H., 2241 Abe, H., 51 1 Abraham, M. H., 175, 865, 1985 Abraham, R. J., 1911 Adachi, H., 1091 Agnel, J-P. L., 3359 Ahluwalia, J. C., 265 1 Aiba, M., 3941 Aicart, E., 1603 Al-Azzawi, S. F., 3511 Alberti, A., 3347 Al-Bizreh, N., 3587 Alderman, D. W., 3673 Al-Haidary, Y. K., 3027, 3043 Allen, G. C., 165, 355, 3891, Amorelli, A., 1723 Anazawa, I., 275 Anderson, B., 4087 Anderson, S. L. T., 1897, 3363, Andreoli-Ball, L., 3991 Anid, S., 3413 Anpo, M., 751, 2771 Ansermet, J-P., 3785 Antonini, A.C. R., 1889 Aoi, H., 2421 Aoyama, T., 2209 Apam-Martinez, D., 4073 Aracil, J., 539 Archer, G. P., 2499 Aroney, M. J., 4169 Arora, K. S., 1729 Asakura, K., 1329, 2445, 2457 Atherton, N. M., 3257 Auroux, A., 3169 Aveyard, R., 675 Ayyoob, M., 2377 Baba, K., 459 Back, D. M., 2585 Bagchi, S., 1501 Baglioni, P., 467 Bakshi, M. S., 3517 Balard, H., 3865 Bald, A., 3877 Baldini, G., 979 Barczynska, J., 3877 Barna, T., 229 Barone, G., 1919 Barouch, E., 3093 Barratt, M. D., 3249 Barzaghi, M., 3279 Basosi, R., 3331 Basumallick, I. N., 2697 Baulch, D. L., 1575 Bazsa, G., 215, 229 4049, 4061 3547 Beaumont, P. C., 3423 Ben Ouada, H., 3865 Benaglia, H., 3347 Benmouna, M., 1563 Benoit, H., 1563 Berclaz, T., 4105 Berei, K., 367 Bernardinelli, G., 4105 Berroa de Ponce, H., 255, 1671 Berry, F. J., 2783 Berthier-Celalyan, A., 4105 Bertoldi, M., 1405 Beyer, H.K., 1447 Bhat, R., 2651 Binks, B. P., 675 Birch, G. G., 2635 Blandamer, A. H., 1889 Blandamer, M. J., 1243, 1889, 2703, 2906 Blesa, M. A., 9 Blinov, N. N., 1075 Bloor, D. M., 2087 Bonini, B. F., 3347 Bonnefoy, J., 941 Boon, P. J., 3341 Borbely, G., 1447 Borckmans, P., 1013 Borgarello, E., 261 Borowko, M., 1961 Bourdillon, C., 941 Bowers, J., 3821 Branca, M., 3279 Brandreth, B. J., 1741 Breen, J., 293 Bretz, N. H., 3293 Briggs, B., 1243, 2703 Brown, M. E., 57, 1349 Brown, P., 3059 Bruce, J. M., 2855, 3423 Brustolon, M., 2875 Brydson, R., 617, 63 1 Bulow, M., 2247, 3001 Burgess, J., 1243, 1889, 2703 Burget, U., 885 Burnell, E. E., 3129 Busca, G., 237, 1405, 1423 Buscarlet, L.A., 3359 Buxton, G. V., 1101, 11 13 Caballero, A., 2369 Caceres, M., 539 Caceres-Alonso, M., 1603 Caceres-Alonso, M., 3991 Carbone, A. I., 207 Caro, J., 2347 Carr, N. J., 1357 Carter, C. M., 3673 Castronuovo, G., 1919 Cavani, F., 237 Cavasino, F. P., 207 Celik, F., 2305 Centi, G., 237 Cesaro, A., 2573 Chagas, A. P., 1065 Chandra, H., 609, 3401 Chatterjee, J. P., 2697 Che, M., 751, 2771 Cheek, P. J., 1927, 3435 Chen, L. F., 3641 Cheng, V. K. W., 899 Chien, J. C. W., 1123 Chinchen, G. C., 2135 Chirico, G., 979 Christensen, P. A., 2795 Christidis, T. C., 3263 Chudek, J. A., 1145, 1737 Clarke, J. K . A., 251 1 Clarke, R. J., 365 Clint, J. H., 675 Coates, J. H., 365 Cohen, H., 4157 Coles, B. A., 2357 Coller, B. A. W., 899 Coluccia, S., 751 Compton, R.G., 473, 483, 2013, 2057, 2155, 2357 Contarini, S., 2335 Conway, B. E., 3389 Cook, A., 1691 Corma, A., 31 13 Costas, M., 1603, 3991 Covington, A. K., 1393 Crowther, N. J., 1211 Dadok, J., 2595 Daldrup, N., 2553 Dalley, N. K . , 3673 Danil de Namor, A. F., 255. 1671, 3539, 2441 Das, S., 1057 Dash, A. C., 75, 2387 Dash, N., 75 Davydov, A., 37 Dawber, J. C., 41 Dawber, J. G., 41, 713 Day, M. J., 2013 de Bleijser, J., 293 Delben, F., 2573 Delmon, B., 3905 Del Vecchio, P., 1919 Deryio-Marczewska, A., 295 1 Diaz Peiia, M., 539 Dickinson, E., 871 Dines, T. J., 3445AUTHOR INDEX Disdier, J., 261 Domen, K., 511 Dong, S., 2979 Dougal, J. C., 657 Doumain, B., 3905 Dowling, K. M., 4169 Duarte, M. Y., 97, 367 Duce, P. P., 865 Duckworth, R. M., 1223 Duplritre, G., 2831 Dyster, S., 11 13 Eagland, D., 121 1 Eaton.G., 2181, 3459 Egawa, C., 321 Einfeldt, J., 931 Einicke, W-D., 3597 Ekechukwu, A. D., 1871 Eley, D. D., 2069 Elia, V., 1919 El Jamal, M. M., 3169 Elliot, A. J., 1101 Elvidge, D., 2703 Engel, W., 617, 631 Eriksson, P-O., 3129 Eszterle, M., 575 Evans, J. C., 1723, 3243, 3249 Everett, D. H., 1455 Exner, D., 4097 Eyears, J. M., 1437, 3097 Facelli, J. C., 3673 Fernandez, A., 1543 Fernandez-Pineda, C., 647 Fiedler, K., 3001 Filipczuk, S. W., 4169 Finter, C. K., 2735 Fischer, H., 3187 Flanagan, T. B., 459 Fletcher, P. D. I., 113 1 Flint, N. J., 3917 Forbes, J., 3821 Foresti, E., 237 Foresti, M. L., 97 Forissier, M., 3169 Fornes, V., 31 13 Forni, L., 2397, 2477 Forster, H., 491 Foster, R., 1145, 1737 Fraenkel, D., 1817, 1835 Franklin, K.R., 687, 2755 Franks, F., 2595 Fubini, B., 1405 Fujihira, M., 2667 Fujii, K., 3121 Funabiki, T., 2987 Furedi-Milhofer, H., 1301 Gal, D., 1075 Gabrail, S., 41 Gabryi, B., 3487 Gaffney, S. H., 2545 Gallardo-Jimenez, M. A., 3435 Galwey, A. K., 57, 729, 1349, Gamba, A., 3279 Gans, P., 657 Gardner, P. J., 1879 1357 Garrone, E., 2843 Geblewicz, G., 561 Geertsen, S., 1101 Geoffroy, M., 4105 Georges, V., 1531 Giamello, E., 1405 Gilbert, B. C., 3319 Gilbert, R. G., 3107 Gill, D. S., 1729, 3517 Gill, J. B., 657 Gilot, B., 801 Girault, H. H., 2147 Giuliacci, M. E., 2311 Go, T., 3951 Goldfarb, D., 2335 Gonzalez-Elipe, A. R., 3961 Gopalakrishnan, R., 365 Grabielle-Madelmont, C., 2609 Grampp, G., 366 Grant, D. M., 3673 Gratzel, M., 197, 1703 Gray, A. C., 1509 Gray, P., 993 Green, P., 2109 Green, S.I. E., 41 Green, W. A., 2109 Grepstad, J. K., 1863 Griffin, R. G., 3691 Griffiths, J. F., 1575 Grigera, J. R., 2603 Grigo, M., 931 Grimson, M. J., 1563 Gritzner, G., 1047 Grothe, K., 3267 Grzybkowski, W., 155 1, 3973 Guardado, P., 1243, 2703 Guarini, G. G. T., 331 Guarino, G., 2279 Guglielminotti, E., 2195 Guidelli, R., 97, 367 Gupta, D. Das, 1057 Guyan, P. M., 2855 Hadjiivanov, K., 37 Hagele, G., 3649 Hakin, A. W., 1889, 2703 Hall, D. G., 773, 2087, 2215, 2227, 3059 Hall, N. D., 1889 Halle, B., 1033 Hamada, K., 1267 Hanawa, T., 1587 Handreck, G. P., 1847, 4191 Hanson, G. R., 1475 Harrer, W., 366 Harries, R. R., 3891 Harriman, A., 2109, 2795, 2821 Harris, R. K., 3649 Harvey, P. R., 4181 Hasebe, T., 187 Hashimoto, K., 87 Haslam, E., 2545 Hatayama, F., 2465 Hausen, H-D., 3207 Hayashi, K., 2209 Hazoume, R.P., 3983 (4 Hazra, D. K., 1057 Heatley, F., 343 Hegarty, B. F., 251 1 Hegde, M. S., 2377 Heineken, F. W., 3263 Helle, N., 3293 Henzel, N., 3293 Herley, P. J., 729 Herrmann, J-M., 261 Hertz, H. G., 2735 Hey, M. J., 2069 Heyward, M. P., 815 Hidalgo, M. del V., 9 Higgins, J. S., 3487 Hill, A., 255 Histed, M., 3307 Hoare, I. C., 3071 Holmes, N. R., 3891 Holzwarth, J. F., 2807 Homer, J., 2959 Hommel, H., 3865 Honda, K., 3941 Hoshino, K., 2667 Hounkonnou, N. M., 3983 House, W. A., 2723 Howard, J. A., 3307 Howson, M. R., 2723 Hubbard, C. D., 1243, 2703 Hudson, B. D., 1911 Huis, D., 293 Hunter, R., 1311 Hurst, H. J., 3071 Hutchings, G. J., 1311 Ichikawa, K., 3015 Ige, J., 1 Ikeda, S., 151 Imai, H., 923 Imamura, H., 765 Imanaka, T., 851, 2173 Inoue, A., 1195 Irinyi, G., 1075 Ishiguro, S., 2409 Ishikawa, T., 1941 Isobe, T., 1199 Ito, D., 1375 Ittah, B., 1835 Iwamoto, E., 1679 Iwamura, H., 3475 Iwasawa, Y., 321, 1329, 2445, Iyer, R.M., 2047 Jackson, P., 3649 Jackson, S. D., 1741 Jackson, S. K., 3243 Jaeger, N., 4097 Jaeger, N. I., 1751 Jaenicke, W., 366 Janssen, R., 3747 Janzen, E. G., 3275 Jaroniec, M., 2951 Jeminet, G., 951 Jens, K-J., 1863 Jin, T., 3015 Johnson, G. R. A., 501 Johnson, I., 551 2457AUTHOR INDEX Johnston, C., 309, 2001, 3605 Joly, H. A,, 3307 Jonasson, R. G., 231 1 Jones, A. R., 2914 Jonson, B., 1897, 3363, 3547 Jorge, R. A., 1065 Jorgensen, N., 309, 2001, 3605 Joiwiak, M., 2077 Juillard, J., 951, 959, 969, 1713, Kacperska, A., 3877 Kaim, W., 3207 Kaizu, Y., 1517 Kaji, K., 3487 Kakei, K., 1795 Kanaya, T., 3487 Kane, H., 851 Kaneko, K., 1795 Kanno, T., 281, 2099 Kariv-Miller, E., 4023 Kasahara, S., 765 Kato, C., 2677 Kato, S., 151 Kawasaki, Y., 1083 Kay, R.L., 2595 Keeble, D. J., 609 Keith, S., 3633 Keller, A., 2904 Kemp, T. J., 2027 Kermode, M. W., 1911 Kevan, L., 467, 2335 Kimura, T., 2099 Kinnaird, S., 2135 Kirby, C., 355 Kiricsi, I., 491 Kirste, B., 3267 Kishore, N., 2651 Kiss, I., 367 Kitamaru, R., 3487 Kiwi, J., 1703 Kleine, A., 4097 Klinowski, J., 2902 Klinszporn, L., 1551, 3973 Klissurski, D., 37 Kobayashi, A., 1795 Kobayashi, H., 1517 Kobayashi, M., 281, 2099 KoEiiik, M., 2247 Kkiik, M., 3001 Koda, S., 1267 KodejS, Z., 2885 Koksal, F., 2305 Kolar-AniC, L. Z., 3413 Kolbert, A.C., 3691 Komatsu, H., 2537 Kondo, J., 511 Kondo, M., 2771 Kondo, S., 1941 Kondo, Y., 11 I Konishi, Y., 281 Kontturi, A-K., 4033, 4043 Kordulis, C., 1593 Kornhauser, I., 785, 801 Kosugi, N., 1795 3175 KdtZ, N. E., 9 Kotake, Y., 3275 Kowalak, S., 2035 Kraehenbuehl, F., 1973 Krausz, E., 827 Krebs, P., 2241 Kremer, M. L., 4145 Kristyan, S., 917 Kubelkova, L., 1447 Kubo, A., 3713 Kubokawa, Y., 751, 2129, 2771, Kumamaru, T., 1679 Kurimura, Y., 841, 1025 Kuroda, H., 1329, 1795 Kuroda, K., 2677 Kuroda, Y., 2421 Kurreck, H., 3267, 3293 Kusabayashi, S., 11 1 Kuwabata, S., 1587, 2317 Lahy, N., 1475 Laing, M. E., 2013 tajtar, L., 19 Lambi, J. N., 1 Lancaster, N. M., 3141, 3159 Land, E. J., 2855, 3423 Larsson, R., 1897, 3363, 3547 Laschi, F., 3331 Laubry, P., 969, 3175 Laval, J-M., 941 Lawrence, K.G., 175 Lea, J. S., 1181 Leaist, D. G., 581 Lee, B. J., 3891 Lefever, R., 1013 Lefferts, L., 149 1 Legrand, A. P., 3865 Lengyel, I., 229 Levine, H., 2619 Levitt, M. H., 3691 Levy, A., 1817 Levy, M., 1835 Lewandowski, A., 4013 Lewis, T. J., 1531 Lewnard, J. J., 3927 Leyendekkers, J. V., 397, 1653 Leyte, J. C., 293 Lhermet, C., 2567 Lilley, T. H., 1927, 2545, 3435 Lincoln, S. F., 365 Lindblom, G., 3129 Lindner, Th., 631 Lips, A., 1223 Llewellyn, J. P., 153 1 Logan, S . R., I259 Louis, C., 2771 Lu, Z., 2979 Lycourghiotis, A., 1593 MacCorquodale, F., 3233 Machej, T., 3905 Machida, K., 2537 MacKay, R. L.. 1145, 1737 Mackley, M., 2910 Maezawa, A., 851 Malanga, C., 97 Malet, P., 2369 41 37 (4 Mandel, M., 2483 Maniero, A. L., 2875 Marcandalli, B., 2807 Marcus, Y., 175, 1465, 3575 Marczewski, A. W., 2951 Markovid, M., 1301 Maroto, A.J. G., 9 Marsden, A., 2519 Martin, C. C., 3359 Martin, R. R., 231 1 Martinet, P., 3175 Martins, L. J. A., 2027 Maruya, K., 51 1 Mason, D., 473, 483, 2057 Mathlouthi, M., 2641 Matsumoto, T., 1375 Matsumura, Y., 87 Matsuoka, K., 1277 Matteoli, E., 1985 Maxwell, I. A., 3107 Mayagoitia, V., 785, 801 McAleer, J. F., 441 McDowell, C. A., 3713 McMurray, N., 379 Mead, J., 675 Medda, K., 1501 Mehta, G., 2297 Mensch, C. T. J., 65 Merkin, J. H., 993 Merwin, L. H., 3649 Messow, U., 3597 Meunier, F., 1973 Meyerstein, D., 2933, 4157 Mile, B., 3307 Mills, A., 379, 1691 Mines, J. R., 1911 Mintchev, L., 1423 Mirti, P., 29 Mitsushima, I., 851 Miura, K., 2421 Miyagawa, S., 2129 Miyajima, K., 2537 Miyakawa, K., 1517 Miyake, N., 3475 Miyanaga, T., 2173 Miyata, H., 2129, 2465, 2677, Mohamed, M.A-A., 57, 729, Mohammadi, M. S., 2959 Moiroux, J., 941 Moller, K., 1751 Moran, L., 3821 Morel, J-P., 2567 Morel-Desrosiers, N., 2567 Morimoto, T., 2421 Morris, H., 3307 Morris, J. J., 865 Morterra, C., 1617 Morton, J. R., 413 Moscarello, M. A., 3821 Moseley, P. T., 441 Mosseri, S . , 2821 Mousset, G., 969, 3175 Muhler, M., 631 3121, 4137 1349AUTHOR INDEX Mukai, T., 2465, 4137 Mukherjee, T., 2855, 3423 Murray, A., 2783 Murray, B. S., 871 Nagamura, T., 3529 Nagao, M., 1277 Nahor, G. S., 2821 Naito, S., 4115 Nakagaki, M., 2537 Nakagawa, Y., 2129 Nakamura, E., 3475 Nakamura, T., 1287 Nakamura, Y., 11 1 Nakao, N., 665 Nakayama, N., 665 Nandan, D., 2047 Napper, D.H., 3107 Narayanan, S., 521 Nazhat, N. B., 501 Neagle, W., 361 5, 3625 Neta, P., 2109 Newman, K. E., 1387, 1393, Nicolis, G., 1013 Nishihara, C., 433 Nishikawa, S., 665 Nishio, E., 1639 Nisi, M., 2279 Nomura, H., 151, 1267 Norris, J. 0. W., 441 Northing, R. J., 2013 Noszticzius, Z., 575 Nowicka, B., 3877 Nucci, L., 97 Oas, T. G., 3691 Oehler, U. M., 3275 Ohno, T., 2465 Ohshima, K., 1639 Ohtaki, H., 2409 Ohtani, A., 3941 Ohtani, S., 187 Okabayashi, H., 1639 Okamoto, K., 2317 Okamoto, Y., 851 Okubo, T., 703, 1163, 1171, 1949, 3377, 3567, 4161 Oldfield, E., 3821 Oliva, C., 2397, 2477, 3279 Oliver, C. E., 3257 Oliver, S. W., 1475 Ollivon, M., 2609 Olm, M. T., 3341 Olofsson, G., 551, 4087 Ommen, J. G. van, 1491 Onishi, T., 511 Ono, T., 2465, 3121, 4137 Ono, Y., 1091 Oosawa, Y., 197 Opella, S.J., 3803 Overbeek, J. Th. G., 3079 Ozeki, S., 1795 Ozutsumi, K., 2409 Packer, K. J., 3857 Page, F. M., 1145 Painter, D. M., 773, 2087 3885 Pal, M., 1501 Pan, C-f., 1341 Pandey, J. D., 1853 Pandey, P. C., 2259 Pang, P., 1879 Paoletti, S., 2573 Papirer, E., 3865 Pappin, A. J., 1575 Parrott, D., 1131 Parsons, B. J., 3423 Passelaigue, E., 17 13 Patil, K., 2297 Patsalides, E., 4169 Patterson, D., 1603, 3991 Peacock, R. D., 3445 Pedatsur, N., 2821 Pedersen, J. A., 3223 Pedulli, G. F., 3347 Peet, W. J., 3319 Pelizzetti, E., 261 Pena-Nuiiez, A. S., 2181 Penar, J., 739 Penman, J. I., 2013 Perutz, R. N.. 2901 Petersen, E. E., 3927 Pethybridge, A. D., 2723 Pezzatini, G., 367 Pfeifer, H., 2347, 3777 Piccini, S., 331 Pichat, P., 261 Pickering, I. J., 2795 Pickl, W., 1311 Piekarski, H., 529, 591 Pierens, R.K., 4169 Pilarczyk, M., 1551, 3973 Pilbrow, J. R., 1475 Pilkington, M. B. G., 2155 Plath, P. J., 1751 Pogliani, L., 3331 Pogni, R., 3331 Pointud, Y., 959, 1713 Polavarapu, P. L., 2585 Poplett, I. J. F., 3857 Pota, G., 215 Pradhan, J., 2387 Preston, K. F., 413 Price, W. E., 2431 Prior, D. V., 865 Pushpa, K. K., 2047 Quinquenet, S., 2609 Quist, P-O., 1033 Radford, K. J., 3319 Radke, C. J., 3927 Radulovic, S., 1243, 2703 Raffi, J. J., 3359 Rai, R. D., 1853 Rajam, S., 1349 Rajaram, R. R., 391 Raleigh, D. P., 3691 Rao, B. G.. 1773, 1779 Rao, K. J., 1773, 1779 Rao, K. M., 2195 Ratcliffe, C. I., 3731 Rayment, T., 2915 Rebenstorf, B., 1897, 3363, 3547 (vii) Rebuscini, C., 2397 Rees, L. V. C., 2911, 3641 Reller, A., 2327 Renuncio, J.A. R., 539 Rhodes, C. J., 1187, 3215 Richardson, N. V., 2909 Richardson, S. M., 2909 Richoux, M-C., 2109 Riis, T., 1863 Ripmeester, J. A., 3731 Riva, A., 1423 Robson, B., 2519 Rochester, C. H., 309, 2001, 3605, 3615, 3625, 3633 Rojas, F., 785, 801, 1455 Ronemus, A. D., 3761 Rooney, J. J., 251 1 Ross, J. R. H., 1491 Rossi, C., 3331 Rowlands, C. C., 1723, 3243, Rowlinson, J. S., 4125 Rubio, R. G., 539 Rudham, R., 4181 Ruegge, D., 3187 Ryan, C. M., 4023 Saadalla-Nazhat, R. A., 501 Saba, A., 3279 Sacchetto, G. A., 2885 Saito, M., 1025 Saito, Y., 275 Saji, T., 2667 Sakai, K., 3529 Sakaiya, H., 1941 Sakamoto, Y., 459 Sakata, Y., 511 Salazar, F. F., 3539 Saleh, J. M., 3027, 3043 Salvagno, S., 1531 Sanz, J., 31 13 Sarkany, A., 2267 Sartorio, R., 2279 Sato, T., 275 Sauer, H., 617 Savile, G., 2907 Sawabe, K., 321 Sawaki, Y., 3475 Say, B.J., 3649 Sayari, A., 413 Sbriziolo, C., 207 Scarano, D., 2327 Schelly, Z. A., 575 Schiffrin, D. J., 561 Schiller, R. L., 365 Schlenoff, J. B., 1123 Schlogl, R., 631 Schmelzer, N., 931 Schollner, R., 3597 Schonert, H., 2553 Schulz, A., 3207 Schulz, R. A., 865 Schwarz, H. A., 2933 Schwarz, W., 1703 Scott, S. K., 993, 2904, 2908 3249 Schulz-Ekloff, G., 4097AUTHOR INDEX Seidl, V., 1447 Sellers, R. M., 355 Senna, M., 1199 Senoda, Y., 1091 Sermon, P. A., 391 Serpelloni, M., 2609 Serpone, N., 261 Seuvre, A-M., 2641 Shamil, S., 2635 Shan, X., 3821 Sheppard, N., 2913 Shimidzu, T., 3941 Shindo, H., 433 Shukla, A. K., 1853 Shukla, R. K., 1853 Sidahmed, I. M., 1153 Simmons, R. F., 1871 Sinclair, G.R., 1475 Sinfelt, J. H., 3785 Singh, B., 1729 Singh, P. P., 1807 s’Jacob, K. J., 1509 Slade, L., 2619 Slichter, C., 3785 Smith, E. R., 899 Smith, T. D., 1475, 1847, 4191 Soffer, N., 3575 Sokolowski, S., 19, 739 Somsen, G., 529 Soria, J., 3961 Soriyan, 0. O., 1 Speight, J. M., 2069 Spoto, G., 2195 Stainsby, G., 871 Stange, G., 2807 Stark, J. M., 3243 Stead, K., 2905 Stearn, G. M., 2155, 2357 Steel, A. T., 2783 Stell, J. K., 3319 Stevens, J. C. H., 165 Stewart, P. L., 3803 Stirling, C. J. M., 1531 Stocker, M., 1863 Stoeckli, F., 1973 Stone, F. S., 2843 Stone, W. E. E., 117 Stramel, R. D., 1287 Struve, P., 2247, 3001 Stuart, W. I., 3071 Subba Rao, M., 1703 Sudol, E. D., 3107 Suga, K., 2667 Sugahara, Y., 2677 Sun, L-M.. 1973 Suzuki, T., 1795 SvetliEid, V., 4023 Swallow, A.J., 2855, 3423 Swellem, H. I., 3511 Sykes, A. F., 1575 Symons, M. C. R., 609, 1181, 1187, 2181, 2499, 3341, 3401, 3459 Szamosi, J., 9 I7 Tabner, B. J., 3917 Taga, K., 1639 Taga, T., 2537 Tagawa, T., 923 Takada, T., 765 Takagi, K., 3475 Takagi, Y., 1025 Takaishi, T., 2967 Takato, K., 841 Takisawa, N., 2087, 3059 Takriti, S., 2831 Tamaki, J., 21 73 Tanaka, F., 1083 Tanaka, K., 601, 2895 Tanaka, K-i., 601 Tanaka, T., 2987 Taniewska-Osiriska, S., 2077, Tanimoto, M., 41 I5 Tardajos, G., 1603 Taylor, D. M., 1531 Taylor, M. J., 3857 Taylor, P. J., 865 Tazaki, K., 231 1 Tempest, P. A., 4049, 4061 Tewari, J., 1729 Thampi, K. R., 1703 Theocharis, C. R., 1509 Thomas, J. K., 1287 Thomas, J. M., 617, 631, 2795, Thompson, J. S., 2519 Tiddy, G. J. 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R., 2545 Webb, G., 2135 Weilbacher, E., 3293 Wells, C. F., 815, 1153 Welsh, M. R., 1259 White, T. J., 3071 Wijmenga, S. S., 2483 Wilkinson, D. P., 3389 Williams, B. G., 617, 631 Williams, C., 2915 Williams, D. E., 441 Williams, R. A., 713 Wilson, B. E., 3673 Winstanley, D., 1741 Wong, J., 1773, 1779 Wood, N. D., 11 13 Wormald, C. J., 1437, 2912, 3097, 3141, 3159, 3587 Wurzburger, S., 2279 Wyn-Jones, E., 773, 2087, 3059 Yamada, M., 2457 Yamada, Y., 751 Yamamoto, Y., 2209 Yamane, T., 2173 Yamasaki, S., 1679 Yamashita, H., 2987 Yamashita, S., 1083 Yao, S., 1375 Yasse, B., 3905 Yasugi, E., 2421 Yerlett, T.K., 3587 Yoffe, A. D., 2899 Yoneyama, H., 1587, 2317 Yoshida, S., 87, 2987 Yuqing, L., 2289 Zahn, G., 3597 Zainel, H. A., 351 1 Zecchina, A., 751, 2195, 2327, Zeitler, E., 617, 631 Zelano, V., 29 Zhao, X., 3951 Zibrowius, B., 2347 Zielinski, R., 151 Zundel, G., 885 2843 Zhu, B-Y., 3951 (viii)THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY SYMPOSIUM No. 24 Orientation and Polarization Effects in Reactive Col I isions To be held at the Physikzentrum, Bad Honnef, West Germany, 12-14 December 1988 Organising Committee: Dr S. Stolte Professor R.A. Levine Dr K. Burnett Professor R.N. Dixon Professor J.P. Simons Dr H. Loesch The Symposium will focus on the study of vector properties in reaction dynamics and photodissoci- ation rather than the more traditional scalar quantities such as energy disposal, integral cross-sec- tions and branching ratios. Experimental and theoretical advances have now reached the stage where studies of Dynamical Stereochemistry can begin to map the anisotropy of chemical interac- tions.The Symposium will provide an impetus to the development of 3-0 theories of reaction dyna- mics and assess the quality and scope of the experiments that are providing this impetus. The following areas will be covered: (A) Collisions of oriented or rotationally aligned molecular reagents (B) Collisions of orbitally aligned atomic reagents (C) Photoinitiated 'collisions' in van der Waals complexes (D) Polarisation of the products of full- and half-collisional complexes.The programme and application form may be obtained from: Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 87 Catalysis by Well Characterised Materials University of Liverpool, 11-13 April 1989 Organising Committee: Professor R. W. Joyner (Chairman) Professor A. K. Cheetham Professor F. S. Stone Dr K. C. Waugh Professor P. B. Wells The understanding of heterogeneous catalysis is an important academic activity, which complements industry's continuing search for novel and more efficient catalytic processes. The emergence of rele- vant, in particular in siru techniques and new developments of well established experimental ap- proaches to catalyst characterisation are making a very significant impact on our knowledge of catalyst composition, structure, morphology and their inter-relationships.Well characterised cata- lysts, whkh will be the subject of the Faraday Discussion, include single-crystal surfaces, whether of metals, oxides or sulphides; crystalline microporous solids, such as zeolites and clays, and ap- propriate industrial catalysts. The elucidation of structure/function relationships and catalytic mech- anism will be important aspects of the scientific programme. Contributions describing novel methods for synthesising well characterised catalysts and also reporting important advances in characterisa- tion techniques will also be included. The preliminary programme may be obtained from : Mrs Y. A. Fish, The Royal Society of Chemistry, Burlington House, London WIV OBN.THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 88 Charge Transfer in Polymeric Systems University of Oxford, 11 -1 3 September 1989 This Discussion aims to bring together physicists and chemists interested in the mechanism of elec- tron and ion transport in polymeric systems.The systems include conducting polymers, redox polymers, ion exchange membranes and modified electrodes. Discussion topics will cover ex- perimental evidence from spectroscopy, electrochemistry and new techniques such as the quartz microbalance. Theoretical models ranging from band theory through polarons to localised chemical structures will be critically evaluated and compared with experiment. The following have agreed to participate in the Discussion: R.Murray W. J. Albery M. B. Armand D. Bloor P. G. Bruce R. Friend A. J. Heeger A. R. Hillman A. G. MacDiarmid M. Ratner S. Roth W. Salaneck G. Tourillon C. Vincent G. Wegner Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 30 November 1988 to: Professor W. J. Albery, Department of Chemistry, Imperial College, South Kensington, London SW7 2AY. Full papers for publication in the Discussion Volume will be required by May 1989. THE FARADAY DIVISION OF THE ROYAL SOCIETY OF CHEMISTRY GENERAL DISCUSSION No. 89 Structure of Surfaces and Interfaces as Studied using Synchroton Radiation University of Manchester, 4-6 April 1990 Organising Committee: Professor J.N. Sherwood (Chairman) Professor D. A. King Dr G. King The Discussion will focus on the wealth of novel information which can be obtained on the nature and structure of surfaces using the full spectral range of synchroton radiation. Emphasis will be placed on the scientific results of recent investigations rather than on technical aspects of experimen- tation. Papers will be welcome which shed new light on the structure of the complete range of interfaces: solidkolid, solid/gas, solifliquid, gasiliquid and "dean" surfaces induding both static and dynamic in siru examinations. It is hoped that the discussion will define the utility of synchroton radi- ation examinations in surface science studies at a time of expansion of the availability of such sources and the inauguration of new and more powerful sources.Contributions for consideration by the Organising Committee are invited and abstracts of about 300 words should be sent by 31 May 1989 to: Professor J. N. Sherwood, Department of Pure and Applied Chemistry, University of Strath- Clyde, Thomas Graham Building, 295 Cathedral Street, Glasgow G1 1XL Full papers for publication in the Discussion Volume will be required by December 1989. Dr C. Norris Dr R. Oldman Dr G. ThorntonFARADAY DIVISION INFORMAL AND GROUP MEETINGS Division jointly with Dalton Division Inorganic Solids and their Surfaces (including the Nyholm Lecture by R. Hoffmann) To be held at the Scientific Societies' Lecture Theatre, London on 22 November 1988 Further information from Mrs Y A.Fish, The Royal Society of Chemistry, Burlington House, London W1 V OBN Polymer Physics Group jointly with Physical Crystallography Group Diffraction from Polymers To be held at the Geological Soaety, London on 30 November 1988 Further information from Dr M. JRichardson, Division of Materials, National Physical Laboratory, Queens Road, Tedding ton, Middlesex lW11 OLW Polar Solids Group with the Applied Solid State Chemistry Group Computer Modelling of Inorganic Solid Structures To be held at the Scientific Societies' Lecture Theatre, London on 2 December 1988 Further information from Dr A. E. Comyns, R & D Department, Laporte lndusties Ltd., Moorfield Road, Widnes WA8 OW Theoretical Chemistry Group Beyond the Born-Oppenheimer Approximation To be held at Trent Polytechnic, Nottingham on 14 December 1988 Further information from Dr R.G. Woolley, Department of Physical Sciences, Trent Polytechnic, Clifton Lane, Nottingham NG118NS Electrochemis try Group New Ideas in Electrochemistry To be held at the University of Cambridge on 15-16 December 1988 Further information from Dr S. P. Tyfield, CEGB, Berkeley Nudear Laboratories, Berkeley, Gloucestershire GL13 9PB ~~~~ ~~ Colloid and Interface Science Group Aggregation in Colloidal Systems To be held at the Scientific Societies' Lecture Theatre, London on 16 December 1988 Further information from Dr R. Buscall, ICI plc, Corporate Colloid Science Group, PO Box 11, The Heath, Runcom, Cheshire WA7 4QE High Resolution Spectroscopy Group High Resolution Molecular Spectroscopy To be held at the University of Birmingham on 1920 December 1988 Further information from Dr M.N. R. Ashfold, School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS Neutron Scattering Group Muon Spectroscopy To be held at the University of Nottingham on 20-22 December 1988 Further information from Dr S. Cox, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 OQX - Electrochemistry Group with the Electrotechnology Group of the SCI Battery Workshop To be held at the University of Oxford on 3-4 January 1989 Further information from Dr S. P. Tyfield, CEGB, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB Electrochemistry Group with the Organic Reaction Mechanisms Group Electron Transfer Reactions To be held in London on 5 January 1989 Further information from Dr S.P. Tyfieid, CEGB, Berkeley Nudear Laboratories, Berkeley, Gloucestershire GL13 9PBGas Kinetics Group Reactions of Ions and Free Radicals To be held at the University of Warwick on 6 January 1989 Further information from Professor R. G. Donovan, Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ Neutron Scattering Group Neutron and X-ray Scattering: Complementary Techniques To be held at the University of Kent at Canterbury on 29-30 March 1989 Further information from Dr R. J. Newport, Physics Laboratory, University of Kent, Canterbury CT2 7NR Division jointly with the Colloid and Interface Science Group Annual Congress: Surfactant Interactions in Colloidal Systems To be held at the University of Hull on 4-7 April 1989 Further information from Dr J.F. Gibson, The Royal Society of Chemistry, Burlington House, London W1 V OBN Electrochemistry Group Spring Informal Meeting To be held at the University of Warwick on 1 O-12 April 1989 Further information from Dr S. P. Tyfield, CEGB, Berkeley Nudear Laboratories, Berkeley, Gloucestershire GL13 9PB Electrochemistry Group with the Electroanalytical Group Electroanalytical Biennial Meeting To be held at Loughborough University of Technology on 12-14 April 1989 Further information from Dr S. P. Tyfield, CEGB, Berkeley Nuclear Laboratories, Berkeley, Gloucestershire GL13 9PB ~~ ~~ Industrial Physical Chemistry Group with the Thin Films and Surfaces Group of the IOP Materials for Non-linear and Electro-optics To be held at Girton College, Cambridge on 4-7 July 1989 Further information from The Meetings Officer, Institute of Physics, 47 Belgrave Square, London SWlX 8QX ~~ ~ ~~ ~~~ Polymer Physics Group Biennial Meeting To be held at the University of Reading on 13-1 5 September 1989 Further information from Dr M.J. Richardson, Division of Materials, National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 OLW Division with the lnstitute of Physics Sensors and their Applications To be held at the University of Kent at Canterbury on 19-22 September 1989 Further information from The Meetings Officer, Institute of Physics, 47 Belgrave Square, London SWlX 8QX Division with the Deutsche Bunsen Gesellschaff, Division de Chimie Physique of the Societe Franpise de Chimie and Associazione ltaliana di Chimica Fisica Transport Processes in Fluids and Mobile Phases To be held at the Physikalische Institut, Aachen, West Germany on 2528 September 1989 Further information from Professor G.Luckhurst, Department of Chemistry, University of Southampton, Southampton SO9 5NH Division Autumn Meeting: Chemistry at Interfaces To be held at Loughborough University of Technology on 26-28 September 1989 Further information from Professor F. Wilkinson, Department of Chemistry, Loughborough University of Technology, Loughborough LE11 3TU (xii)JOURNAL OF CHEMICAL RESEARCH Papers dealing with physical chemistry or chemical physics which appear currently in J. Chem. Research, The Royal Society of Chemistry's synopsis + microform journal, include the following: Factors affecting the Stability and Equilibria of Free Radicals.Part 15. Effects of the Acceptor Group on Spin Distribution and Other Properties Alexandru T. Balaban, Ursula Bologa, Miron T. Capriou, Nicoleta Grecu, Nicolae Negoig and Robert 1. Watter (1 988, Issue 9) Arturo Horta, Ligia Gargallo, lrmina Hernandez-Fuentes, Cristina Abradelo and Deodata Radic (1 988, Issue 9) Ambroz and Terence J. Kemp (1 988, Issue 9) and Aromatic Compounds by Time-resolved Atomic Resonance Absorption Spectroscopy Subhash C. Basu and David Husain (1 988, Issue 10) Benzo-bisdit hiazole) Gotthelf Wolmershausser, Gerhard Wortmann and Martin Schnauber (1 988, Issue 11 ) Frank Hibbert and Rowena J. Sellens (1988, Issue 11) Species in Aqueous Perchlorate Solution at Different Temperatures and Ionic Strengths Concetta De Stefano, Carmelo Rigano, Silvio Sammartano and Rosario Scarcella (1 988, Issue 11 ) Conformational Analysis and Dipole Moments of Methylsuccinic Acid and its Esters Enrique Saiz, E.S.R.Studies of the Photochemistry of Octacyanotungstate(v) Ion in a Polymer Matrix Hanna B. Absolute Rate Data for the Reaction of Atomic Germanium, Ge(43P~), with Halogenated Olefins Structural and Magnetic Properties of the Radical-cation Salt BBDTA+'FeCb- (BBDTA = Electrolyte Effects on the Reactions of Hydroxide Ion in 70% (v/v) Dimethyl Sulphoxide-Water Studies on Sulphate Complexes. Literature Data Analysis of the Stability of HSOQ and NaS04- (xiii)NOMENCLATURE AND SYMBOLISM Units and Symbols. The Symbols Committee of The Royal Society, of which The Royal Society of Chemistry is a participating member, has produced a set of recommendations in a pamphlet 'Quantities, Units, and Symbols' (1 975) (copies of this pamphlet and further details can be obtained from the Manager, Journals, The Royal Society of Chemistry, Burlington House, London W1V OBN). These recommendations are applied by The Royal Society of Cemistry in all its publications. Their basis is the 'Systeme International d'Unit6s' (9). A more detailed treatment of units and symbols with specific application to chemistry is given in the IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units (Pergamon, Oxford, 1979). Nomenclature. For many years the Society has actively encouraged the use of standard IUPAC nomenclature and symbolism in its publications as an aid to the accurate and unambiguous communication of chemical information between authors and readers. In order to encourage authors to use IUPAC nomenclature rules when drafting papers, attention is drawn to the following publications in which both the rules themselves and guidance on their use are given: Nomenclature of Organic Chemistry, Sections A, B, C, D, E, F, and H (Pergamon, Oxford, 1979 edn). Nomenclature of Inorganic Chemistry (Butterworths, London, 1971 , now published by Pergamon). Biochemical Nomenclature and Related Documents (The Biochemical Society, London, 1978). Compendium of Chemical Terminology: IUPAC Recommendations (Blackwells, Oxford, 1987). A complete listing of all IUPAC nomenclature publications appears in the January issues of J. Chem. SOC., Faraday Transactions. It is recommended that where there are no IUPAC rules for the naming of particular compounds or authors find difficulty in applying the existing rules, they should seek the advice of the Society's editorial staff. (xiv)

ISSN:0300-9599    

DOI:10.1039/F198884BP161

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

S. Chem. SOC., Faraday Trans. I, 1988, 84( 1 l), 3649-3672 Perspectives in High-resolution Solid-state Nuclear Magnetic Resonance, with Emphasis on Combined Rotation and Multiple-pulse Spectroscopy Robin K. Harris,* Peter Jackson, Lawrence H. Merwin and Barry J. Say Department of Chemistry, University of Durham, South Road, Durham DHI 3LE Gerhard Hagele Institut fur Anorganische Chemie und Strukturchemie, Universitat Diisseldorf, Universitatsstrasse 1, Diisseldorf, Federal Republic of Germany Recent trends of general interest in high-resolution NM R of solids are mentioned, and some examples briefly discussed. Stress is laid on the use of the multiple-pulse technique, particularly when combined with magic-angle spinning to give CRAMPS. Two studies of proton CRAMPS are described, one concerning hydrogen bonding in carboxylic acids and the other involving phosphonic acid derivatives.The relationship between proton isotropic chemical shifts and hydrogen-bond distances is explored in some detail. A clear correlation is found. As was found by Carrington' in an earlier Special Issue of Faraday Transactions (on Reaction Dynamics and Spectroscopy), it is difficult to know how to formulate an introductory Keynote Paper, although in his case the paper was first delivered as a Faraday Lecture. To attempt a comprehensive review of the advances in solid-state NMR in recent years would clearly not be feasible in an article of reasonable length, yet to' write on a single topic would not provide anything different in kind from the ensuing articles. Consequently, we are attempting to use a mixture of these two approaches.First, we propose to highlight a few developments of major significance, with brief examples where appropriate from our own laboratory. Secondly, we will develop in a little more detail a particular area which appears to us to be underused, although it has a respectably long pedigree,' namely combined rotation and multiple-pulse spectroscopy (CRAMPS). In this approach we will inevitably be briefly mentioning work carried out by a number of our colleagues, to whom we are greatly indebted. The ensuing articles in this Special Issue show something of the wide diversity of solid- state NMR experiments and their areas of application. However, it must be said that it would have been easy to increase the number of articles by an order of magnitude and still have totally left out many important aspects.This Special Issue is thus by no means comprehensive, but perhaps gives readers a feel for the excitement and rapid pace of developments in the NMR of solids. Unfortunately, within the length of our own article it has not proved generally feasible to fully describe many of the experimental techniques discussed nor to give a suitable number of appropriate references. General Solid-state NMR Developments Although it is difficult to pick out the highlights of a rapidly developing area such as solid-state NMR, and doubtless any choice is subjective, the following appear to us to be some of the trends of general interest, at least as far as high-resolution spectroscopy is concerned (relaxation studies form a separate topic).36493650 Perspectives in High-resolution Solid-state NMR (1) Multinuclear spin-; experiments. Most of the 24 elements having non-radioactive spin-; isotopes have now been studied by high-resolution NMR of solid samples using the magic-angle spinning (MAS) technique with or without cross-polarization (CP). Initially 13C was the favoured nucleus, followed by “Si and 31P, but the range is now much wider. For instance, a later article in this issue deals with ‘*’Xe. It seems clear that renewed interest in mixed metal oxides (for ceramics and warm superconductors) will lead to greater use of the ‘’Y nucleus. (2) Spectra of quadrupolar nuclei. Since quadrupolar interactions are frequently much larger than dipolar terms and sometimes approach Zeeman energies in magnitude, the study of spin > + nuclei in solids is in some ways more difficult than the observation of spin-: systems.For spins which are odd multiples of: it is often only feasible to observe the central ,; - - ; transition, and even that may be influenced by second-order effects. However, this is no longer inhibiting study of such nuclei, and most of the Periodic Table is now therefore accessible to solid-state NMR. The information that is available on quadrupolar properties complements the usual NMR parameters. There are only two important spin-1 nuclei, namely 2H and ‘*N. It is curious that although the former has been intensively studied and is very useful (as epitomised by a later article in this Special Issue), the nitrogen- 14 nucleus has been largely neglected for solids.(3) Spinning-sideband analysis. Spinning sidebands are either a bane or a blessing, depending on one’s viewpoint or objectives. Much effort has been put into spinning faster or using special pulse sequences to eliminate the effects. However, it is increasingly common to find realisation that sidebands contain important information on molecular structure and dynamics, and analysis of sideband manifolds is now routinely done. Suitable experiments yield accurate information about shielding anisotropy, dipolar interactions and quadrupolar coupling. (4) Two-dimensional NMR. The plethora of pulse sequences for (for example) correlating NMR parameters via two-dimensional Fourier transformation in solution- state studies is slowly being extended to solid-state NMR, with new information being revealed. Examples occur in ensuing articles, and are certain to become more common in the near future, ( 5 ) Geometry information.The dipolar interaction, being ‘ through-space ’, gives direct data on interatomic distances. However, it needs to be disentangled from other influences on spectra, and both spinning-sideband analysis and two-dimensional NM R play their part. Far more information can be obtained from single-crystal work. Although this is relatively uncommon, it is very rewarding, as can be seen from a later paper in this Special Issue. (6) Data for shielding theory. Theoreticians have long been concerned to understand the influences on shielding.However, solution-state data are far from ideal, both because intermolecular environments are heavily time-dependen t and because information is reduced to isotropic averages. Consequently, solid-state NMR can provide much more useful information. Spinning sideband analysis (and other methods) yield data on shielding tensor components. Moreover, there are two situations which provide useful comparisons even for isotropic averages, viz. (i) crystallographic splittings, where known local differences in fixed environments cause shift differences for chemically identical but crystallographically different sites in the same sample and (ii) spectra for polymorphs, which supply similar information. It has to be said that theoreticians do not seem to have yet risen to the challenges.(7) Indirect (‘ scalar ’) coupling. High-power proton decoupling not only eliminates the relevant dipolar interactions but also the J-coupling which is used to such good effect by solution-state NMR spectroscopists. However, some schemes3 can restore the splittings due to, say, JCH in I3C spectra of solids. We anticipate a considerable increase in such work, which is technically demanding, and in other operations involving spectrum editing.R. K. Harris et al. 365 1 (8) High-resolution spectra of abundant spins. Elimination of dipolar interactions for 'H and 19F NMR in solids requires either very high-speed spinning or CRAMPS but both are now in a phase of considerable expansion. Moreover, the CRAMPS method has recently been shown2d to be of advantage when added to high-power decoupling for, say, 31P.Because we believe CRAMPS to be still an under-rated and underused technique, we shall discuss some applications to hydrogen bonding in more detail below. Moreover, the value of the 'multiple-pulse' method for eliminating the effects of homonuclear coupling while retaining those of heteronuclear interactions is considerable in many areas in addition to the observation of abundant spins, and we shall give, briefly, two examples of such applications below. The above discussion does not address the question of what materials best benefit from solid-state NMR study. Indeed, the implications of the above are that pure crystalline materials are of the highest interest. Although much effort is put in this direction, it is our view that the future of solid-state NMR applications lies much more in the area of heterogeneous and/or amorphous materials. However, to develop that topic would require another Special Issue of Faraday Transactions ! All the discussion in this article and all the new results relate to the use of powdered or microcrystalline samples rather than single crystals.Some Examples Spectroscopy is about spectra, and generalities such as the above tend to lose their meaning without examples. In this section, therefore, we propose to illustrate some of the foregoing topics, not with any pretensions to great novelty, but rather to set the scene for the general reader. Spinning-sideband Analysis for Spin4 Nuclei4 For rigid molecular systems where static bandshapes of powdered samples are dominated by shielding anisotropy, data from spinning sidebands should readily yield information about tensor components. However, the moments method of Maricq and Waugh4" is subject to large errors, and the graphical method of Herzfeld and B e r g e ~ ~ ~ is also not entirely satisfactory.The obvious answer lies in full simulation of the sideband pattern. Even this can lead to difficulties because, as Clayden et aZ.5 pointed out, the sideband pattern is insensitive to the asymmetry parameter, q, when the situation is not far from axial symmetry. Fig. 1 illustrates the point by showing the way in which errors of fitting sideband patterns vary with q for a well behaved case (q = 0.87) and a badly behaved case (true q = 0, but apparent q = 0.12).The point is further made by consideration of the lg5Pt spectrum of K,Pt(OH),. Although X-ray studies reported6 it had space group R3, implying axial symmetry, this was in the absence of information about the positions of the protons. Our earlier sideband analyses7 by the method of Maricq and Waugh produce q = 0.24.3. We now finds that total sideband simulation and fitting for spinning speed 1907 Hz shows q = 0 to be a better solution (with an r.m.s. error of 3.8 x whereas q = 0.23 gives an r.m.s. error of 8.0 x Part of the problem lay in the use of Andrew-Beams rotors, which have a variable uncertainty in the magic-angle setting and hence give problems for the accurate measurement of sideband intensities. Such rotor systems are, of course, now superseded by the double- bearing type.3652 I I I I 1 I (0 1 .60 - . . . 1 50 - . . rn . . . 8 40 - I 1 1 .C.m8m I A Perspectives in High-resolution Solid-state NMR . I I I I I I I I . ( b ) 0 - - 6 - - . - . 2 - - . I... I . I I 1 I I I I I 0.7 0.8 0.9 1 .o v 1 . Fig. 1. Plots to show the variation of errors (sum of the squares for deviations of simulated intensities from the experimental values) with shielding asymmetry parameter, q, for fitting spinning-sideband manifolds. The data are those appropriate for sodium salts of 1,2-ethane- diphosphonic acid, H,O,PCH,CH,PO,H,. (a) High asymmetry (r,~ = 0.87), as for the disodium salt. (6) Low asymmetry (q minimises at 0.12 but the system is actually axially symmetric, i.e. q = 0), as for the tetrasodium salt.Values of the anisotropy, u3,-6, have been set at -64.7 and - 61.4 ppm for (a) and (b), respectively. Quadrupolar Spinning Sidebands So far relatively little use has been made of spinning-sideband patterns for quadrupolar nuclei. Yet in principle these can yield magnitudes of quadrupole coupling constants, 1x1 = e2qQ/h, to greater accuracy than NQR. One reason for this situation is that frequently values of 1x1 are > 0.5 MHz, rendering spinning-sideband patterns unusable or even invisible. However, for many other cases analysis is feasible, especially for nuclei with low quadrupole moments such as 7Li(Z = g). Fig. 2 shows an example,’ the 7Li spectrum of pentamethyldiethylenetriaminelithium borohydride. The envelope of the spinning-sideband pattern clearly shows the distribution to be expected from aR.K . Harris et al. 3653 80 60 40 20 0 -20 -40 -60 -80 vlkHz Fig. 2. The 77.8 MHz proton-decoupled 'Li MAS spectrum of N,N,N',N',N"-pentamethyl- diethylenetriamine lithium borohydride, showing spinning sidebands spanning all three transitions: -!- -f, --it); and fez. Experimental conditions: spinning speed 3.3 kHz, number of transients 124, recycle delay 15 s. The centreband has not been taken to its full height. The sharp spike nearby is an artefact. 180. C n t , - + -Ntr --+-Nt, __j Fig. 3. The pulse sequence used for the two-dimensional DIPSHIFT experiment: t , is the rotor period; N is fixed, typically 2 or 4; t, is the multiple-pulse sequence cycle time; n is incremented to form the two-dimensional array.MPPD = multiple-pulse proton decoupling. HPPD = high- power proton decoupling. quadrupolar powder bandshape. Although an accurate analysis of the spinning- sideband pattern has yet to be carried out, rough measurements show 1x1 = 125 kHz. The DIPSHIFT Experiment The pulse sequence shown in fig. 3 has been suggested by Munowitz and Griffin" to separate dipolar and shielding information in a two-dimensional mode. Multiple-pulse decoupling is used for a variable fraction of a spin-echo sequence, and synchronisation of the 180" refocussing pulse with the rotor period is essential. Summation in the dipolar domain produces a spinning sideband pattern that characterises the dipolar interaction alone. In the absence of molecular motion, the pattern for a simple two-spin system depends only on the internuclear distance.Simulation of the sideband pattern, with variation of the distance to fit the experimental observation, yields the geometry information. Fig. 4(a) shows the 31P dipolar pattern obtained for disodium phosphite pentahydrate Na2HPO;5H20, and fig. 4(b) gives the result of a simulation with3654 Perspectives in High-resolution Solid-state NMR L: 20 10 0 -1 0 -20 VlkHZ Fig. 4. Expanded 31P CPMAS dipolar spectra for disodium phosphite pentahydrate : (a) experimental case, from projection of DIPSHIFT plots ; (b) comp;ter-simulated spectrum corresponding to a P-H bond distance of 1.43 A. rPH = 1.43 A. We believe the accuracy of this determination to be k0.05 A. Anisotropy in the indirect coupling constant, JPH, would affect the spectrum in the same way as the dipolar interaction, but it is probably negligible and has been ignored.Two-dimensional J-Resolved Spectra3d We have used the pulse sequence shown in fig. 5 to obtain coupled 13C spectra in the two- dimensional mode of camphene (I). This is a solid in which the molecules are relatively mobile, so a simple 90" pulse is adequate as a preparation pulse. Multiple-pulse proton CR. K. Harris et al. 3655 > ' t l ' t2 > Fig. 5. The pulse sequence used to obtain the 13C J-resolved two-dimensional spectrum of cainphene (I). t , is the rotor period; N is incremented to form the two-dimensional array. MPPD = multiple-pulse proton decoupling. HPPD = high-power proton decoupling. A- I i d Fig. 6. Two-dimensional J-resolved 13C spectrum of camphene (low-frequency region only) : (a) contour plot; (b) projection onto the chemical-shift axis.Peaks marked by an asterisk arise from an impurity. For the (tentative) assignments see the molecular structure (I) in the text. The chemical shifts for (d) and (g) are 6, = 25.8 and 39.5 ppm, respectively. 80 experiments made up the 2D array, with the evolution time incremented by 2 rotor periods between experiments. For each experiment 400 transients were acquired, with recycle delays of 2 s. During t, 10 8-pulse MPPD cycles were used per rotor period. The MAS rate was 2.78 kHz. decoupling is applied during the first half of the spin-echo sequence (i.e. for time tl) and normal high-power decoupling during the second half. The time t , has to be an integral number of rotor periods in order for the 180" pulse to give a true echo, but ("C, 'H) coupling is not refocussed.Double Fourier transformation therefore leads to the spectrum shown in fig. 6. Clearly assignments based on multiplet structure can be made and coupling constants can be determined. It may be noted that peaks (e) and (b) are only separated by 0.3 ppm. In attempting to extend this work (in CP mode) to more rigid molecules we have come up against limitations on the phase stability of the high-power decoupler in our Bruker CXP 200 spectrometer. Fluorine-19 CRAMPS Most CRAMPS studies have involved observation of the 'H nucleus. However, perfluorocarbons are an important class of organic compounds, and the CRAMPS3656 Perspectives in High-resolution Solid-state NMR I 1 I I I 1 -100 -200 -300 -400 100 0 s, @Pm) I I I i - 50 -1 00 -150 - 200 s, (PPm) Fig.7. Fluorine-19 spectra of sodium perfluorooctane sulphonate: (a) MAS alone; (b) CRAMPS with MREV-8 (8-pulse cycle time 36 ps). In each case spinning is at 4.0 kHz and the recycle delay is 10 s. The numbers of transients used are (a) 100, (b) 64. Note that the frequency scales of (a) and (b) differ. Table 1. Fluorine-19 chemical shifts for solid sodium perfluoro-octanesulphonate CF,CF,CF,CF,CF,CF,CF,CF,SO;Na+ a b c d e f g h site(s) 4dPPm)" a - 83.0 b - 129.8 c-g - 124.7 h - 118.2 aFrom the signal arising from CFC1,. method offers an attractive alternative to very high-speed MAS. (Dec et aZ.ll found it necessary to use up to 23 kHz to get good quality I9F spectra of Kel-F.) Sodium perfluoro-octanesulphonate, C,F,,SO;Na+, has interesting surfactant prop- erties and so was chosen as an example.Single-pulse operation with MAS at 4.0 MHz produced the discouraging spectrum shown in fig. 7(a), whereas CRAMPS (using the same spinning speed) gave reasonable resolution as shown in fig. 7(b). Note that the scaling factor associated with the MREV-8 pulse sequence implies that the effective spinning speed is 8 kHz. Assignment of the spectrum is straightforward and is given in table 1.R. K. Harris et al. 3657 CRAMPS Studies of Hydrogen Bonding in Carboxylic Acids Hydrogen bonding is important throughout chemistry, and has received much attention by spectroscopists. Developments in single-crystal X-ray and neutron diffraction methods have delivered detailed geometric information about hydrogen-bonded systems by more exactly locating hydrogen atom positions.Such experiments are, however, time- consuming and expensive, and may be limited by a lack of suitable sample crystallinity. Infrared spectroscopy can give information about stretching frequencies in hydrogen- bonded OH groups, but complex splittings in strongly hydrogen-bonded solids make detailed analysis difficult, especially if more than one type of acid site is present. However, a number of papers have reported correlations between stretching frequencies and hydrogen- bond distances. 12-19 Deuterium NMR has also been of use in studying deuterated hydrogen bonds, the observed quadrupole coupling constant, x = e2qQ/h, being a direct measure of the electric field gradient at the deuterium nucleus.A linear correlation between x and the bond-stretching force constant is well known, both experimentally2'. 21 and theoreti- ally.^^,^^ Such studies have also correlated x and hydrogen-bond distances obtained from deuterated c r y ~ t a l s . ~ ~ - ~ ~ Since deuteration inevitably changes hydrogen-bond distances, it is desirable to obtain proton NMR data in order to understand more fully hydrogen bonding in solids. The introduction of multiple-pulse techniques has enabled proton shielding tensor components to be measured in both polycrystalline and single-crystal static samples. Berglund and Vaughan have summarised proton NM R data, deuterium quadrupole coupling constants and crystallographic data for 24 hydrogen- bonded solids.3" Several correlations were made between observed proton tensor components and both quadrupole coupling constants (for corresponding deuterated samples) and hydrogen- bond distances.Of greater subsequent interest, however, has been their correlation between hydrogen-bond distance, defined as the oxygen-oxygen separation, r,, (), and the isotropic proton shielding relative to that for tetramethylsilane, A@, which showed an apparent linear trend. Earlier theoretical studies, by other workers,31 on the shielding tensor of the hydrogen-bonded proton in the (H20), dimer were considered. The results did not take account of any increase in the donor oxygen-proton covalent bond length ro-H as ro was increased. Modifications were made in the light of neutron diffraction data, which have established a general relationship between ro and rg-H,32 to yield a curve with an average slope agreeing with experimental results, but which underestimated shifts by some 8 ppm (fig.8). Rohlfing et al. later pointed out3' that the (H20), model did not satisfactorily consider changes in geometry and charge distribution. Their ab initio calculations of geometries and shielding tensors of protons in (H,O),, [H30,]- and [H,O,]+, and in hydrogen-bonded dimers of RCOOH and ROH (R = H, F, OH and NH,), seemed to point to a more linear correlation (with considerable scatter) between AO and ro o, in line with experiment. The authors explained that a more complicated correlation than linear was likely, given the limited number of theoretical points and the large scatter obtained.Jeffrey and Yeon have argued34 that the 'hydrogen-bond length' referred to above, ro *, should be replaced by the proton-acceptor oxygen distance, r H <), since proton positions in crystals can now be accurately located by diffraction methods. Using the same NMR data as Berglund and Vaughan, but obtaining rH <) distances directly from neutron diffraction studies, or by recalculating X-ray results, they obtained a linear relationship between AG and rH o, again with increased scatter at longer H---0 distances. The development of proton CRAMP NMR has allowed direct measurement of isotropic proton shifts in solids with greater speed and accuracy than either single-crystal3658 Perspectives in High- resolu t ion Solid-state NMR -2s J 1 2.3 2.4 2.5 2.6 2.7 2.0 2.9 3.0 ro- - - O I A Fig.8. Plot of isotropic shift, Ac, us. oxygen-oxygen separation, ro...o, for hydrogen-bonded protons, as reported by Berglund and V a ~ g h a n . ~ ~ The solid curve represents the results of modified theoretical calculations made on the (H,O), dimer, and is offset to higher frequency (downwards) by 8 ppm. or static powder multiple-pulse NMR and without the more difficult chemical modifications required for dilute-spin magic-angle spinning (MAS) NMR studies of deuterated sample^.^^'^^ CRAMPS results, however, have so far failed to make a great impression on hydrogen-bonding correlation studies. Therefore, in the present work a total of 75 solid samples have been analysed (40 of which have been previously studied by X-ray or neutron diffraction) with a view to further understanding proton shielding in hydrogen bonds.All samples are carboxylic acids or their acid salts. Table 2 gives -CO,H proton isotropic shifts for the samples (nos. 1-40) we have analysed by CRAMPS, together with crystallographic data. For completeness, data are given for other hydrogen-bonded protons (COH and H,O) in the same systems. Some NMR results summarised by Berglund and Vaughan are also included (nos. 41-48) for cases where samples were unavailable to us for CRAMPS analysis. Table 3 reports CRAMPS shifts for acid protons in samples where no crystallographic reference has been found. The following points should be noted. (1) Only peaks that could be un- ambiguously assigned are reported.Many samples give spectra with overlapping peaks, making absolute assignment difficult. (2) Mobile or reorientating molecules or groups (H,O, NHg etc.) often produce broad, featureless peaks with the CRAMPS technique, since correlation times for reorientation may be of the order of the multiple-pulse cycle time, leading to a loss of the ability of the pulse sequence to suppress dipolar broadening. Protons bonded to nitrogen may also give rise to broad resonances, caused by incomplete removal of (14N, 'H) direct dipolar coupling by magic-angle spinning.2b, 85 Such broadening or splitting is well known in solid-state 13C NMR and arises from the quadrupolar nature of the 14N nu~leus.~~-'' Again, where absolute assignment is difficult, results are not reported.(3) rH---O data are only included for samples where neutron diffraction studies have been performed, or for samples with distances recalculated by Jeffrey and Yeon from X-ray dcta. Standard X-ray analyses are known to underestimate 0-H bond lengths by ca. 0.1 A, making results derived from such studies unreliable." (4) F o r samples reported here with no crystallographic data referenced, relative intensities are indicated in parentheses where more than one CRAMPS peak is observed. (5) An accurate isotropic shift for the carboxylic protons in oxalic acid dihydrate (6 = 17.0 ppm) has been determined by isotopic dilution (deuterium enrichment)R. K. Harris et al. 3659 Table 2. Carboxylic acid proton isotropic shifts and crystallographic data for CRAMrS results (1-40) and results reported by Berglund and Vaughan (41-48) (distances are given in A and 6 in PPm) sample donor group 6" rH...O X or Nb ref.1 NaH phthalate .iH,O 2 KH,(oxalate), * 2H20 3 KH oxalate 4 KH( +)tartrate 5 oxalic acid + 2H,O 6 a-fumaric acid 7 maleic acid 8 malonic acid 9 pimelic acid 10 aspirin 1 :I salicyclic acid 12 pyromellitic acid - 2H20 13 terephthalic acid 14 isophthalic acid 15 (+)tartaric acid 16 phthalic acid 17 NH,H( + ) tartrate 18 P-EDTA 19 L-aspartic acid 20 (1-naphthy1)acetic acid 21 azeleic acid 22 glycolic acid 23 benzoic acid 24 p-anisic acid 25 p-toluic acid 26 p-chlorobenzoic acid 27 p-nitrobenzoic acid 28 rn-nitrobenzoic acid COOH COOH COOH COOH COH COH COOH COOH COOH COOH COOH COOH COOH COOH COOH COH COOH COOH COOH COOH COOH COOH COOH COH COH COOH COOH COH COH COOH COOH COOH COOH COOH COH COH COOH COOH COOH COOH COOH COOH H2O 17.1 18.7 14.4 16.4 6.6 4.5 16.9 12.9 16.0 13.3 12.7 12.4 13.2 13.0 12.3 9.8 14.5 1.8 5.4 4.4 4.0 3.7 2.7 1.7 7.0 4.8 12.7 16.0 6.8 4.8 19.2 15.4 13.1 12.9 12.4 7.7 7.3 12.7 13.3 14.0 13.7 12.8 13.4 2.49 2.499 2.523 2.532 2.735 2.782 2.506 2.684" 2.502 2.643 2.68 2.71 2.677" 2.645 2.620 2.549 2.687 2.841 2.608 2.581 2.682 2.633 2.707 2.839 2.909 2.685 2.55 2.74 2.80 2.460 2.577 2.650 2.679 2.643' 2.691 2.714 2.633 2.632 2.629 2.6 18 2.660 2.648" f 1.480 1 .54d 1 .67d 1.61d 1 .72d 1.91d 1.64 1.71 1.86 1.95 1.643" 1.774 1.753 X X X X N X X X X X X X X X N X X X X X X N X X X X X X 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 643660 Per spec t ives in High- r es o h t ion So 1 id-s t a t e NMR Table 2.(cont.) sample 29 o-nitrobenzoic acid 30 3,5-dimethylbenzoic acid 3 1 p-hydroxybenzoic acid - H,O 32 2-aminobenzoic acid I 33 2-aminobenzoic acid I1 34 3-aminobenzoic acid I 35 4-aminobenzoic acid 36 p-hydroxycinnamic acid 37 m-bromobenzoic acid 38 p-bromobenzoic acid 39 m-chlorobenzoic acid 40 cinnamic acid 41 KH malonate 42 KH oxidiacetate 43 KH dicrotonate 44 NH,H oxalate-iH,O 45 KH phthalate 46 trichloroacetic acid 47 oxalic acid (anhydrous) 48 KH maleate COOH COOH COOH H,O H,O COOH COOH COOH COOH COOH COH COOH COOH COOH COOH COOH COOH COOH COOH COOH COOH COOH COOH H P 13.2 12.2 13.0 6.7 5.2 16.5 12.3 13.3 13.2 12.4 5.6 13.0 13.6 13.3 13.7 20.5 19.6 18.2 14.0 5.3 14.0 13.9 12.6 21 .o 2.645 2.63 2.658 2.81 1 2.827 2.498 2.654 2.640" 2.627' 2.632 2.885 2.60 2.646 2.664 2.630 2.468 2.476 2.488 2.561 2.780 2.546 2.666 2.702 2.437 1.458 1.234 1.328 1.348 1.59" 1.84" 1.7W 1.658 1.85' X X X X N X X 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 a Reported using the usual high-frequency-positive convention.X = X-ray data; N 3 neutron diffraction data. " rH...o values recalculated by Jeffrey and Yeon. Average of 3 values. Average of 2 values. The 0---0 distance in salicylic acid was not given in the report of the crystal structure. Table 3. Proton isotropic shifts determined by the CRAMPS method where no crystallographic reference has been found sample donor groupa db 1 Na,H citrate 2 (NH,),H citrate 3 Na salicylate 4 1,2,4-benzenetricarboxylic acid 5 phenylmalonic acid COOH (1) COH (1) COOH (1) COH (1) COH COOH (2) COOH ( 1 ) COOH (1) COOH (1) 19.2 6.3 19.2 6.4 15.1 14.I 12.7 14.0 12.3R. K. Harris et al. 366 1 Table 3. (cont.) sample donor group’ ab 6 2,2’-biphenyldicarboxylic acid 7 3-phenylpropionic acid 8 3,4-dihydroxycinnamic acid 9 4-nitroanthranilic acid 10 L-glutamic acid 11 hippuric acid 12 quinoline-2-carboxylic acid 13 palmitic acid 14 vanilic acid 15 naphthalene- 1,4,5,8-tetracarboxylic acid 16 phenylpropiolic acid 17 ferulic acid 18 4-chloroanthranilic acid 19 3-nitrophthalic acid 20 tribromoacetic acid 21 sorbic acid 22 phenylsalicylate 23 N-phenylanthranilic acid 24 2-indolylcarboxylic acid 25 m-anisic acid 26 m-toluic acid 27 3,5-dinitrobenzoic acid 28 3-iodobenzoic acid 29 4-chloro-2-nitrobenzoic acid 30 3,Sdimethoxy benzoic acid 31 sinapic acid 32 5-methylanthranilic acid 33 4-amino-3-methylbenzoic acid 34 3,4-dihydroxybenzoic acid 35 3-hydroxybenzoic acid COOH (1) COOH ( I ) COOH COOH ( I ) COH (2) COOH COOH COOH ( 1 ) COOH ( 1 ) COOH COOH COOH ( I ) COH (1) COOH COOH COOH ( I ) COH (1) COOH COOH COOH COOH COH COOH ( I ) COOH (1) COOH COOH COOH (1) COOH (1) COOH COOH COOH COOH COOH COOH COOH COOH (1) COH (1) COH (1) COOH (1) COH ( I ) 14.0 12.4 13.6 12.3 8.4 12.9 16.3 17.0 15.2 15.6 13.6 13.4 5.4 11.1 13.2 13.9 5.I 13.2 11.0 12.6 13.4 10.3 12.5 12.0 11.0 12.9 13.5 12.9 13.7 13.0 13.8 12.4 13.3 12.9 13.0 13.6 12.1 8.5 13.7 8.3 a Numbers in parenthesis indicate the relative intensities where more than one peak is resolved.Chemical shift data are given in ppm.3662 Perspectives in ( a ) High-resolution Solid-state NMR I r I I 1 20 10 0 s, (PPm) Fig. 9. 'H-CRAMP spectra of typical hydrogen- bonded solids : (a) 1,2,4-benzenetricarboxylic acid (the peak at S, = 1.74ppm is due to a small amount of adamantane added as an internal reference) ; (b) sodium hydrogen phthalate hemihydrate. For both spectra 8 transients were acquired, with recycle delays of 20 s. - L a . . 2.3 2.4 215 216 2:7 210 2I9 3.Q ro- - - O I A Fig. 10. Plot of AC us. ro...o for selected data. Experimental points for all carboxylic acid protons listed in table 2 : 0, CRAMPS results; 0, results from Berglund and Vaughan;30 ., theoretical The solid line is the theoretical curve derived by Berglund and Va~ghan,~O displaced by 8 PPm.combined with MAS.36 The CRAMPS result reported here, after careful scaling and referencing, is in excellent agreement. Two typical CRAMP spectra are shown in fig. 9, illustrating the resolution obtained with a well tuned MREV-8 sequence at 200 MHz. The spectrum of benzene-1,2,4- tricarboxylic acid [fig. 9(a)] clearly shows two distinct carboxylic peaks at 6 = 14.1 and 6 = 12.7 ppm, with relative intensities of 2 : 1. The remaining three aromatic protons give rise to the peak at 6 = 8.0 ppm and the shoulder at 6 = 7.2 ppm. The sharper peak at 6 = 1.74 ppm is due to a small amount of adamantane added as an internal reference. Fig. 9(b) gives the CRAMP spectrum of sodium hydrogen phthalate hemihydrate,R. K .Harris et al. 3663 showing the high-frequency shift of the acid proton (6 = 17.1 ppm). The remaining peaks are due to the aromatic protons, showing inequivalence, and the protons in the water of crystallisation, and cannot be unambiguously assigned. Other typical CRAMP spectra have been reported by several workers, together with more detailed discussions of linewidths and resolution. 2,85 Therefore only the relevant isotropic shifts observed are discussed here. The experimental errors in proton measurements reported in the paper by Berglund and Vaughan were of the order of the scatter in their correlation plot (fig. 8). They remarked that the actual correlation may improve with more accurate data. Here, proton shifts are determined to within 0.5 ppm and it should be noted that errors in the experimental determination of bond distances are small.In their limited data set, Berglund and Vaughan observed an apparent increase in scatter with increasing bond length. This was interpreted as an increased influence of surrounding atoms with increased bond distance. Our work on a variety of chemical systems points to the opposite conclusion that surrounding atoms or groups probably have an equal effect on the proton shift at all bond lengths. To consider the origins of the scatter, we concentrate attention here on the carboxylic acids only. Fig. 10 shows the plot of A@ us. ro . for all the carboxylic acids listed in table 2. All bonds are to either COOH or COO- carbonyl oxygens. Points for bonds to both types of acceptor are included, since there is good and no obvious discontinuity, suggesting that the effect on the proton shielding carboxylic and carboxylate acceptors is about the same.In both cases (I1 and carbonyl oxygen can be considered as having a partial negative charge: overlap of both 111) the 0 / H H I i - 0 ,o ‘C’ I R 1 0 H H’ I 0’ 0- \C/ I R I 0 H’ 0 0 - \c’ I R I 0 / H Fig. 10 also shows the correlation curve proposed by Berglund and Vaughan derived from the (H20), model. This shows remarkable agreement with the experimental data. The curve is displaced by 8 ppm. As suggested by Berglund and Vaughan, this can be explained as the deshielding effect of induced currents around atoms neighbouring the hydrogen bond. The effect of the atoms or groups bonded to the hydrogen-bonded system on the electron density of the donor oxygen is likely to be important also.The fact that both aromatic and aliphatic carboxylic acids lie on the same curve implies, however, that the deshielding effect of the benzene ring is small compared with the effect of the atoms in the carboxylic group. The small remaining scatter may be accounted for by such slight deshielding by more distant groups or by effects due to crystallographically close neighbours. It is also expected that variations in the 0-H---0 bond angle will have an effect on the proton shift, since this will change the two oxygen-proton distances for a given oxygen-oxygen separation. The other points on the graph are theoretical results from Rohlfing et aZ.33 that correspond to carboxylic acid protons involved in hydrogen bonds to oxygen.These selected points now agree well with the experimental data in slope, although there is a shielding offset of some 6 ppm. This is probably due to the fact that in each theoretical case, the acceptor oxygen was part of an R-0-H group, instead of a carboxylic or carboxylate group, and the calculations take only the isolated dimer into account. It would perhaps be useful to pursue further the theoretical ideas of earlier workers, and calculate ab initio proton shifts for protons in hydrogen bonds, allowing to increase as y o . . is decreased.3664 Perspectives in High- resolu t ion Solid-state NMR -5 ib Q -15 -20 -2 5 1.2 1.4 1.6 1.8 2.0 Fig. 11. Plot of A 8 DS. rH...O for carboxylic acid protons: 0, CRAMPS results; e, results from Jeffrey and Y e ~ n .~ ~ Of the carboxylic acid hydrogen-bond shifts listed in table 2, 16 have corresponding H---0 distances that have been measured or recalculated. This modest number allows the plotting of r , ..o us. 6 for this chemical type alone. Fig. 11 shows the result. A linear trend is observed, although the number of points is still not large and a substantial proportion of the data are derived from the single-crystal or powder NMR results reported by Jeffrey and Yeon. Therefore, small deviations from linearity cannot be discounted. The average slope for this acid type is less than the average slope for the data reported (for a variety of chemical types) by Jeffrey and Yeon, but the scatter is much decreased. Indeed, the scatter observed in this case is very similar to that observed in the corresponding plot of A 8 against ro ..o.The form of this plot can be explained by similar arguments to the ones above: the relatively small scatter is due to the next substituent or crystallographic neighbours. The theoretical studies on RCOOH and ROH dimers did not report H- - -0 distances. It would be interesting to discover if such ab initio calculations can reproduce their apparent success in correlating ACT with ro-..o in this case, for AS against rH...o. Thus we have increased the data set of relevant isotropic proton chemical shifts by analysing 40 new samples of hydrogen-bonded carboxylic acids with increased accuracy by the CRAMPS method, and have improved results for several samples already studied by earlier NMR techniques.‘ Coarse’ trends reported by earlier workers in correlations between A@ and both ro...o and rH...o have been confirmed, but the increased number of samples analysed and the concentration on a particular chemical type has allowed the correlations to be refined. The apparently greater scatter at longer bond lengths mentioned by Berglund and Vaughan appears to be due to the greater diversity of chemical types they studied in comparison to the cases with shorter bond lengths. Increased work on samples well characterised by crystallographic methods for other chemical types should enable hydrogen-bond distances to be deduced in many cases, although with lower precision than diffraction studies, by proton NMR alone. Proton CRAMPS Studies of Phosphonic Acids and Derivatives Phosphonic acids having the general structure (IV), and their derivatives, are of chemical and biochemical interest in a number of ways. Thus, several gem-diphosphonates have been showngo to have effective alkaline-earth ion sequestration properties : ethane- 1 -R.K. Harris et al. 3665 4 O R-P ‘%?OH OH hydroxy- 1,l -diphosphonic acid monohydrate, in particular, has been demonstrated” to be an effective inhibitor of calcium hydroxyapatite crystal growth in vitro and to inhibit pathological calcification in vivo. Furthermore, oligophosphonate complexes of technetium-99 and indium- 133 have foundg2 application in modern in vivo diagnostic techniques. The form of the phosphonate ligand has been conclusively shown to influence the organ specificity of the technique.The aminophosphonic acid series mimics in some respects the amino acids of biochemical significance. The hydrogen bonding of phosphonic acids is clearly an important influence on their properties. This mostly involves the POH group as the hydrogen-bond donor. Relatively few compounds of this type have had their structures fully determined by X-ray diffraction. Consequently, we felt it was of value to study the high-resolution solid-state NMR of phosphonic acid derivatives. The results of 13C and 31P spectra will be discussed elsewhere; this report concentrates on ‘H CRAMPS. Tables 4 and 5 list our results, the former containing data for compounds of known crystal structure, and the latter information for other systems.Table 4 includes crystallographic data and gives the nature of the hydrogen-bond acceptor group in each case. Fig. 12 illustrates CRAMP spectra for two of the compounds. The X-ray diffraction data show that the four aminophosphonic acids exist in the solid state as zwitterions. With the exception of compound (VIII) this implies that the hydrogen-bond acceptor atom is an oxygen with a partial or full negative charge, since it is in a POSH- group (but is not the hydroxyl oxygen). This is also true for compound (VII). For compound (VIII) the situation is more complex, as discussed below. Compound (V) is also a special case, but the acceptor atom for the remaining systems is a double-bonded oxygen of a P(O)(OH), group. -0p’ 0 ‘roz- 0 6Hz ;k----CH 5Na’. 11 H,O / \ -02p P 0,- (V) ‘o.-H- .-O’ Ph P03H, Ph ‘PO,H, (IX ) (X 1 W,H- P O A I p3HZ (VI) WII) PO3 H, (-JP03H2 c H3-c-OH H,O C H,-A-OH 2Na: 4H,O I I I H,NCH,CH,C-OH PO3 H2 PO,H- H ‘P03Hz POJ-4 (X 1) (X 11) H i L - P o 3 H , ‘POSH- (VIII) (XIII) In three cases where the crystal structure is known there is more than one band in the appropriate CRAMPS region.Fig. 12 (a) shows the spectrum of nitrilotrimethylene- triphosphonic acid, N(CH,PO,H,),. A diffraction study proves that the compound exists in a zwitterionic form (VIII), but with only one molecule in the asymmetric unit. Both facts are confirmed by our observation of a single 15N resonance at a chemical shift of - 330.8 ppm from the [NO,]- resonance of ammonium nitrate. However, there are sixTable 4. Proton CRAMPS data" for phosphonic acids of known crystal structure compound acceptor crystallographic group asymmetric unit" reference p met hanedip hosp honic acid 1 1.9(3) 2.542, 2.565, 2.604 P=O I 10.3(1) 2.677 P=O 1 - m 2 crl K ethane- 1,1,2,2-tetraphosphonic acid anhydride, 17.2 2.439 Poi-' 94 pentasodium salt, undecahydrate (V) 5' ethane- 1-hydroxy- 1,l -diphosphonic acid monohydrate (VI) H2O 1 P=O 14.5(2) 1 1.0(3) 2.612, 2.618, 2.696d P=O ethane- I-hydroxy- 1,l -diphosphonic acid, disodium salt 1 1.9 2.610 PO,H- 1 benzenephosphonic acid 11.9 2.554, 2.608 P=O 1 tetrahydrate (VII) 2 nitrilomethylenetriphosphonic acid (zwitterion VIII) 16.3(1) 2.458 PO,H-' 2 s aminomet hanep hosp honic acid 11.9 2.570 PO,H-' 1 98 2-aminoethanephosphonic acid 12.4 2.546 PO,H-' 1 99 3-aminopropanephosphonic acid 12.2 2.522 PO,H-e 1 100 2 12.5(4) 2.524, 2.602 PO,H-' 1 101 2.532, 2.551 P=O h a Given for POH hydrogen bonds only: assumed to give resonances at 6, 3 10.0 ppm.The relative intensities are given in parentheses where appropriate. In molecular units. See the text and structure (V). This band is probably assignable to a hydrogen bond involving a C-OH donor group and a P=O acceptor. It is not included in fig. 13. These acceptor groups are zwitterionic, but the hydroxy oxygen is not involved.R. K . Harris et al. 3667 Table 5. Proton CRAMPS data" for phosphonic acids of unknown crystal structure relative asymmetric predicte$" compound MPPm)" intensities unit* ro.. -o/A car box yme thy lp hosp honic acid ethane- 1,1,2-triphosphonic acid 1-phenylethane- 1,2- diphosphonic acid 1 -phenylethane- 1,2,2- triphosphonic acid propane- 1,1,3,3- tetraphosphonic acid I -phenyl-trans- 1,4- tetralindiphosphonic acid (IX) tetralindiphosphonic acid (XI 1 -phenyl-cis- 1,4- N,N-dimethylamino- 13.5, 12.4 11.6, 10.9 11.5 15.9, 10.3 11.4 10.9 12.1 16.9, 12.8, 11.1 methanediphosphonic acid hydroxypropane- 1,l- diphosphonic acid (XI) diphosphonic acid (XII) (me thylenephosphonic acid) (XIII) 3-amino- 1- 13.3 az,acycloheptane-2,2- 16.3, 11.4 ethylenediaminetetra- 13.9 (broad) 1 : 1 d e 1 : l e e - 2.50,2.55 2.58, 2.63 2.59 2.46, 2.67 2.60 2.63 2.56 2.44, 2.53, 2.62 2.5 1 2.45, 2.60 2.49 " Given for POH hydrogen bonds only: assumed to be all resonances at 6 , 2 10.0 ppm.* In molecular units. The isotopes in parentheses refer to the NMR signals onowhich the deductions are based.As predicted fro? fig. 13. Likely errors range from ca. k0.02 A for short hydrogen- bond lengths to ca. k0.04 A for the longer bonds. Signals imperfectly resolved (relative intensities are not clear). Not obtained. different hydrogen bonds in the unit cell, five of which involve POH as the donor group. The CRAMPS experiment reveals only two signals in the region 6, = 10-20 ppm, with an intensity ratio 1 :4. These are 9ssigned as in table 4. It is perhaps surprising that the hydrogen bond of length 2.602A does not give rise to a resolvable signal, but rather appears to be subsumed into the peak at S, = 12.5 ppm. However, that peak is broad, and the hydrogen-bond acceptors in this case are of two different types (half of them involving the anionic part of the zwitterion).The N-H---0 hydrogen-bond resonance is at lower frequency (6, = 9.2 ppm). The remaining CRAMPS peak, at ca. 4.5 ppm, arises from the methylene protons, with insufficient resolution to distinguish the different types. Note that the resonance at 9.2 ppm assigned to the N-H---0 hydrogen bond appears to be of lower intensity compared to the other resonances in the spectrum. The primary reason for this is that there are spinning sidebands associated with this line which are not shown in the figure. A second possible reason is that it is the zwitterionic proton that is involved. Thus it is bonded to 14N, so there may be incomplete removal of direct 'H-14N dipolar coupling by magic-angle ~pinning,~ as mentioned in the preceding section.The signal perhaps contributes to the broad underlying component in the spectrum. The breadth of this3668 Perspectives in High-resolution Solid-state NMR I . 20 10 0 20 10 0 s, @pm) Fig. 12. Proton CRAMP spectra of (a) nitrilotrimethylene triphosphonic acid (VIII) (recycle delay 10 s, number of transients 32) and (6) I-phenylethane- 1,2,2-triphosphonic acid (recycle delay 20 s, number of transients 20). In each case the 8-pulse cycle time for the MREV-8 sequence is 44 ps. resonance may also arise as a result of rapid exchange processes. If such exchange processes have correlation times of the order of the multiple-pulse cycle times, complete averaging of the dipolar interaction will not take place. Methanediphosphonic acid and ethane- 1 -hydroxy- 1,l -diphosphonic acid mono- hydrate(V1) also give rise to two signals in the POH hydrogen-bonding region of the CRAMP spectra.In each case the asymmetric unit has been shown to be a single molecule, but a number of different hydrogen bonds are implied. The CRAMPS observations are roughly in agreement with the X-ray results. For compound (VI) one of the signals contributing to the more intense peak at S, = 11 .O is assumed to be a hydrogen bond, with COH as the donor group and P=O as the acceptor. For the compounds listed in table 4, apart from those mentioned above, a single POH CRAMPS peak is expected from the X-ray results and is observed, with the exception of benzenephosphonic acid, for which two CRAMPS signals are expected but only one is observed (presumably because of resolution limitations).NMR suggests that of the compounds listed in table 4, the one containing the strongest hydrogen bond is (V), ethane- 1,1,2,2-tetraphosphonic acid anhydride pentasodium salt undecahydrate (6, = 17.2 ppm). This is gonfirmed by the X-ray data, which show that it has the shortest 0---0 distance (2.439 A). This hydrogen bond is the3669 -18 -I 2 . 4 2 . 5 2.6 2.7 r o -. - 0 18, Fig. 13. Plot of proton isotropic shielding (relative to the signal due to tetramethylsilane) us. the oxygen-oxygen bond distance, for hydrogen bonds of a series of phosphonic acids. The linked points refer to unresolved NMR signals. The solid curve represents the best fit to the observed data and the dashed lines indicate likely uncertainty limits arising from variations in the hydrogen-bond acceptor group, lack of spectral resolution etc.only one of those listed in table 4 to have a PO:- oxygen as the acceptor. Moreover, it is the only one which is intramolecular, and it is symmetric (the asymmetric unit is half a molecule). NMR results show that none of the hydrogen bonds listed in table 5 is as strong as in this case. Fig. 12 (b) shows the CRAMP spectrum of I -phenylethane- 1,2,2-triphosphonic acid, for which no single-crystal X-ray diffraction pattern has been published to our knowledge. This is an example where the CRAMPS technique gives immediate information on hydrogen bonding: it shows that there are two distinct types of bonding, in a 1 : 1 ratio, one being rather weak (6, = 10.3 ppm) and the other moderately strong (6, = 15.9 ppm).For the remaining compounds of table 5 the CRAMPS data give similar information on the number and relative strength of P-OH hydrogen bonds. Using the known hydrogen-bond distances from X-ray crystal-structure studies, an attempt was made to correlate oxygen-oxygen bond distances with proton shielding. The results are presented in fig. 13. While it is clear from the graph that the general trend of the results of Berglund and Vaughan3' seems to be followed, the experimental curve is shifted to lower shielding of that derived by theoretical calculations") on the (H,O), dimer, and there appears to be slightly different skewing. Moreover, there is still some considerable scatter on fig. 13. This partly arises because several different acceptor groups are involved.These discrepancies can be related to a number of factors (see also above) : (1) Chemical-shift referencing in CRAMPS work is complicated by the scaling of the shift by the pulse sequence, by broad linewidths and by difficulties in phasing. As a result, shifts can only be reported to 0.5 ppm. (2) The use of the oxygen-oxygen bond distance assumes that the hydrogen bond is linear, which may not be the case. The more accurate correlation of proton-to-acceptor oxygen distance (yo H) used by Jeffrey and YeonS4 may not be used here because only two diffraction studies of the compounds reported here give 0---H distances to sufficient accuracy. (3) Some hydrogen bonds are3670 Perspectives in High-resolution Solid-state NMR not of fixed length but rather are quite mobile (e.g.those involving H,O). (4) There is a general lack of X-ray data which, of course, limits the number of points on the curve. ( 5 ) In four cases, as discussed above, we cannot resolve separate resonances when X-ray data show these should exist. Regardless of these problems, it is considered that the 'H CRAMP spectra give a reasonable indication of the number and relative strength of the hydrogen bonding in these materials. Approximate hydrogen-bond distances ro . may be calculated using fig. 13 for the compounds of table 5 , and they are listed here. As more X-ray data become available it will be possible to examine the factors influencing the correlation of fig. 13 in more detail and hence to use CRAMPS data to make more accurate predictions of hydrogen-bond geometries.The fact that the curve of fig. 13 for phosphonic acid hydrogen bonding lies ca. 3 ppm displaced from that for carboxylic acids (see the preceding section) presumably arises from the relative shielding of 'free' RPO(OH), hydroxy protons in comparison to 'free' RCO(0H) hydroxy protons. Experimental All the spectra discussed were obtained using a Bruker CXP 200 spectrometer. This operated in standard configuration for normal MAS or CPMAS experiments using initially an Andrew-Beams rotor assembly and later a double-bearing system. Proton (200.13 MHz) and fluorine (188.28 MHz) CRAMP spectra were also recorded with the CXP spectrometer, at ambient temperature, but with a modified single-channel high- frequency probe and specially designed ' broomstick ' sample rotors.The system has been described in detail elsewhere. '02 An MREV-8 multiple-pulse sequence, lo3 with a pulse duration of 2 p s and an 8-pulse cycle time of 48 p s (36 p s for 19F), was used to suppress ('H, 'H) or (19F, "F) dipolar coupling, with ca. 4.0 kHz MAS sufficing to remove shielding anisotropy. The phase of the preparation pulse was inverted for alternate transients, which were then subtracted from the averaged data. Optimum offsets and recycle delays were determined by observation of single transients. The chemical shift scaling factor introduced by the pulse sequence was determined by calibration with adamantane (for 'H, 6 = 1.74 ppm) or calcium fluoride (for "F, 6 = - 107.7 ppm).Referencing was also carried out via these signals but shifts are reported with respect to tetramethylsilane and CFCl,, respectively. Proton shifts are thought to be accurate to 0.5 ppm, but errors for "F may be up to 5 ppm (because of the substantially larger offsets involved). This is generally greater accuracy, at least for 'H, than with single-crystal or static powder methods. Although we usually report chemical shifts on the high-frequency-positive (6) scale, in the case of the CRAMPS work on hydrogen bonding the plots us. ro .-o are presented using relative shielding (A@) in order to conform with literature theoretical work. All samples of carboxylic acids, and also sodium phosphite, camphene, benzene- phosphonic acid, 2-aminoethanephosphonic acid and 3-aminopropanephosphonic acid were commercially available, and recrystallization was only performed where necessary to obtain specific polymorphic forms. Sodium perfluoro-octanesulphonate was given by ICI plc.Other samples were specifically synthesized. For the CRAMPS studies less than 50 mg of finely ground or powdered sample was needed to fill the rotor, but for CPMAS studies ca. 300 mg is normally used. We thank J. Espidel, IS. Wade and I. McNaught for permission to use some of their results prior to full publication. We are particularly grateful to G. J. Nesbitt for the development of CRAMPS methodology. P.J. thanks the S.E.R.C. for a Research Studentship and L. H. M. is grateful similarly to Durham University. We are indebted to ICI plc for the sample of sodium perfluoro-octanesulphonate.The CXP 200 spectrometer was purchased under S. E. R. C. research grant GR/B81298.R. K. Harris et al. 367 1 Note added in proof: After submission of this article, we came across a paper by S. Kulpe, I. Seidel and K. Szulzewsky (Cryst. Res. Techno/., 1984, 19, 669), which gives X-ray data for N,N-dimethylaminomethanediphosphonic acid. This compound should therefore appear in table 4 of the present paper instead of table 5. The X-ray study show: that there are 3 hydrogen bonds for this system, with ro...o = 2.415, 2.505 and 2.583 A (the shortest bond is apparently symmetrical). The agreement with the predictions of our work is remarkably good. References 1 A. Carrington, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 1089. 2 (a) L. M.Ryan, R. E. Taylor, A. J. Paff and B. C. Gerstein, J. Chem. Phys., 1980, 72, 508; (b) G. Scheler, U. Haubenreisser and H. Rosenberger, J. Magn. Reson., 1981, 44, 134; (c) H. Rosenberger, G. Scheler and Y. N. Moskvich, Phys. Stat. Sol. A , 1982, 72, K49; (d) R. K. Harris, P. Jackson, P. J. Wilkes and P. S . 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ISSN:0300-9599    

DOI:10.1039/F19888403649

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I , 1988, 84(11), 3673-3690 Carbon- 13 Chemical-shift Tensors in Single-crystal Me thoxybenzenes Carl M. Carter,? Julio C. Facelli, D. W. Alderman and David M. Grant* Department of Chemistry, University of Utah, Salt Lake City, Utah 841 12, U.S.A. N. Kent Dalley and Bruce E. Wilson Department of Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. Using a two-dimensional NMR orientational correlation technique, carbon- I3 chemical-shift tensors have been measured in single crystals of 1,6dimethoxybenzene, 1,3,5-trimethoxybenzene and 1,2,3-trimethoxy- benzene. The two-dimensional technique greatly extends the single-crystal method to materials with a much larger number of different carbon-I3 resonance lines. The manner of dealing with chemically identical, but magnetically inequivalent carbons in the unit cell is discussed.The X-ray structure of 1,2,3-trimethoxybenzene is reported for the first time, and a redetermination of the X-ray structure for 1,4-dimethoxybenzene is given. The principal values of all carbon- 13 chemical-shift tensors in the three molecules and the orientation of their principal axes have been obtained. Using multiple regressional analysis the principal values of the tensors have been discussed in terms of additive substituent effects. Ab initio calculations of the shielding tensors in anisole (methoxybenzene) and benzene were used to calculate substituent effects which agree closely with the parameters obtained from the regressional analysis. The chemical shielding of a nuclear spin arises from the interaction of the surrounding electrons with the externally applied magnetic field, and thus there is an intimate relationship between this parameter and the electronic structure of a molecule.Since the electron distribution within a molecule is never spherically symmetric, the electronic interaction with the magnetic field has a distinct directional dependence. This anisotropy or directional information in the shielding is described by the chemical-shielding Only the isotropic chemical shift (i.e. the trace of the shift tensor) may be measured in common liquid NMR experiments or in solid-state NMR when using the magic-angle spinning (MAS) technique. ' 9 Single crystals, however, provide complete information on the chemical-shift tensor as both the principal values, and the orientations of the principal axes of the tensor can be obtained directly from the measurements.The experimental data yield only the symmetric portion of the tensor consisting of six element^,^ and the associated matrix may be diagonalized to give the three principal values and the corresponding directions of the principal axes system (PAS). In traditional single-crystal NMR studies3v4 the shift tensors are obtained by following the displacements of the resonance lines as the crystal is rotated through small angular increments about an axis perpendicular to the magnetic field. This technique depends on identifying and indexing lines as they cross over one another as the crystal is rotated. It also is necessary to match up sets of lines from three mutually perpendicular rotations.Using this traditional method experimenters have been limited to the study of crystals with no more than 15-20 distinct lines arising from magnetically inequivalent carbons in t Present address : General Electric Corporation, NMR Instruments, Fremont, California 94539, U.S.A. 36733674 13C Chemical Shifts in Single-crystal Methoxybenzenes the unit cell.4 As two chemically equivalent carbons can give separate distinct lines if their tensors orient differently in the unit cell, the number of lines multiplies rapidly even in relatively simple substances with more than one molecule per unit cell. Thus it can become impossible using traditional methods to follow lines in spectra of even modestly complex molecules.This work discusses carbon- 13 shift tensors in single crystals of 1,4-dimethoxybenzene (1,4-DMB), 1,3,5-trimethoxybenzene (1,3,5-TMB) and 1,2,3-trimethoxybenzene (1,2,3- TMB). It is in cases such as 1,2,3-TMB with 36 lines (four molecules per unit cell of nine lines each) that the traditional method breaks down due to assignment complexities, thereby preventing the determination of all chemical-shift tensors. Thus for 1,2,3-TMB the two-dimensional chemical-shift correlation technique recently developed in this laboratory5 was necessary to determine the tensor elements. These two-dimensional NMR spectra provide better resolution, as the data are spread over two dimensions, but equally important, they also provide the correlation information for the resonance frequencies at two different crystal orientations separated by a large angular displacement.Line indexing over large angular displacements is required to determine a tensor reliably. The placement of the principal axes of an experimental NMR tensor on the molecular frame is possible only when an X-ray structure is available for the crystal. A high-quality X-ray structure has been published6 for 1,3,5-TMB, and an older X-ray structure without modern refinements was also available for 1 ,4-DMB.7 The very accurate orientational data obtained from this study required a redetermination of the crystal structure for 1,4-DMB and a new X-ray structure for 1,2,3-TMB. The chemical motivation for this paper is three-fold. First, the three-dimensional shift tensor data can be used to discuss the additivity of aromatic substituent effects on principal shielding components instead of the traditional isotropic shifts.Substituent effects, which can be correlated with various physical and chemical properties of aromatic m01ecules,~-’~ provide an experimental basis for discussing variations in 0- and n-electron densities. Second, solid-state NM R studies involving complete tensor values can explain subtle discrepancies between solid MAS and liquid isotropic spectra.’ One of the most commonly observed differences is the presence of additional resonance lines or ‘splittings ’ which arise from unaveraged interactions between two or more conformations frozen out in a solid structure. A number of these conformational variations have been verified by X-ray studies of the crystal structure.In all molecules in this study a steric effect is present owing to methoxy substituents which lie in the plane of the aromatic ring6’7p14 and perturb the adjacent ortho protons. Similar effects have been proposed to explain departures from the additive rules observed in the carbon- 13 isotropic shifts in ortho-substituted methoxybenzene~.~~, l6 Finally, there is a specific interest in the 1,4-DMB molecule because it has been used as a model compound for testing novel solid-state NMR experiments. 17, l8 The chemical-shift tensors of 1,4-DMB have been determined by others,18 but never before using the single-crystal method with its greater accuracy and enhanced orientational information. It has recently become possible to relate the details of chemical-shielding tensors to the electronic structure of molecules via ab initio calculations of the chemical shieldings.The full carbon- 13 shielding tensor has been calculated for many small molecules, but larger molecules generally have exceeded available computational resources. l9 Supercomputers make it possible to apply ab initio theories to molecules of the size studied here, and the theoretical results for anisole (methoxybenzene) are presented here to provide a theoretical analysis of methoxy substituent effects.C. M. Carter et al. 3675 Experimental Sample Preparation The three compounds (1,4-DMB, 1,3,5-TMB and 1,2,3-TMB) were obtained from Aldrich (99 O h ) and used without further purification. Their single crystals were grown by slow solvent evaporation from saturated methanol solutions.NMR Equipment and Techniques All spectra were taken using a Bruker CXP-200 instrument operating at 50.25 MHz for carbon and 200.2 MHz for protons. The details of the two-dimensional chemical-shift anisotropy correlation experiments, along with the modified probehead, have been reported el~ewhere.~ This method uses a modified Jeener pulse sequence with a 90" flip- back pulse and a 90" observing pulse at the beginning and the end of the mixing period, respectively. During the mixing period, which lasts for 35 ms, the crystal is rotated 45" between the two different orientations. A 3 ms contact time was used to initiate the experiment, and a 7 s recycle delay was provided at the end of the FID to allow adequate spin relaxation.Air at ambient temperature was blown across the coil to insure that these relatively low-melting-point substances remained solid while the high-power decoupler was on. The 256 increments on F l and the 512 points collected in F2 were transformed after zero filling to give a 512 x 512 magnitude spectra. All shifts were referenced to TMS using the methine peak at 29.5 ppm in solid adamantane as a standard. Magic-angle spinning (MAS) spectra were obtained for each compound mixed with adamantane to reference the corresponding isotropic shifts. The average of the principal shifts obtained from single-crystal spectra were identified with these isotropic shifts in order to reference the single-crystal data. To maximize the filling factor and to use one crystal for all three rotational axes, the crystals were ground to fill the volume enclosed by three intersecting orthogonal cylinders.A shortened 5 mm NMR tube was used as the sample holder, and the three orthogonal rotations were achieved by inserting the crystal along each of the three cylindrical grinding axes. X-Ray Equipment and Parameters The tendency for both 1,4-DMB and 1,2,3-TMB to sublime at room temperature required intensity data to be collected at ca. - 150 "C. Crystal and intensity data were obtained using a Nicolet R3 automated diffractometer fitted with a Nicolet LT-1 low- temperature device which passes cold N, gas, directly over the crystal. Graphite monochromated Mo Ka radiation (A = 0.71073 A) was used, and data were collected to a sin (8/R) limit of 0.65.Intensity data for both crystals were obtained using a variable- speed 8-28 scan procedure. For each data set three standards were measured every 97 reflections. The standards showed no systematic changes in intensity which indicated crystal and electronic stability. The orientation matrices and lattice parameters for the crystals were obtained using a least-squares procedure involving angular settings of several carefully centred reflections. Results X-Ray Structural Results for 1,4-,DMB and 1,2,3-TMB The experimental X-ray and the crystal data are given in table 1. Both 1,4-DMB and 1,2,3-TMB crystallize in orthorhombic space groups, and the structures were solved using direct methods. The carbon and oxygen atoms in both structures were refined 121 FAR 843676 I3C Chemical Shifts in Single-crystal Methoxybenzenes Table 1.Crystal and experimental X-ray data formula formula weight F(OO0) crystal size/mm spaoce group a/+ b/!$ CIAO VIA3 Z dJg cmb3 p1crn-l sin (O/A) observed data unobserved data F < 3 4 F ) R goodness of fit max. shift /e. s.d . no. of datalparameters max. peak in A m%p/e A-3 min. peak in A/eA-3 Cf3HIOO2 138.3 296 Pbca 0.4 x 0.4 x 0.3 7.173 (2) 6.277 (3) 16.552 (2) 745.6 (4) 4 1.23 0.82 0.65 689 164 0.067 0.77 0.002 0.29 10.4 - 0.28 C9H1203 168.2 360 approximate sphere, d = 0.5 Pna2, 12.974 (9) 5.121 (3) 12.822 (8) 851.8 (6) 4 1.31 0.92 0.65 874 151 0.064 0.94 0.010 7.2 0.27 - 0.26 Table 2. Positional ( x lo4) and thermal ( x lo3 A2) parameters for 1,4-dimethoxybenzene (e.s.d. values are given in parentheses) atom X Y Z Ueqa C1 lOOlS(4) 859 (5) 5774 (2) 0 1 10129 (3) 1574 (3) 6561 (1) MI 9164(6) 3490(6) 6749(2) H11 9404 (46) 3814 (55) 7325 (21) H12 9626 (50) 4760 (58) 6427 (20) H13 7839 (54) 3298 (59) 6683 (19) c2 9052 (4) 1895 (5) 5 161 (2) H2 8551 (39) 3348 (51) 5248 (16) c 3 9052 (4) 1025 (5) 4388 (2) H3 8463 (38) 1760 (46) 3957 (17) a Qq defined as one-third of the trace of the orthogonalized qj tensor.Values for hydrogens are isotropic thermal parameters. anisotropically. At this point in the refinement it was possible to locate all the hydrogen atoms for both compounds in their respective difference maps. The hydrogen atoms of 1,Q-DMB refined to geometrically acceptable positions. However, this was not the case for the hydrogen atoms in 1,2,3-TMB.Positions for these hydrogens were obtained from the difference maps, and these atoms were allowed to ride on the carbon atoms to which they were bonded throughout the refinement process. Only the isotropic parameters of the hydrogen atoms were refined. The positional and isotropic thermal parameters of the resulting structures are listed in tables 2 and 3. Computer drawings of these two molecules are shown in fig. 1 along with the structure reported for 1,3,5-TMB.6C. M. Carter et al. 3677 Table3. Positional ( x lo4) and thermal ( x lo3 A2) parameters for 1,2,3-trimethoxybenzene (e.s.d. values are given in parentheses) atom X Y z q q a Cl 0 1 M1 H11 H12 H13 c 2 0 2 M2 H2 1 H22 H23 c 3 0 3 M3 H3 1 H32 H33 c 4 H4 c 5 H5 C6 H6 4371 (5) 4224 (4) 3450 (5) 2737 3580 3573 5202 (5) 5817 (3) 6513 (5) 7038 6178 6788 54 12 (4) 6253 (3) 6423 (6) 5836 6480 7040 4764 (5) 4989 3946 (5) 3430 3723 (5) 3069 1625 (12) 241 (9) - 1755 (13) - 1008 -2916 - 2541 3314 (13) 3562 (8) 1452 (13) 1213 1746 4874 (12) 6472 (9) 8251 (16) 9784 7439 9394 4759 (14) 579 1 3062 (1 4) 3089 1522 (13) 726 - 61 1974 (0) 2879 (4) 2854 (6) 2777 2193 3441 1994 (5) 2862 (4) 3006 (5) 2553 302 1 3773 1109 (5) 1194 (4) 351 (6) 335 - 288 499 258 (5) - 399 265 (5) - 320 1108 (6) 1146 35 (2) 44 (1) 48 (2) 25 (14) 48 (20) 112 (39) 33 (2) 38 (1) 43 (2) 31 (17) 42 (18) 204 (58) 33 (2) 41 (1) 48 (2) 36 (17) 92 (30) 78 (28) 37 (2) 138 (41) 40 (2) 76 (26) 39 (2) 32 (16) - a Ueq defined as one-third of the trace of the orthogonalized qj tensor.Values for hydrogens are isotropic thermal parameters. Fig. 1. ORTEP molecular structures of 1,4-DMB, 1,3,5-TMB6 and 1,2,3-TMB. The 1,4-DMB molecules were located about a centre of inversion so that the asymmetric unit of the compound consisted of one-half of the molecule. The interior angles of the benzene ring in all three molecules do not deviate significantly from the expected value of 120", but the exterior angles about the ips0 carbon atoms bonded to oxygen deviate considerably from the idealized values of 120", as may be seen in table 4. The deviations from 120" are due to the interaction between two of the methyl hydrogens and the proximate ortho hydrogen (see fig. 1). The effect of this steric interaction is also observed in the larger COC angles.Almost identical angular features 121-2CL 6 Table 4. Important substituent angles" in methoxybenzene compounds compared with optimized theoretical resultsb _. ___ trigonal angles torsional anglesc 3 121.1 (4) 123.6 (4) 5 122.5 (4) 123.4 (4) 1,2,3-TMB 1 120.6 (5) 124.7 (6) 2 119.2 (5) 121.7 (5) 3 119.6 (6) 125.1 (6) [119.8] [125.4] [ 12 1.21 [ 125.81 115.3 (4) 114.91 114.1 (4) 113.11 114.6 (4) 119.1 (5) 115.3 (6) compound position A B C D E designation K - 5 1,4-DMB 1 120.0 (2) 124.5 (2) 115.5 (2) 116.9 (2) 1.0 (4) C2ClOlMl k2 [118.8] [ 125.91 [ 1 15.31 [114.2] [120.6] [125.3] [114.1] [115.5] 114.41 117.6 (4) -6.2 (7) C6C505M5 116.5 (5) 10.9 (9) C6ClOlMl 113.8 (5) 75.9 (7) ClC202M2 116.3 (5) 3.8 (9) C4C303M3 h 3 09, ? E s 1,3,5-TM B 1 122.1 (4) 123.2 (4) 114.7 (4) 117.5 (3) - 3.4 (7) C6C 101 M 1 118.5 (4) 0.0 (7) C4C303M3 3 1 15.41 9 $ 0 a k anisoled 1 [119.4] [126.3] [114.3] [115.2] _ _ ~ - ______ 6- a E.s.d.values in parentheses. Angles designated by scheme 1. a 3G level. Values from $ ref. (14). 3: 2 Theoretical calculations given in brackets were obtained using GAUSSIAN 82 at STO- Torsional angles from X-ray have no theoretical equivalent as crystal forces can be expected to dominate these angles.C. M. Carter et al. 3679 Scheme 1. are found for C1 in I,4-DMB, for C1 and C3 in 1,2,3-TMB and for CI, C3 and C5 in 1,3,5-TMB. The only exception is for the B and C angles about C2 in 1,2,3-TMB, which are near 120". This difference may be expected, as the M2 methyl group is rotated out of the plane of the benzene ring with a ClC202M2 torsional angle of '75.9". This unusual conformation for the M2 methoxy groupl4, 2o makes a significant change in the shielding tensor of the carbon at M2.The unit cells for each of the three methoxybenzenes contain four molecules, but inversion symmetry between pairs of molecules in the Pbca space group for I,4-DMB and translational symmetry present for molecular pairs in the Cc space group of 1,3,5- T'MB decrease by a factor of two the number of expected NMR lines to 16 and 18, respectively, in these two molecules. In the Pna2, space group for 1,2,3-TMB, neither inversion nor translational symmetry is present to reduce the number of observable resonances, and all 36 lines from the four molecules in the unit cell are observed. Optimized Theoretical Structures Complete optimization of the structures of 1,4-DMB and 1,3,5-TMB were performed at the STO-3G level using the GAUSSIAN 82 program.21 In general there is good agreement (see table 4) between the optimized structures and the X-ray structures, and it would seem appropriate to use the STO-3G optimization routine whenever an X-ray structure is unavailable. It is important to note in table 4 the many similarities between the structure of these compounds with the STO-3G optimized geometry of anisole,l* for which the experimental X-ray structure is unavailable.Single-crystal NMR Results Two typical, one-dimensional single-crystal spectra of I ,2,3-TMB are given in fig. 2. Most of the 36 transitions may be observed, but even so, the number of lines is invariably < 36 owing to serious overlapping of peaks.To deal with the ambiguities in following such lines, the two-dimensional technique5 provides correlated spectral information for two crystal orientations separated by 45". A representative two-dimensional spectrum of 1,2,3-TMB is shown in fig. 3 along with the corresponding one-dimensional spectral projections on each axis. While many peaks in each of the one-dimensional projections are not resolved completely, the two-dimensional spectrum clearly defines all 36 frequencies, and correlates these lines between the two crystal orientation^.^ Thus it may be observed that two-dimensional experiments on single crystals can extend significantly chemical-shift measurements to materials containing a larger number of inequivalent nuclei than possible using one-dimensional methods. To appreciate the importance of these two-dimensional data consider the least-squares fit of a representative rotation3680 W 8 # @ : @ * 0 0 0 0 W e m 0 0 0 OQ e' m e A I3C Chemicul Shifts in Single-crystal Methoxybenzenes I 20 kHz Fig.2. Two single-crystal spectra of 1,2,3-TMB at different orientations. The four molecules per unit cell yield nine lines each for a total of 36 lines. Many but not all of these lines are observable in these one-dimensional spectra.C . M. Carter et al. 368 1 250 ppm from TMS -25 Fig. 4. Least-squares fit of two-dimensional data from a single rotation of 1,2,3-TMB showing the correlation of 36 lines over 180" of rotation. pattern given in fig.4. Without the correlative power of the two-dimensional approach it would not be possible to unscramble the large number of crossing lines. The principal shift values are labelled and ordered so that the lowest-field (high- frequency) component is oI1 and the highest-field (low-frequency) component is 033. The average of the three principal values (i the trace) equals the shift from solid-state MAS techniques. The tensor principal values for the three methoxybenzenes are reported in table 5 and the orientations of the principal axes in the molecular frame are given in The orientation of the principal axes of a tensor relative to the sample frame is obtained directly from the NMR single-crystal measurements. To convert these nieasurables into tensors either in the crystallographic axes (CA) or in the molecular frame, one need only to compare the NMR and X-ray data using the symmetry existing between molecules within the unit cell. X-Ray structural data on single crystals provide the orientations of the molecular frames relative to the CA.The 033 components of ring carbons have been found consistently to be oriented perpendicular to the plane of the aromatic ' ' 1 22 Thus the X-ray orientations of the normals to the benzene rings may be identified with the principal axes of the upfield components, 033, and used to orient some of the tensor axes in the molecular frame. The 1,4-DMB data illustrate nicely the use of the 033 axes as a way to identify the molecular frames relative to the laboratory axes. In this case the normals to the molecular planes defined by the orientations of the 033 axes cluster in four sets of essentially parallel directions, with standard deviations from each average direction of fig.5.3682 I3C Chemical Shifts in Single-crystal Methoxybenzenes Table 5. Principal valuesa of the chemical-shift tensors assignment 11 22 33 average M1 c 1 c 2 c 3 MI M3 M5 c 2 c 4 C6 C1 c 3 c 5 M1 M2 M3 c 1 c 2 c 3 c 4 c 5 C6 1,4-dimethoxybenzenes 80 72 13 232 159 70 200 131 22 193 137 6 1,3,5- trimeth~xybenzene~ 80 69 11 80 70 11 80 69 9 155 108 29 152 105 17 151 107 1 240 168 73 238 169 73 240 169 74 1,2,3- trimethoxybenzene 83 71 9 88 83 10 82 70 13 218 172 73 179 164 71 217 172 72 187 123 7 227 136 10 186 121 8 55 154 118 112 53 54 53 97 91 86 161 160 161 54 60 55 154 138 153 106 124 105 a All values are in ppm referenced to TMS.Each reported value is averaged from all the molecules in the unit cell. These values are taken from ref. (5) for 1,3,5-TMS with a typographical error in the positional designation corrected by exchang- ing the C2 and C6 labels in the original data. only 0.89, 0.47, 0.47 and 0.71", respectively. These angular deviations of < 1" reflect the experimental accuracies associated with measuring the line positions. Furthermore, these four directions from the NMR data subtend angles between one of the four axes and the other three axes of 22.1, 28.9 and 63.7". In the low-temperature X-ray structure given above, the corresponding normals are separated by 23.1, 29.5 and 64.3", respectively, indicating a consistency of 1' or less between the NMR and X-ray data.Four different vectors, mapping the NMR data on the X-ray data, are sufficient to identify the directions of the principal shift axes in the molecular frame. The orientations for the principal axes reported in fig. 5 for 1,4-DMB are the averages obtained for the PAS of each tensor in all four molecules in the unit cell. and the methods used to assign orientations of the PAS are similar to the methods described above for 1,4-DMB and in part for 1,2,3-TMB below. The crystal of 1,3,5-TMB, however, differs from the other two crystals in this study in that only two unique c~~~ axes exist because of the translational symmetry element, and the orientation of either the remaining CT,, The shift values for 1,3,5-TMB were taken from previousC.M. Carter et al. 3683 Fig. 5. Tensor orientations of (a) 1,4-DMB, (b) lY3,5-TMB and (c) 1,2,3-TMB. In all cases oS3 is perpendicular to the plane of the benzene ring. (---) Orientation of oI1 and (. . .) orientation of fs22. or 022 axis is required to establish the relationship between the CA and the NMR sample frame. By recognizing that corresponding ol1 or 022 axes for equivalent carbons in symmetry-related molecular pairs must have the same relationship to their respective molecular frames, the geometrical transformation between the NMR sample frame and either the CA or the molecular frame may be obtained. This makes it possible to place the tensor orientations on the molecular frame. One is aided in this effort by a recognition that the oI1 axes for the ring carbons lie, within a few degrees, of either the C-H or C-0 bond By utilizing these guidelines along with the crystal symmetry, the assignments of tensor axes in 1,3,5-TMB follows in a straight forward manner and the results are given in table 5 and fig. 5.For 1,2,3-TMB the orientation of the CT,, components of the aromatic carbons again fell into four groups of six lines, which are sufficient to define the four unique normals to the molecular planes. Thus an analysis similar to that above for 1,4-DMB was used to match the X-ray and NMR data to give the CA relative to the NMR sample frame. It is then possible to obtain the orientations of a composite shift tensor in the molecular frame (see fig. 5). The very low dispersion among the 03, orientations and good agreement with the X-ray orientations of the normal for a given ring provide strong supporting evidence that o,, axes are perpendicular to aromatic rings.A complication was encountered in the data reduction for 1,2,3-TMB because one of the sample rotation axes was nearly parallel to one of the two-fold crystallographic screw axes. Had the rotation axis been exactly along this symmetry axis, the 36 lines would have collapsed into 18 lines, but the rotation pattern realized for an axis very near to this symmetry axis consisted of 18 pairs of closely positioned signals which move essentially together under rotation. Such pairs correspond to chemically equivalent nuclei from two molecules related by the two-fold screw axis in the unit cell.The paired lines can become indistinguishable through parts of the rotation, and unfortunately some of the line assignments are obscured when these ambiguities occur in the region where the degenerate or nearly degenerate lines connect with the other two rotational patterns. This resulted in an inability to follow the identity of all resonances of chemically equivalent carbons through all three rotational patterns. The number of ambiguous permutations in line assignments would be large without recognizing that allowed connection of lines between the three rotations must comply with the following criteria: First, a line cannot change its designated identity merely upon rotation of the crystal, and therefore, after following a specific line through the three rotations, it must re-connect with itself at the starting point.Secondly, allowed solutions must preserve the symmetry of the crystal structure (i.e. only four sets of nine3684 13C Chemical Shifts in Single-crystal Methoxybenzenes tensors related by the crystal point symmetry of the unit cell are possible). After eliminating many assignment permutations failing to comply with these two criteria, four sets of line assignments still remained. The carbon tensors in each of these four assignment sets were determined by a least-squares fit of the data, giving a sum of squares for the deviations of 767,772,774 and 774 ppm2, respectively, making these four ' allowed ' sets of line assignments statistically indistinguishable. Fortunately, in every instance the four sets represented a permutation of tensor between chemically equivalent carbons. This ambiguity has only the effect of exchanging the special designation of the principal axes of the tensors between two equivalent carbons in symmetry-related molecules.Minor variations in the tensor principal values calculated for these four ' allowed ' permutations fall within the present experimental errors in our measurements. Also, this near degeneracy does not affect, within experimental error, the orientations of the principal axes in the molecular frames. The values reported in table 5 , along with the orientations in fig. 5 , are taken from the fit with the smallest variance. Substituent-effect Analysis and Discussion Considerable effort has gone into explaining and predicting effects of substituents on various physical and chemical properties of organic m01ecules.~-~~ Electronic effects of multiple substituents in aromatic rings are often additive, with minor deviations attributed to saturation arising from two or more substituent perturbation^.'^ Beginning with the early work of Hammett on aromatic-substituent parameters," various techniques have been employed to provide a more detailed and quantitative understanding of how substituents interact with an aromatic ring.NMR data are particularly well suited to these studies, as the placement of a substituent in a benzene ring changes the NMR chemical shifts at various positions on the These changes are of interest, as they provide information on the variations in Q- and n- electron densities.11-13 Previous NMR studies have dealt mostly with the averaged or isotropic chemical shift determined from liquid 11-13 but the tensorial approach to variations in the shielding has the potential to provide a much better understanding of three-dimensional changes in the electronic The molecules considered in this study are particularly attractive because the methoxy group acts both as a a-electron acceptor and a n-electron donor.8* lo, l3 Thus both induction and resonance perturbations of the aromatic ring are present in these methoxybenzenes and are reflected quite differently in the individual components of the carbon- 13 shielding tensors. Using multiple regression techniques the additivity of substituent effects on the tensor components were explored.The principal shielding values were analysed in terms of five parameters, four electronic effects (ipso, ortho, meta and para) and a 'steric' or conformational effect arising from the interaction of the methyl group with the proximate ortho hydrogen. As the principal values of the shift tensor of solid benzene vary in the literat~re,~ these parameters were allowed to vary independently in the analysis. The experimental values exhibited additivity in all three of the chemical-shift tensor components for all ring positions, except that two of the meta parametric values were too small to be statistically significant. The results of the multiple regression along with standard errors of the fit are given in table 6, where they are also compared with theoretical calculations based on anisole. The success of the fit is provided in the plot of experimental versus predicted principal shifts given in fig.6. The correlation coefficient of the fit is 0.9986. The substituent effects reported for Q,, and a22 at the ortho, meta and para positions in table 6 are consistent with the Hammett parameters for the methoxy substituent.8*10 When ranked in order of magnitude, the substituent values are ortho =para > meta. The ortho effect on both oI1 and c~~~ is only slightly larger than the corresponding paraC. M . Carter et al. 250 - 200 - h I& 150- .9 5 3685 $x' Table 6. Multiple regressional substituent parameters for the principal chemical shift in methoxybenzenes". * _____________ ~~ structural parameters 6 1 1 0 2 2 033 ips0 11.3f2.4 (13313) ortho -31.6f 1.7 ( - 30, - 27) meta -0.2f 1.6 (1, -1) (-18, -15) para -9.6 f 2.6 steric -4.5 k2.1 (ortho-methyl) (- 12, - 13) 30.0 f 3.3 (23724) -7.7f 1.9 (- 13, -9) 0.0 f 2.0 (-2,O) - 14.3 f 3.2 (-11, -8) -1.9k2.9 (-6, -6) 58.3 f 3.6 8.1 _+ 2.6 (55752) (13914) (4, -2) (- 170) (-11, -11) - 4.4 _+ 2.4 -4.2 f 3.7 - 11.4 f 3.2 a All values in ppm.Theoretical predictions of these substituent parameters appear in parentheses below fitting parameters (IGLO, LORG, respectively). The theoretical parameters have been calculated from work on anisole and benzene. effect, but both are much larger than the small meta effect. These results are in keeping with the resonance model associated with an orthu-para director such as the methoxy group. While the all and a22 components at the para position are strongly influenced from variations in the n-electron resonance structures, it is not surprising that the para substituent effect for a33, which depends primarily on the a-electrons, is negligible.The ortho-substituent effects on all and a22 are influenced strongly by n-electron resonance3686 13C Chemical Shifts in Single-crystal Methoxybenzenes effects, whereas a,, will be affected also by a a-inductive effect due to the close proximity of the substituent. Electron withdrawal at the @so carbon by the directly bonded, electronegative oxygen atom is along the C-0 a-bond, which is nearly parallel to the all axis. Therefore, such changes can only affect the all component indirectly, giving the smallest ips0 substituent effect of 11.3 (see table 6).The effect on the ips0 and a,, components are much larger (30.0 and 58.3 ppm, respectively) as they have symmetry features (axes perpendicular to the C-0 bond) which will reflect the a-charge polarization arising from the oxygen atom. These trends are quite consistent with generally held concepts of how shifts will depend on inductive effects (i.e. electron withdrawal leads to downfield shifts). Note that theoretical results indicate that the shielding about a given axis is dominated by the electrons in the plane containing the atom and perpendicular to the shielding a ~ i s . l ’ * ~ ~ Apparently, the oxygen inductive effect is relayed through the a-bond structure into the ips-ortho bond in such a way that the a,,(ipso) parameter is larger than the a,,(ipso) value.This inductive perturbation of the a-electron structure is further supported by a downfield a,, parametric shift (8.1 ppm) at the ortho position. Small upfield a,, shifts at the meta and para positions indicate that the a-electronic effects are likely minimal beyond the ortho positions. The change in the tensor due to the steric interactions of the proximate methoxy group with the perturbed ortho carbon occurs mainly in the a3, component shifting it upfield (- 11.4 ppm). The steric forces, which lie in the molecular plane, can be expected to affect the a-electrons consistent with similar cases in which ‘steric compression’ has been Thus the origin of isotropic steric shifts (only 5-6 ppm) at the ortho p ~ s i t i o n ~ ~ , ’ ~ is concentrated mainly in one tensor component, which is actually several times larger than changes observed in the isotropic values. The 1,3,5-TMB molecule provides an interesting case for studying this steric effect because the three separate protonated carbons exhibit three very different sterically perturbed environ- ments.Although each protonated carbon has the same number of ortho and para methoxy groups, C2 has no methoxy proton steric effect, C4 has a single steric interaction while C6 has two sterically perturbing methoxy groups (consider fig. 1). Hence the effect is seen to change dramatically in the a,, component for C2, C4 and C6 (see table 5). These steric effects in 1,3,5-TMB are slightly larger than the average - 11.4 ppm per interaction found in the multivariate analysis for a,, (see table 6).Deviations in the methoxy torsional angles given in table 4 especially at C1 and C3 in 1,2,3-TMB may account for the reasonably large dispersion found in the a,, steric parameter. The corresponding all and a2, steric contributions conversely vary by only a few ppm (-4.5 and - 1.9 ppm, respectively). The small meta-substituent parameters, compared to the other parameters, are consistent with the a-acceptor, It-donor behaviour of a methoxy group (see table 6). Ab Znitio Calculations In order to obtain a better theoretical understanding of the structural features that govern the shielding interactions in methoxybenzenes, IGL02S-28t and LORG2’T calculations of the carbon- 13 shielding tensors in anisole and benzene were performed.Calculations for the di- and tri-substituted compounds in this series were not feasible with available computer resources. Owing to the high linearity observed in the experimental data it was felt that it would be sufficient to calculate the carbon-13 shielding tensors in anisole, from which all of the substituent parameters could be theoretically predicted. IGLO calculations were performed as described previo~sly~~v 25 using a double-c basis set. The calculated values are referred to methane (absolute shielding 21 9 ppm), as explained before. LORG calculations were done using the 4-3 1 G t IGLO, individual gauge for localized orbitals ; LORG, localized orbital/localized origin.C. M. Carter et al. 3687 Table 7. Calculated principal shielding valuesa in anisole and benzene compound position slob olI oZ2 033c oiso ~~ ~ benzene C 0 253 157 -10 130 anisole C, 5.8 266 180 45 164 C, 0.4 211 138 -8 114 C, 1.5 253 155 -6 134 C, 0.9 235 146 -11 123 C, 0.7 255 155 -7 134 C, 1.3 223 144 3 123 ( non-planar)d CH, - 83 81 3 56 (planar) CH, - 73 66 7 49 a All values in ppm referenced to methane.Numbering according to scheme 2. Angle between o,, and either the C-H or C-0 bond for ring carbons. The o,, axis lies perpendicular to the benzene plane for ring carbons and along the C-0 bond for methyl carbons. Shielding principal values calculated for a conformation in which the methoxy group is out of the plane of the benzene ring. 6 2 5 3 Scheme 2. basis set and also referenced to methane (absolute shielding 221 ppm).The STO-3G completely optimized geometry of anisole was used in these calculations. l4 The calculated principal values of the carbon-13 shielding tensor for anisole and benzene are entered in table 7 and the corresponding theoretical substituent parameters in table 6. It is important to note that qualitative agreement with the experimental results requires the use of a STO-3G fully optimized geometry for anisole. Results, obtained with a geometry3’ which assumes all C-C bonds in the benzene ring to be equal, fail to follow many of the experimental trends of the measured carbon-13 shielding tensors. Calculations performed using the LORG2’ method are very similar to those obtained with the IGLO method. In table 6 the IGLO and LORG calculated substituent effects are compared with those obtained for the regression analysis in the polysubstituted compounds.Both theoretical substituent parameter sets agree well with the values obtained from the regression analysis. The most notable exceptions are the para effect in oll and the ortho steric effect in both oll and Q ~ ~ . The presence of the substituents on the benzene ring introduce only minor perturbations in the orientation of the shielding axes from those in the benzene reference. The calculated angles between oll and the C-H or C-0 bond are given in table 7. Q,, is in all cases perpendicular to the benzene ring, in agreement with the experimental evidence.3688 13C Chemical Shifts in Single-crystal Methoxybenzenes Table 8. Paramagnetic bond contributions to the methyl shielding tensor for two conforma- tions of anisole and dimethyl ether" planar anisole C-H, 0.1 - 19 C-H2, 3 5 - 27 c-0 0.0 - 17 out-of-plane anisole C-H, 0.1 - 18 C-H2,3 0.2 - 16 c-0 0.1 - 19 dime thy le t her C-H, 0.I - 19 '-'2,3 0.2 - 17 c-0 0.0 - 24 - 45 - 38 - 24 - 52 - 47 - 26 - 47 -41 - 30 a i, j and k^ are the directions, respectively, along the designated bond, perpendicular to the desig- nated bond in the 0-C-H plane, and perpen- dicular to both the designated bond and the 0-C-H plane. H, is the proton in the C-0-C plane and Hz,3 are those out of that plane. All values in ppm. A negative sign in paramagnetic bond contributions indicates a downfield ~ h i f t . ~ ~ - ~ l In all cases the calculated deviations of oll from the direction of the C-H vector are small, ranging from 0.4 to lSO, in modest agreement with the experimental values, ranging from 1 to 4" (see fig.5). No consistent trend is observed in a for either the experimental or calculated values for the C-H carbon tensors. The angular displacements between the C-0 bond and the direction of ol1 for the @so carbons on the other hand range from 9 to 4" and is consistent with the calculated value of 5.8" for anisole. In all cases oI1 lies approximately in the direction bisecting the C-C-C angle of the benzene ring, giving evidence that the orientation of o,, (and consequently 022) is determined primarily by the z-electron structure of the benzene ring. The deviation of the C-0 bond from the bisector of the C-C-C ring angle apparently has only a minor effect on the orientation of the shielding tensor.In the case of C2 in 1,2,3-TMB, the axis for o,, lies along the C-0 bond, which is in the direction bisecting the Cl-C2-C3 angle. Again, this is a consequence of the M2 methyl group rotating out the plane of the benzene ring. The experimental values of the methyl shift tensors in this series of compounds agree within experimental error for all of the methyl tensors but one, the carbon tensor at M2. When the methoxy group lies in the aromatic plane, values of oll = (73) 81 1.3 ppm, 022 = (66) 70 & 1.5 ppm and 03, = (7) 1 1 & 1.9 ppm. The theoretical values given in parentheses are in reasonable agreement with the experimental results. When the methoxy group lies out of the aromatic plane in 1,2,3-TMB, the methoxy values are oll = (83) 88 ppm, 022 = (81) 83 ppm and o,, = (3) 10 ppm.Again theoretical values in parentheses agree reasonably well. The experimental values for o,, are very similar to the o,, components in other methyl groups, which have been found to be almost independent of the substituent for a large number of The theoretical and experimental differences between the out-of-plane less in-plane values are: ACT,, = (10) 7.0 ppm, Ao22 = (15) 13 ppm and A o , ~ = (-4) - 1 ppm.C. M. Carter et al. 3689 This ability to predict subtle conformational features validates the following analysis of the IGLO bond contribution^^^,^^ to the methyl shielding tensor. Table 8 contains an IGLO bond a n a l y ~ i s ~ ~ . ~ ~ of the contributions of the C-H and C-0 bonds to the methyl shielding tensor for both the planar and out-of-plane methoxy conformations, and these are compared with the results for dimeth~lether.~~ Several important conclusions can be made from the results in table 8.The relatively large value, a,"," = 5 ppm, for the C-H,,, bond indicates compression of these bonds due to steric inter- actions with the ortho proton. Note also that a:." is -27 ppm for C-H,,,, while it is -- 19 ppm for C-HI. The value for C-H,, which is free from steric interactions, is in good agreement with the value of -19 ppm in dimethyl ether. Finally, the a:: components in the planar anisole conformation compare well with those calculated for dimethyl ether and other methoxy groups.25 Calculations on an anisole molecule with the CH3 group out of the plane of the benzene ring show that the a:" and a:." components are very similar to those obtained in dimethyl ether, indicating a lack of steric interactions with an ortho proton.On the other hand, significant downfield shifts are observed in the 02; component. When the methoxy group is forced out of plane the C-0 bond is destabilized by the absence of the conjugative interactions between the oxygen lone pairs and the n-electronic struct~re,'~. 2o therefore the antibonding C-0 orbital will have a lower energy in the particular conformation than in the planar one. This antibonding orbital has the proper symmetry to be mixed with the occupied C-H orbitals through the angular momentum operator, producing a downfield shift in azp in the same way as discussed for a more electronegative sub~tituent.~~ However, relatively minor differences in the CO bond contributions were noted between the two anisole conformations, indicating negligible perturbation of the ground-state C-0 orbital by the conformational change.This work was supported by the U.S. Department of Energy (DE-FG02-86ER13510) and the San Diego Supercomputer Center funded by the NSF. The Nicolet R3 automated X-ray diffractometer at the BYU was acquired with partial support from the U.S. National Science Foundation (CHE-83-0668 1). The authors thank Drs W. Kutzelnigg and M. Schindler for a copy of the IGLO program and to Dr T. Bouman for a copy of the LORG program. References 1 M. Mehring, High Resolution NMR in Solids (Springer Verlag, Berlin, 2nd edn, 1983).2 C. A. Fyfe, Solid State NMR for Chemists (C.F.C. Press, Guelph, 1983). 3 U. Haeberlen, High Resolution NMR in Soliak, Supplement I , Adounces in Magnetic Resonance 4 W. S. Veeman, Prog. NMR Spectrosc., 1984, 16, 193. 5 C. M. Carter, D. W. Alderman and D. M. Grant, J. Magn. Reson., 1985,65, 183; C. M. Carter, D. W. 6 B. R. Stults, Cryst. Struct. Commun., 1979, 8, 401. 7 T. H. Goodwin, M. Przybylska and J. M. Robertson, Acta Crystallogr., 1950, 3, 279. 8 R. D. Topsom, Prog. Phys. Org. Chem., 1976, 12, 1 . 9 C. K. Ingold, Structure and Mechanism in Organic Chemistry (Cornell University Press, Ithaca, NY, (Academic Press, New York, 1976). Alderman and D. M. Grant, J . Magn. Reson., 1987, 73, 114. 2nd edn, 1969). 10 L. P. Hammett, Physical Organic Chemistry (McGraw-Hill, New York, 2nd edn, 1970). 1 1 G. C. Levy, R. L. Litcher and G. L. Nelson, Carbon-I3 NMR Spectroscopy (Wiley, New York, 2nd 12 H. Spieseche and W. G. Schneider, Tetrahedron Lett., 1961, 468; S . Fliszar, G. Cardinal and M. T. 13 A. Pross and L. Radom, Prog. Phys. Org. Chem., 1977, 13, 1 . 14 H. Konschin, J. Mol. Struct., 1983, 105, 213. 15 S. R. Salman and F. S. Kamounah, Magn. Reson. Chem., 1987, 25, 966. 16 R. R. Biekofsky, A. B. Pomilio, R. H. Contreras, D. G. de Kowalewski and J. C. Facelli, submitted edn, 1980). Beroldin, J. Am. Chem. Soc., 1982, 104, 5298. for publication.3690 I3C Chemical Shifts in Single-crystal Methoxybenzenes 17 A. Bax, N. M. Szeverenyi and G. E. Maciel, J. Magn. Reson., 1983,52, 147; N. M. Szeverenyi, A. Bax 18 M. M. Maricq and J. S. Waugh, J. Chem. Phys., 1979, 70, 3300. 19 J. C. Facelli, D. M. Grant and J. Michl, Acc. Chem. Res., 1987, 20, 152 and references therein. 20 M. A. Natiello, R. H. Contreras, J. C. Facelli and D. G. De Kowalewski, J. Phys. Chem., 1983, 87, 21 J. S. Binkley, M. J. Frisch, D. J. De Frees, K. Ragharachari, R. A. Whiteside, H. B. Schelgel, E. M. 22 C. M. Carter, D. W. Alderman, J. C. Facelli and D. M. Grant, J. Am. Chem. Soc., 1987, 109, 2639. 23 B. M. Fung and C. F. Kong, J . Am. Chem. Soc., 1984, 106, 6193. 24 J. C. Facelli, A. M. Orendt, A. J. Beeler, M. S. Solum, D. M. Grant, J. Michl, G. Depke, K. D. 25 M. S. Solum, J. C. Facelli, J. Michl and D. M. Grant, J. Am. Chem. Soc., 1986, 108, 6464. 26 W. Kutzelnigg, Zsr. J. Chem., 1980, 19, 193. 27 M. Schindler and W. Kutzelnigg, J. Am. Chem. SOC., 1983, 105, 1360. 28 M. Schindler and W. Kutzelnigg, J. Am. Chem. Phys., 1982, 76, 1919. 29 A. E. Hansen and T. D. Bouman, J. Chem. Phys., 1985, 82, 5035. 30 H. M. Seip and R. Seip, Acta Chem. Scand., 1973, 27, 4024. 31 J. C. Facelli, D. M. Grant and J. Michl, Znt. J. Quantum Chem., 1987, 31, 45. and G. E. Maciel, J. Magn. Reson., 1985, 61, 440. 2603. Fluder and J. A. Pople, GAUSSZAN 82 Program (The Carnegie-Mellon University, 1982). Malsch and P. Murthy, J. Am. Chem. Soc., 1985, 107, 6749. Paper 8/00955D; Received 9th March, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403673

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chern. Soc., Faraday Trans. I, 1988,84(11), 3691-3711 Enhancement of the Effect of Small Anisotropies in Magic-angle Spinning Nuclear Magnetic Resonance Daniel P. Raleigh,? Andrew C. Kolbert,? Terrence G. Oas,$ Malcolm H. Levitt and Robert G. Griffin* Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39, U. S. A . A variety of novel methods in magic-angle spinning NMR is described. The effects have in common the enhancement of the influence of small anisotropies on the NMR spectrum by deliberate intervention, i.e. either by applying pulses, carefully chosen continuous r.f. fields, or by adjustment of the spinning speed. It is shown that rotational sidebands in two-dimensional spin-echo NMR are often much larger than in one-dimensional NMR, owing to the interference of the n-pulse with the rotational echo formation.It is also demonstrated that in systems containing heteronuclear spin pairs the application of a weak continuous r.f. field of carefully chosen intensity can reintroduce small heteronuclear couplings into the spectrum. This is known as rotational resonance recoupling and is due to the interference of coherent spin rotations with the normal averaging effect of the sample rotation. Related effects can occur in homonuclear spin systems when an integer multiple of the spinning speed matches the difference between isotropic chemical shifts. In this case no extra r.f. field is necessary to amplify the effect of the non-secular parts of the dipolar interaction.Greatly enhanced polarization exchange as well as strong spectral effects are demonstrated. The application of these novel methods to the measurement of small interaction tensors and thereby to the extraction of important structural information is discussed. 1. Introduction Solid-state magic-angle spinning (MAS) NMRl allows specific information to be derived from studies of polycrystalline materials, especially when isotopic labels can be introduced into the systems of interest. The NMR spectrum is influenced by a range of tensorial interactions, such as chemical shielding, through-space and indirect di- polar-dipolar nuclear interactions, all of which, in principle, contain useful information as to the local electronic and nuclear configurations in the neighbourhood of selected molecular sites.It is the separation of these pieces of information which has offered the greatest challenges in solid-state NMR. For dilute spin systems, MAS greatly improves the sensitivity and resolution of the spectrum by converting the broad static powder lineshapes into sideband patterns centred at the isotropic chemical shifts of the various species.1-8 Often this increase in resolution is achieved without significant loss of information, since the magnitudes of the anisotropies which contribute to the broad static lineshape may still be extracted by analysis of the sideband intensitie~.~. However, this is no longer true if the anisotropies t Also at : Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts $ Present address : Whitehead Institute of Biomedical Research, Massachusetts Institute of Technology, 021 39, U.S.A.Cambridge, Massachusetts 021 39, U.S.A. 369 13692 Enhancemetit of Small Anisotropies in MASNMR are small or if a number of different anisotropies coexist. Small anisotropies give rise to sidebands of negligible intensity, especially for powdered samples where averaging over orientations is involved. Enhancement of the sideband intensities by reducing the spinning speed cannot in general be achieved without introducing unacceptable overlap between signals from different sites. A different problem is encountered if a site is influenced by a number of anisotropic mechanisms, such as shielding anisotropy as well as heteronuclear dipolar coupling.It is extremely difficult to characterize multiple interactions by the limited amount of information offered by a few sideband amplitudes. A variety of methods have been proposed for obtaining anisotropic information more efficiently from magic-angle spinning spectra. Two-dimensional correlation of shifts and dipole couplings10-12 separates the anisotropic information into orthogonal frequency domains, greatly assisting the analysis, although this method still fails if the dipole couplings are small. In a completely different approach, trains of n-pulses have been applied synchronously with the sample rotation to measure small chemical-shift ten~0rs.l~ This method is made difficult by problems of pulse imperfections. Mechanical jumping of the sample14 and hopping of the rotation axis15 can be successful in allowing the direct measurement of anisotropies providing spin-lattice relaxation times are long and a loss in sensitivity is acceptable.In this article we examine a number of different approaches to enhancing the effects of these small anisotropies on MASNMR spectra. First we discuss two-dimensional spin-echo experiments involving a small number of n-pulses. It is shown that the sideband patterns in the o, dimension are closely related to the patterns which would be observed in a simple one-dimensional spectrum conducted at a much lower spinning speed. This effective reduction of the spinning speed can be achieved without loss of resolution, since it is active only in the o, dimension. Secondly, we examine some methods which involve interfering with the normal averaging effect of the magic-angle rotation by establishing a rotational resonance condition.In heteronuclear spin-pair systems it is shown that the magic-angle averaging of the heteronuclear dipolar interaction can be impeded by irradiating one spin species with an r.f. field of intensity such that olI = no,, in which w,, is the nutation frequency, w, is the spinning speed and n is a small integer. Dramatic perturbations of the S-spin lineshape are obtained which allow a separation of chemical shielding and dipolar interactions. The effect has been termed rotary resonance recoupling and a preliminary account has appeared elsewhere. l6 In the case of dilute homonuclear spin pairs the averaging of the dipolar interaction may be impeded without applying an extra r.f.field, if the rotational resonance condition oy = nu, is established, in which o:O is the separation between the isotropic chemical shifts. Strong spectral perturbations and greatly enhanced exchange of Zeeman magnetization are observed.” This is an extension of the early observations of Andrew and co-workers. l9 In this article we will not provide detailed theoretical descriptions of these effects, or discuss their applications in detail, but instead emphasize the general physical phenomena which they illustrate. The effects highlight the different behaviour of homogeneous and inhomogeneous systems as understood by Maricq and Wa~gh.~T In inhomogeneous systems such as dilute spin-; nuclei in high field, the spin eigenvalues t Maricq and Waugh5 distinguish inhomogeneous and homogeneous systems by whether the Hamiltonian does or does not commute with itself at different times.This is equivalent to our usage, in which the two types of systems are distinguished by whether the spin eigenstates do not or do change in time. Note, however, that as Maricq and Waugh indi~ate,~ these definitions are not identical with inhomogeneous and homogeneous spectral-broadening mechanisms, inhomogeneous referring to a superposition of independent systems with different eigenvalues, and homogeneous referring to a situation where each system provides a large number of closely spaced eigenvalues. The absence of spin-state transitions under sample rotation implied by Maricq and Waugh’s sense of inhomogeneous is closer but not identical to the quantum-mechanical definition of ‘adiabatic’ :20 an inhomogeneous system is always adiabatic, but whether a homogeneous system is adiabatic or not will depend upon how rapidly the eigenstates change.D.P . Raleigh, A . C. Kolbert, T. G . Oas, M . H. Levitt and R . G. Grifin 3693 may change as the sample is rotated, but the eigenstates do not. In homogeneous systems, as typified by homonuclear dipole coupled spin systems, the eigenstates as well as the eigenvalues are strongly dependent upon the rotation angle. For inhomogeneous systems, if the spin system is prepared in an eigenstate, it will remain in that eigenstate as the sample is rotated, the state acquiring a phase factor equal to the integral of the eigenvalue over time.For second-rank tensors rotational echoes are formed as the anisotropic contributions to the eigenvalues average to zero over a rotational period, and this general behaviour is independent of the spinning speed. In homogeneous systems, on the other hand, rapid spinning is necessary to achieve an averaging effect, since the eigenstates themselves must be averaged in a sort of motional narrowing process. The behaviour of inhomogeneous systems under magic-angle spinning is detrimental to the measurement of small anisotropies. Since the eigenvalues never differ substantially from their average, the eigenstates do not acquire a significant differential phase factor, and as a result rotational sidebands are small. All of the methods described below have the feature in common that they induce a normally inhomogeneous spin system to behave in a homogeneous manner by stimulating transitions between the eigenstates during the rotational period.In the spin-echo methods, n-pulses exchange eigenstates and therefore interfere with rotational-echo formation. In rotary resonance re- coupling, an applied r.f. field continuously induces transitions so that the spin system is converted from inhomogeneous to homogeneous. In the homonuclear spin-pair experiments the system behaves approximately inhomogeneously, under normal circumstances, since the homonuclear dipole interaction is effectively truncated by the chemical-shift difference. This approximation breaks down at rotational resonances where the flip-flop terms may induce rapid transitions.In all of these cases, the transition from inhomogeneous to homogeneous causes interesting effects which assist the measurement of small anisotropies, since the averaging of spin eigenvalues is no longer the determining factor in the spin dynamics. 2. Magnetization Vectors and Echoes in Rotating Solids 2.1. Echo Formation in Inhomogeneous Systems Consider an ensemble of spin-: nuclei, where the precession frequencies ~ ( t ) of the spins are different for each member of the ensemble, leading to an inhomogeneously broadened spectral line. Viewed from a frame rotating at wrf, the precession frequencies are Am(t) = m(t)-orf. A familiar example would be dilute 13C spins in a polycrystalline solid, where the random orientation of the shielding tensor with respect to the static field creates a distribution of precession frequencies. The initial preparation of transverse magnetization by cross-polarization or a n/2 pulse creates a state of uniform phase $(O) at time t = 0, and each magnetization vector will have acquired a phase #(t) at time t given by (1) where in general the integrated precession angle is #(t> = #(O) + O(0 + 0 The NMR signal will be given by in which the brackets denote powder averaging. The signal will damp out for long t, because of the different precession angles O(0 -+ t ) accumulated by the magnetization vectors associated with different crystallites.3693 Enhancement of Small Anisotropies in MASNMR As is well known, a Hahn echo may be formed in such a system by applying a strong radiofrequency n-pulse close to resonance.If the pulse has phase 5, the magnetization phases are converted from #(t) into 25 - #(t), and after a subsequent time t’ the phases are (4) In a static solid the frequencies cu are time-independent. Therefore, O(t --f t + t’) is the same as O(0 + t’), so that O(t + t’) is independent of the member of the ensemble for t’ = t. This is generally not the case if the inhomogeneous interactions are time-dependent, such as in a rotating solid, since O(t+ t+ t’) is in general not equal to O(O+ t’), and the discrepancy will be different for each ensemble member. Therefore, in a rotating solid, a z-pulse at time t does not necessarily induce a spin echo at time 22. Also, in a rotating solid, echoes may occur in the absence of r.f.irradiation, if the interactions vary in such a way that O(0 + t ) is itself independent of the member of ensemble for particular times t. These are the rotational echoes described by Maricq and W a ~ g h , ~ which will be discussed further below. #(t + t’) = 2< - #(t) + e(t + t + t’) = 25 - #(O) - O(0 -+ t ) + O( t -+ t + t’). 2.2. Spin Magnetization Vectors in Rotating Solids In a rotating solid having anisotropic shielding interactions, the precession frequency of each magnetization component is periodically time-dependent, the characteristic period being the time for the rotor to complete one revolution, z, = 27r/o,. Accordingly, it is natural to expand the rotating frame precession frequencies in a Fourier series with coefficients A d r n ) : 2 Am(?) = C A d r n ) exp (imqt) ( 5 ) m--2 in which AdTm) = Adm)*.Since the shielding interactions transform under rotation as second-rank tensors, only terms from m = -2 to 2 are required in the sum. The coefficients Adrn) are dependent upon the crystallite orientation and the magnitude, orientation and asymmetry of the characteristic interactions ; precise forms have been given el~ewhere.~’ 21, 22 We point out here that if the rotation axis is at exactly tan-ld2 with respect to the static field, then the coefficient A d 0 ) is independent of crystallite orientation, and is equal to the difference between the isotropic chemical shift and the r.f. carrier frequencies, and that A d r n ) depends on the Euler angle a as Adrn) - exp (ima), where a is one of the three Euler angles expressing the orientation of the particular crystallite in a rotor-fixed reference frame.The three angles {a, p, y } fully describe the crystallite ~rientation.~* 21* 22 The accumulated phase generated from time t to a time t’ is given by [exp (imqt’) - exp (irnco,t)] A d m ) . 1 dt” Aco(~”) = { t’ - t}Aw‘O’ + C - m+O immr (6) In a frame rotating at the isotropic shift Am(’), the phase of the magnetization vector 8(0 + t ) is periodic modulo 2n/m,. Rotational echoes are formed at the end of each rotor period, since the second term in eqn (6) vanishes at those points.5. 21 Spin packets which differ only in the value of a have the same values of IAw(l)[ and 1Ad2)1, and therefore their magnetization vectors follow trajectories with the same variation in phase but different average phases. These points are illustrated in fig.l(a) and (b), which display the magnetization trajectories for a = 60 and 20°, in a frame rotating at the isotropic shift.D. P . Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Grifin 3695 Fig. 1. Spin packet trajectories in the rotating frame showing the effect of a 7t-pulse on rotational echo formation. All calculations used a spinning speed of 2.0 kHz, an anisotropy of 5.0 kHz and y~ = 0, with f l = 60". (a) a = 60", no n-pulse; (b) a = 20", no 7c-pulse; (c) a = 60" and a n-pulse is applied at t = t,/2 about the x-axis; (d) a = 20" and a n-pulse is applied at t = 2 , / 2 about the x- axis. 2.3 n-Pulses in Rotating Solids As pointed out above, a n-pulse in a rotating solid at time t does not necessarily induce a spin echo at time 2t, since the inhomogeneous interactions are not time-independent, and may even inhibit the formation of rotational echoes.Fig. 2(a) shows a free induction decay (FID) in a normal MAS experiment, which consists of a train of rotational echoes. Fig. 2(b) shows the results of applying a n-pulse at a time 2,/2 after a rotor echo. The train of rotational echoes is almost completely attenuated by the n-pulse, as the refocussing of the magnetization vectors of individual crystallites at nz, is disrupted. This effect is explained in fig. 1. Fig. 1 (a) and (b) show the trajectory of two spin packets in the absence of the pulse. The same two trajectories are shown in fig. l(c) and (4, in which a n-pulse is applied at t = zJ2.From time t = 0 to t = 2,/2, the two vectors follow their normal paths, and at t = 2,/2 the n-pulse instantaneously reverses the accumulated phase and the vectors then continue to precess in the same sense. Since the n-pulse has moved each vector from its normal path, the two magnetization vectors do not return to the x-axis at nz,, and they do not contribute to rotational echo formation. These arguments can be put into a more rigorous form by calculating the effect of n-pulses on the net phase angle 4. The angle which a magnetization vector makes with respect to the x-axis at a time t , after a n-pulse of phase 5 has been applied at time t , (all times are measured from the initial preparation), is given by3696 Enhancement of Small Anisotropies in MASNMR I 0 I 8 tlms I 16 Fig.2. Rotational echo trains measured on a sample of 13C-1 enriched glycine at a spinning speed of 1.03 kHz. The r.f. carrier frequency coincided with the isotropic chemical shift. (a) Normal echo train. (b) A n-pulse is applied t,/2 after the third rotor echo. (c) A train of n-pulses, all of phase 0 with spacing z, beginning 2,/2 after the first rotor echo. (d) A train of n-pulses with spacing 22,, but alternating in phase between 0 and n/2, beginning 2,/2 after the second rotor echo. using eqn (4) e(t, -+ t 2 ) = e(o + t,) - e(o + t,). Physically this equation states that the magnetization vector evolves from t = 0 to t = t,, acquiring net phase $(tl). The n-pulse converts this phase to 25 - # ( I , ) , and the vector then continues to precess between t, and t,, acquiring an additional phase O(t, --+ t,).This expression can be easily generalized to n n-pulses applied at times t,, t,, . . . t, with phases 5 , , t 2 , ... t,. After n n-pulses, the net phase at time I,+, is given by An echo occurs only if the net phase evolution $(t,+,) is independent of orientation, and in a rotating solid this does not happen for an arbitrary set of times {tl, t,, ... t,). For 2m equally spaced n-pulses with spacing (n/m)z,, (where n and m are integers) the condition for echo formation may be derived by solving for $(t,+J = 0, taking #(O) = l p = 0. Rotational echo formation occurs only if m is odd, the echo appearing at t = 2nz,. This has been verified experimentally for n/m = 1/3, 2 / 3 , 1/5, 2/5, 3/5, 1/7, 3/7.23 Two further examples of multiple-pulse echo trains are shown in fig.2(c) and (4. In fig. 2(c) a train of n-pulses spaced 2, apart was applied. Examination of eqn (9) shows that an echo forms every 22, and comparison of fig. 2(a) and (c) verifies that only every second echo is present. The effect of varying the phase is illustrated in fig. 2(4. In this case aD. P. Raleigh, A . C. Kolbert, T. G. Oas, M . H. Leuitt and R. G. Grifin 3697 train of n-pulses alternating in phase between 0 and n/2 was applied with spacing 7,. Eqn (9) predicts that echoes form every 22, and alternate in phase between 0 and n. The predicted effects are clearly displayed in fig. 2(d). Although these echo trains are primarily of pedagogical interest, a detailed understanding of the effects of n-pulses in MAS is clearly important.Many NMR experiments utilize refocussing pulses, and the above discussion illustrates that in rotating solids considerable care must be taken in their placement.24* 25 Furthermore, the ideas developed above are instrumental in understanding the two-dimensional experiments designed to measure small coupling tensors. These experiments delay rotational echo formation in t , by interrupting the precession with n-pulses. A straightforward argument shows that additional sidebands will be present, and fairly simple numerical calculations can be used to calculate the full two-dimensional land~cape.,~ 2.4. Two-dimensional Spin-echo NMR The preceding discussion and fig. 1 (c) and (d) show that applying a n-pulse to a rotating solid can have the effect of amplifying the maximum phase excursions of the magnetization vectors.This has applications in the measurement of small anisotropies, which normally produce only a minor modulation of the NMR signal and therefore small rotational sidebands. Enhancement of the modulation depth by the introduction of one or more n-pulses should facilitate the estimation of these small anisotropies. The phase modulation of the magnetization may also be enhanced by rotating the sample at a slower speed. In fact, there is a close formal analogy between the introduction of a n-pulse and rotating the sample at one-half the speed. Consider the two-dimensional experiment shown in fig. 3(a). After initial preparation of the magnetization at time t = 0, a n-pulse is applied at time t J 2 .After completion of the evolution period of total duration t,, the signal is sampled at times t , + t,, t , 2 0. From eqn (9) the phase of a magnetization component at time t , + t , is given by # ( t , + t,) = 2r - $(O) + O(0 + t , + t 2 ) - 2O(O -+ t , / 2 ) . (10) Since the precession frequencies Aw(t) are dependent on time only as art, the integrated precession angles at different spinning speeds may be related through aO(0 -+ tJa, a,) = O(0 -+ t,, co,/a) (1 1) which is easily proved from eqn (2). Taking a = 2, the fourth term in eqn (10) indicates that the t,-dependence of the signal derived from such an experiment is closely related to a spectrum acquired at one-half the rotation speed. Thus eqn (10) indicates a 4n/w, rather than 2n/cor periodicity of the magnetization phase modulation, indicating spectral sidebands at multiples of coJ2 rather than co,.For small shielding tensors, the intensities of these sidebands are much larger than in the one- dimensional spectrum, just as if the spinning speed were reduced. Indeed, a skew projection of the 2D spectrum may be taken which is rigorously identical with the ID spectrum taken at half the spinning speed, as shown el~ewhere.,~ These effects were first observed by Bodenhausen et a1.26 for the case of an isotropic liquid rotating in an inhomogeneous external field. In a rotating solid, the sidebands contain useful information as to the principal values of the shielding tensors. The two-dimensional spectrum produced in such an experiment may be simulated by explicit evaluation of the two-dimensional signal &, 12) = (exp [i$(t,+ t2)l) = (exp {i[2r - $(O)]> exp [iO(O + t , + t,)] x exp [ - 2i0(0 + t l / 2 ) ] ) .3698 Enhancement of Small Anisotropies in MASNMR II I CP . decou ple x I.*-I - 1 $12 t , / 2 t 2 CI w I I decouple CP x x I U L - I - I t2 t 1 / 3 t l / 3 t l / 3 Fig. 3. Pulse sequences for two-dimensional spin-echo experiment. (a) n-pulse placed in the centre of the evolution period, t J 2 after cross-polarization; (b) n-pulses placed at t , / 3 and 2tJ3 after cross-polarization. Subsequent Fourier transformation of s(tl, t,) with respect to the two time variables yields S(w,, m,), the two-dimensional frequency-domain spectrum. Fig. 4 compares the results of this experiment with numerical simulations based upon eqn (12).Note that this numerical simulation is not a fit: the simulations shown here were performed without adjustable parameters using published values of the chemical shift parameters for N-acetyl valine (NAV). 27 The correspondence is excellent, and both the two-dimensional sideband array and the projection on to the w, axis are reasonably sensitive to changes in the breadth of the anisotropy, and the asymmetry parameter, q. Note that the sideband intensities are much larger than in the one-dimensional spectrum of NAV displayed in fig. 5. In addition, there are two other interesting features of the two- dimensional spectrum. First, the projection on to the ml axis has inverted sidebands. Inverted sidebands have been observed previously in two-dimensional MAS NMR spectra, in particular, in both dipolar chemical-shift and heteronuclear chemical-shift correlation spectra, but have previously been restricted to the two-dimensional landscape.The projection on to either the wl or w, axes in both experiments has always yielded a sideband spectrum in positive absorption mode.l0? l1 Secondly, the two- dimensional spectrum and its w, projection have a rigorous symmetry. The sidebands at (m1,.m2) = (mmr/2, nw,) and [ -mw,/2, (n -m)w,] are of the same intensity, and the w, projection is symmetric about w1 = 0. These symmetry properties are discussed el~ewhere.~~D. P . Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Grifin 3699 - 2 L - I I/__ i 2- I I I 5.0 0 -5.0 ( 0 1 /27c)/kHz I 1 - I -5.0 0 5 .O (0, /2Z)/rnZ Fig.4. Two-dimensional spin-echo spectrum and simulations, for the pulse sequence of fig. 3 (a). The sideband index in the w, dimension is given on the left; the lower spectrum is the projection onto the o, axis. (a) Slices of an experimental 15N two-dimensional spectrum taken parallel to the o, axis. The sample was 15N-enriched N-acetyl valine, the spinning speed, oJ2n = 2.000 kHz. 512 t , values were collected, with 32 acquisitions per t , value and a recycle time of 3 s. Note the sidebands spaced at o , / 2 in the o, dimension. (b) Simulation using published values for the chemical shift tensor of NAV w06/2n = 3.362 kHz, q = 0.24. The pulse sequence shown in fig. 3(b) has two n-pulses applied during the evolution period at times t 1 / 3 and 2t1/3, which lead to a number of interesting effects.From eqn (4), the net phase angle at t , is given by and the two-dimensional signal by 4 t 1 , b) = (exp M t l + t 2 ) 1 > * (14) Application of eqn (6) reveals that the t , FID has terms oscillating at wJ3, 2co,/3, 4coJ3, w, and 2wr, which will result in sidebands spaced at co,/3 in the co, dimension. Fig. 6 compares slices for an experimental two-dimensional spectrum of 15N-NAV taken parallel to w,, and the projection on to w, with numerical simulations. Note that again inverted sidebands appear in the co, projection, but the symmetry of the previous experiment has been broken. The position of the centre band in the cu, dimension of these two-dimensional spectra should be mentioned.In the method of fig. 3(a), the centre band is at zero frequency in the co, dimension because of the presence of a refocussing pulse in the centre of the evolution period. In the method of fig. 3(b), the disposition of the two z-pulses causes the centre band to appear at frequency Aco(O)/3, in which A d o ) is the isotropic shift frequency in the rotating frame.3700 Enhancement of Small Anisotropies in MASNMR I 5 . 0 I frequency /kHz 0 I -5.0 Fig. 5. 15N Magic-angle spinning spectrum of 15N-enriched N-acetyl valine, 0,/27r = 2.000 kHz. Spectrum was taken under standard CP-MAS conditions with C.W. proton decoupling during acquisition. - 2 I I 1 1 I 1 5 .o 0 -5.0 5.0 0 - 5.0 ( 0 1 I2n)llrHz ( 0 1 /270/lrHz Fig. 6. Two-dimensional spin-echo spectrum and simulations for the pulse sequence of fig.3(b). The sideband index in the o2 dimension is given on the left; the lower spectrum is the projection onto the ol axis. (a) Slices of an experimental 15N two-dimensional spectrum taken parallel to the w, axis. The sample was I5N-enriched N-acetyl valine, wJ2n = 2.000 kHz; 512 t , values were collected, with 32 acquisitions per t, value and a recycle time of 3 s. The sidebands in o, are spaced at 0 , / 3 and the centre bands are at Ao(O)/3, where Acd0)/2n = -301.2 Hz. (b) Simulation using published values for the chemical-shift tensor of NAV as given in the caption to fig. 4.D. P . Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Grifin 3701 These experiments can be extended to sequences which will generate sidebands at u,/n for n > 3.Our analytical and numerical calculations indicate, however, that no additional intensity is transferred into the lower-order sidebands as n increases, and in- stead, more of the signal is dispersed into small higher-order sidebands spaced at wJn. This also applies to the experiment of fig. 3(b), which does not produce sidebands significantly more intense than that of fig. 3 (a), although they are more numerous.23 The principal advantage of the second experiment is that the larger number of independent sideband intensities should increase the accuracy of estimated shielding tensors. The methods described above hold promise for assisting the determination of small shielding tensors for which usual spinning speeds lead to vanishingly small sideband intensities.High resolution may be maintained in the w, dimension, and the experiments are insensitive to pulse imperfections if the proper phase cycling of the n-pulses is perfo~rned,~~ in contrast to methods involving trains of many n-pulses. l3 Experimentally, the method is simpler than techniques which require mechanical jumping of the sample15 or rapid switching of the rotor axis.14 A disadvantage of the current techniques is that, like all magic-angle spinning methods, determination of the principal values will require matching of numerically derived data sets with experimental sideband intensities. Extensions of the experiment for measurement of small heteronuclear dipolar couplings are currently being explored. 3. Recoupling in Heteronuclear Spin Pairs A quite different method for the retrieval of small anisotropies arising from the interaction of a pair of spin-: nuclei labelled I and S is shown in fig.7. The experiment involves detection of the S-spin resonance, while a weak r.f. field is applied at the isotropic shift of the I-spin. In most cases a third abundant spin species (usually protons) will also be present, so the experiment would be conducted with a strong decoupling field at the third r.f. frequency. The experimental illustrations shown in fig. 8 are for the case of I = 15N, S = 31P, and the abundant species is 'H. The top trace is the normal 31P MAS spectrum, while the second trace shows the spectrum obtained using the pulse sequence of fig. 7. The heteronuclear dipolar interaction usually behaves inhomogeneously, since the Hamiltonian is truncated by the large difference in Larmor frequencies between I and S.The S-spin MAS spectrum is therefore a set of narrow lines with intensities dominated by the S-spin shielding tensor [fig. 8(a)]. In the presence of an r.f. field at the I-spin isotropic Larmor frequency [fig. 8 (b)], dramatic lineshape perturbations are observed if the intensity of the r.f. field is such that the I-spin nutation frequency ulI = nu,, where n is an integer.16 The spectrum for n = 1 is shown in fig. 8(b). The broad pattern may be shown to contain information as to the I-S dipolar coupling and also the relative orientations of the coupling tensor and the two shielding tens0rs.l' Although a detailed description of this effect will be given elsewhere, it seems appropriate here to discuss the basic physical process in the context of homogeneous and inhomogeneous systems.In the absence of the I-spin r.f. field, the system behaves inhomogeneously, the periodic variation in eigenvalues leading to the spectral sideband pattern observed in fig. 8. In the presence of a very strong resonant r.f. field applied to the I-spins, the system is still inhomogeneous in the Maricq-Waugh sense,5 provided that one passes into the usual rotating frame for the I-spins. The strong, static, transverse field from the r.f. irradiation dominates the periodically fluctuating longitudinal fields, which derive from the modulated I-spin shielding interaction and IS- dipolar coupling. If the transverse field is sufficiently intense, the eigenstates of the I- spins are nearly constant over time and the system is still essentially inhomogeneous : the spin states always remain close to the eigenstates of the Hamiltonian.This in homogeneous behaviour breaks down at the rotary resonance recoupling conditions,3702 . decouple CP Enhancement of Small Anisotropies in MASNMR rZ/2 t 1 o = n o , l5 N I1 Fig. 7. Pulse sequence for the heteronuclear recoupling experiment. High-power proton decoupling is applied during acquisition, while a weak r.f. field is applied to the I-spins and the S-spins are observed. I 20.0 I 0 frequency /kHz I -20 .o Fig. 8. Normal and recoupled 31P MAS spectra of polycrystalline 99% 15N-labelled N-methyldiphenylphosphoramidate. (a) Normal 31P MAS spectrum, wJ2n = 4.3 kHz.(b) Recoupled spectrum, w,, = w,.D. P. Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. GriJSfn 3703 where the rotation-modulated longitudinal fields have frequency components which match exactly the differences between the eigenvalues in the rotating frame. These spectral components induce rapid transitions which demolish the nearly inhomogeneous character of the spin system. The strong spectral perturbations may be related to the size of the transition-inducing terms, namely the resonant Fourier components of the dipolar and I-spin shift interactions, as described in detail elsewhere. Apart from the homonuclear rotational resonance effects discussed below, the above effect has some relationship with the cross-polarization sidebands observed by Stesjkal et aZ.28 and the rotary saturation technique of Redfield.29 4.1.Rotational Resonance in Homonuclear Spin Pairs There are many situations in which it would be advantageous to measure small dipolar couplings due to homonuclear coupled spin pairs such as 13C-13C. With such a technique distances between adjacent components in polymer blends, surfaces and enzyme- substrate or inhibitor complexes could be measured. We now describe an approach to enhancing the detection of these couplings. The Hamiltonian of two homonuclear dipolar coupled spins is, in general, homogeneous in the sense of Maricq and Waugh, since the spin eigenstates depend strongly on the spatial orientation of the sample. The high-field Hamiltonian of the two- spin system is given by H = H,+H, (154 H, = mi( t ) Iiz + mj( t ) Ijz (15b) with H , = A(t) IizIiz + +B(t) (Ii+& -+ I J j J in which A and B are the standard factors.’ The non-commutation of the B term and the single-spin term renders the problem homogeneous in general.However, the system is inhomogeneous in special cases, such as when the chemical shifts of the two spins are identical at all times (since the B term then commutes with the total Zeeman operator). It also behaves inhomogeneously when the members of the homonuclear spin pairs have different resonance frequencies and the homonuclear dipolar interaction is effectively truncated. However, this truncation breaks down under rotational resonance conditions, as discussed below. ‘The effect of a homonuclear dipolar coupling in combination with a chemical shift difference was discussed by Maricq and Waugh.’ They considered the case of a homonuclear dipolar-coupled pair where the isotropic shifts of the two resonances were identical and the two shielding tensors had identical principal values, but different orientations.Using average Hamiltonian theory, these workers showed that the spectrum obtained with synchronous sampling displayed a broad, structured shape instead of a sharp, narrow line. In the more common case where there exists a difference between isotropic shifts, a richer range of effects can be observed. Specifically, when the difference between the chemical shifts is always larger than the dipolar coupling, the MAS NMR spectrum resembles the spectrum of a system where both spin species are magnetically dilute. The most noticeable effect is usually a slight broadening and shifting in the line positions and small changes in the sideband intensities.The line shifts arise from the residual influence of the flip-flop terms, whilst the secular part of the dipolar Hamiltonian behaves inhomogeneously and perturbs the sideband intensities. This situation is actually quite common in 13C-MASNMR, because aliphatic resonances are roughly 80-1 00 ppm upfield from aromatics and 130-170 ppm upfield from carboxyl resonances. On a 7 T (i.e. 75 MHz for 13C) instrument this translates into ca. 7 and ca. 12 kHz, respectively, while 13C-13C dipolar couplings (pOy2h/87c2r3) are typically of the order of 1.5-2 kHz.3704 Enhancement of Small Anisotropies in MASNMR However, at certain spinning speeds a dramatic reappearance of the dipolar coupling is observed.In particular, when the difference in isotropic shifts, ofo, is equal to a multiple of the spinning speed (w: = n o , ) the modulated flip-flop term comes into resonance with the remainder of the Hamiltonian, resulting in dramatic line broaden- ing and efficient cross-relaxation.18~ ' ' 9 30-32 These effects were first noted by Andrew et al.,'s~'9 while Raleigh et aL30 observed similar effects and also showed that the inten- sities of rotational sidebands are dramatically enhanced when ofo = no,. The rotational resonance effect can be understood, at least on a qualitative basis, by considering a model system where the two spins have no shift anisotropy.In a frame rotating at the mean isotropic chemical shift, the Hamiltonian is given by H( t ) = of" (Iiz - Ij,) + H,( t ) in which cop is the difference between the isotropic chemical shifts. Transforming to an interaction frame defined by u&) = exp [ - i ofo : (Iiz - ~ ~ , ) t ] . The A term in HD commutes with UA(t) and does not acquire any additional time dependence. However, the B term acquires an additional time dependence at frequency w;". In a static solid this dependence vanishes from the zeroth-order average Hamiltonian, defined through This is not true in a rotating solid if the intrinsic time dependence of the B term due to the sample rotation interferes with the interaction-frame rotation at frequency ofo. Since the B term contains components oscillating at 2o,, for which the flip- flop term of the dipolar interaction is not averaged in the zeroth-order average Hamiltonian.A more detailed treatment predicts resonances at higher values of I n I if shift anisotropies are present or higher-order terms are taken into account. Although our discussion above is strictly applicable only to systems in which the difference between isotropic chemical shifts always exceeds the dipolar coupling, rotational resonance effects are also present in systems with overlapping shift tensors. This simple argument predicts line broadening when ot0 = n o , but says nothing about the expected lineshape. A more sophisticated treatment l7 allows approximate predictions of lineshapes, but calculation of exact rotational resonance spectra requires numerical simulations of the dynamics of the spin system.For the case of isolated homonuclear spin-; pairs, it is possible to develop essentially exact simulations of the dynamics, using fictitious spin-: operators. Alternatively, Vega and Schmidt have used the Floquet Hamiltonian approach to calculate spectra of dipolar coupled spin pairs,33 while Barbara and Harbison have used a different formalism to calculate the line~hape.~~ The details of our calculations will be deferred to a later p~blication.~' Here we simply point out that by expressing the Hamiltonian in the basis of direct product eigenstates of Iiz and Ijz, the time-evolution operator can be written as the product of two terms, one of which commutes with both Zeeman polarization operators.The other term represents a rotation in a fictitious two-level system and is the product of many non-commuting rotations. This cannot be calculated analytically. It can, however, be calculated numerically to an arbitrary degree of accuracy, and this is the only approximation in the simulations presented below. Fig. 9 shows experimental rotational resonance spectra. In fig. 9(a) we show an MAS spectrum of unlabelled zinc acetate (ZnAc) obtained with o,/271 = 4.37 kHz. The two centre bands are separated by 13.095 kHz, and both lines are narrow (< 30 Hz). The spectrum displayed in fig. 9(b) was obtained from a doubly 13C-labelled sample using oJ2n = 4.37 kHz, which fulfils the rotational resonance condition for the n = 3 or andD.P . Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Grifin 3705 h h A I 15.0 1 0 frequency IkHz I 15.0 Fig. 9. Homonuclear rotational resonance spectra of zinc acetate. (a) Unlabelled zinc acetate obtained with 0,/271 = 4.37 kHz; (b) di-13C-labelled zinc acetate, with 0,/2n = 4.38 kHz (n = 3); (c) di-13C-labelled zinc acetate, with 0,./27c = 3.272 kHz (n = 4). resonance, and the lineshape is now a distorted doublet. The spectrum obtained with the same sample at cur/2n = 3.272 kHz, which fulfils the n = 4 rotational resonance, is shown in fig. 9(c). For the 4cur resonance a broadening rather than a splitting is observed. In fig. 10 and 11 expanded plots of both the n = 3 and n = 4 rotational resonances are compared with numerical simulations.Clearly, there is good agreement between experiment and simulations.3706 Enhancement of Small Anisotropies in MASNMR 1 10 .o 9- 2 8.0 -3.2 -4.0 -4.8 * frequency/kHz Fig. 10. Experimental and calculated homonuclear rotational resonance spectra for di-13C zinc acetate. (a) Experimental carboxyl and methyl centre bands for 0,/271 = 4.370 kHz, with n = 3 resonance. (b) Calculated centre band lineshapes for q / 2 n = 4.370 kHz. [From ref. (17).] The lineshape varies for the different rotational resonances, with the largest splitting and/or line broadening observed for the lower-order resonances. The exact lineshape depends on a number of factors, including the strength of the dipolar coupling, the anisotropy of the two shift tensors, the strength of the J-coupling and the relative orientation of the various principal axis systems.The calculations presented in fig. 10 and 11 used the principal values determined from a static powder spectrum (data not shown) and the known J-coupling. The tensor orientations were assumed to be the same as the values given for other published methyl and carboxyl Details of the parameters used are given in the caption to fig. 1 1 . In this case the relative orientation of the tensors altered the details of the calculated spectra, but the basic features remained the same. This may not be true in general, and other examples undoubtedly could be found where the relative orientations play a more significant role. It does appear, however, that the primary features of the spectrum can be calculated to first order by using the principal values determined from analysis of sideband intensities, in conjunction with known (tabulated) 13C-13C J-couplings by first varying the dipolar coupling and assuming standard orientations for the PAS of the shielding A detailed discussion of the effect of the various parameters on rotational resonance spectra will be presented el~ewhere.~~ 4.2.Rotationally Enhanced Exchange of Zeeman Order Since the complete Hamiltonian for the two-spin systems doe not commute with the single-spin Zeeman operators Ikz, ( Ikz) is not a constant of the motion and longitudinalD. P . Raleigh, A . C. Kolbert, T. G. Oas, M. H . Levitt and R. G . Grifin 3707 10.0 9.2 8-0 -3.2 -4.0 -4.8 frequency /kHz Fig. 11. Experimental and calculated homonuclear rotational resonance spectra for di-13C zinc acetate. (a) Experimental carboxyl and methyl centre bands for o J 2 n = 3.272 kHz, with n = 4 resonance.(b) Calculated centre band lineshapes for wJ2n = 3.277 kHz. The simulations employed the following parameters (in the notation of Spie~s).~' Methyl-group shielding anisotropy : 006/2n = - 1.870 kHz, '1 = 0.17. Carboxyl-group shielding anisotropy : 006/2n = 6.460 kHz, '1 = 0.34; op/2n = 13.085 kHz; dipolar coupling poy2h/(8n2r3) = 2.000 kHz; J = 49 Hz; Euler angles = 0,90,0 and O,O,O, relating the two shielding tensor to the dipolar-tensor principal axis system. polarization of one of the two spins will evolve into other forms of spin order. In a static solid where the spin Hamiltonian is time-independent, the migration of spin order is effectively quenched if the difference in Larmor frequencies of the two spins greatly exceeds their coupling.As we remarked earlier, this is often the case in 13C NMR spectroscopy. The arguments presented in section 4.1 illustrated that this is also true in MAS, provided the rotational resonance condition is avoided. In fact, unless the spins are equivalent, exchange of spin order cannot proceed to completion in a dilute two-spin system. Remarkably, exchange of longitudinal spin order can proceed rapidly to completion when the rotational resonance condition is fulfilled, and we have recently demonstrated this effect." The difference polarization (Zlz-Z2z) is not a constant of the motion, and exchange of spin order between the two sites can be conveniently monitored by observing its evolution.Fig. 12 shows the evolution of the difference magnetization observed in a d i - Y zinc acetate sample for two spinning speeds. The first curve is the calculated transfer for mr/27r = 4.26 kHz, which is 110 Hz off the 30.1, resonance. Little polarization transfer is observed. Exactly on the n = 3 rotational resonance, the difference magnetization decays rapidly, passing through zero at ca. 1.5 ms and reaching 122 FAR 843708 Enhancement of Small Anisotropies in MASNMR t -1.0 -I I I I I I 0.0 10.0 20.0 tlms 1 5 -1.0 1 1 I I I I I I 1 0.0 3 .O tlms 6.0 Fig. 12. Experimental (0) and calculated (solid line) magnetization transfer curves for doubly labelled zinc acetate. (a) 0,/2n = 4.370 kHz, i.e.on the 30, resonance. (b) o,/2n = 4.260 kHz, i.e. 110 Hz off the 3 0 , resonance. [From ref. (17).] a minimum of ca. -f the initial value at 2.0 ms. The oscillations then damp out, decaying to zero. Both the depth and frequency of the oscillations increase with increasing dipolar coupling. The calculation: used a dipolar coupling corresponding to a 1.55 A bond distance which is within 0.05 A of the X-ray distance.36 The initial decay rate also decreases as the order of the rotational resonance increases. Rapid magnetization transfer still occurs for the 40, resonance, although there is no resolved splitting in the spectrum. For the 40, resonance the zero crossing occurs at 3.0ms, as opposed to 1.5 ms for the 304. case. These measurements were made with decoupling during the mixing period.Normally, magnetization transfer is measured without decoupling during the mixing period, since this broadens the resonances and increases the spectral overlap which enhances the transfer rate. If the decoupling field is removed during the mixing period, the characteristic oscillations shown in fig. 12 disappear and the difference magnetization decays monotonically to zero. This is because the random fields due to heteronuclear couplings tend to interfere with the coherently driven magnetization exchange. Since the depth and period of the oscillation depend very strongly upon the dipolar coupling, these rates can be used to estimate carbon-carbon distances in polycrystalline and amorphous materials, provided that the chemical shift tensors of the two sites mayD.P . Raleigh, A . C. Kolbert, T. G. Oas, M. H. Levitt and R. G. Grifin 3709 be estimated. Preliminary Salculations indicate that it should be possible to measure distances of up to ca. 4-6 A. A more detailed study of the potential of this method for distance determinations will be reported elsewhere. 5. Experimental All the experimental measurements described in this work were made on a home-built solid-state spectrometer at the Francis Bitter National Magnet Laboratory, operating at a proton frequency of 3 17 MHz (7.4 T). The MAS probes were also home-built using rotors and stators purchased from Doty Scientific, Inc. (Columbia, SC). The heteronuclear rotational resonance spectra were obtained with a triple-tuned ('H, 31P, 15N) probe.Pulse phases were adjusted using the methods of Rhim and 38 Typical r.f. field strengths were 120 kHz for lH decoupling and 50 kHz for 13C. The exchange of Zeeman order is often measured by selectively inverting one resonance with a rotational synchronized DANTE pulse train,39 but in our case complications arise because the two resonances are spaced nu, apart so the DANTE train would invert both resonances. To make the measurements plotted in fig. 12 we have used a long, weak pulse to invert the methyl resonance selectively. A long pulse is desired for greater selectivity; however, if the pulse is too long, appreciable exchange may occur during the time of the pulse. A useful compromise was empirically found to be a n-pulse of CLZ. 400 ps, corresponding to an r.f.nutation frequency of 1.25 kHz. This r.f. field strength was sufficient to invert the methyl resonances without appreciably perturbing the carboxyl resonance. The 'H decoupling field was reduced to 65 kHz in the magnetization transfer experiments to avoid excessive r.f. heating. The low-level 13C r.f. far the weak inversion pulse was generated by routeing the 13C r.f. through a second set of variable attenuators. The field strength of the weak pulse was calibrated using the two-dimensional nutation method of Bax4' on a static sample. Labelled zinc acetate was synthesized from doubly labelled acetic acid (Cambridge Isotope Laboratories, Woburn, MA) and ZnO. 15N-Labelled NAV was also purchased from Cambridge Isotope Laboratories. [15N]-N-methyldiphenylphosphoramidate was synthesized by reacting diphenylchlorophosphate (Aldrich, Milwaukee, WI) with [l5N]-rnethylamine hydro- chloride (Stohler Isotopes, Cambridge, MA) in a chloroform-trimethylamine mixture and recrystallized from chloroform.All computer calculations were performed with a DEC VAX station 2000. Simulations of the two-dimensional spin-echo spectra typically took 10-15 min of C.P.U. time, whereas calculation of the rotational resonance spectra took 2-3 h, and the individual magnetization curves required ca. 1 h. 6. Conclusions In this article we have described a number of new magic-angle spinning techniques which have in common the enhancement of the effects of small anisotropies. In normal circumstances the systems discussed behave inhomogeneously ; the small influence of the anisotropies on the spin eigenvalues is effectively averaged under magic-angle spinning conditions, and their influence on the spectra is small.By suitable intervention, a transition from inhomogeneous to homogeneous behaviour may be induced ; this may take the form of n-pulses (which exchange eigenstates), continuous r.f. fields or in some cases careful selection of the spinning speed. In section 2 we discussed spin-echo formation in rotating solids and sideband intensities in two-dimensional spin-echo spectra. n-Pulses exchange eigenstates and impede rotational echo formation. The experimental examples hold promise for measuring small chemical shielding anisotropies, but the general principles hold for measuring small dipole couplings as well.In sections 3 and 4 we demonstrated rotational resonance effects in dilute spin pair 122-23710 Enhancement of Small Anisotropies in MASNMR systems which provide dramatic examples of the transition from inhomogeneous to homogeneous behaviour. Under rotational resonance conditions, spin transitions are at their most effective, the averaging of magic-angle rotation on selected interactions is strongly impeded, and the structured lineshapes so produced contain much information as to dipolar interactions and relative orientations of tensors. These effects hold promise as a structural probe for polycrystalline and amorphous systems. We thank Professor G. S. Harbison, Dr T. Barbara, Professor J. S. Waugh, Professor S. Vega and A. Schmidt for helpful discussions and for describing their unpublished work.This work was supported by grants (GM-23403, GM-25505, GM-36920 and RR- 00995). D.P.R. was supported by a US National Science Foundation Graduate Fellowship, and T. G. 0. by a postdoctoral fellowship from the American Cancer Society. The manuscript was prepared by Ms A. Lawthers. References 1 M. Mehring, High Resolution NMR in Solids (Springer-Verlag, Berlin, 2nd edn, 1983). 2 U. Haeberlen, Advances in Magnetic Resonance, Supplement 1, High Resolution NMR in Solids: 3 E. R. Andrew, A. Bradbury and R. G. Eades, Nature (London), 1958, 182, 1659. 4 I. J. Lowe, Phys. Res. Lett., 1959, 2, 285. 5 M. M. Maricq and J. S. Waugh, J. Chem. Phys., 1979, 70, 3300. 6 A. Pines, M. G. Gibby and J. S. Waugh, J. Chem. Phys., 1973, 59, 569.7 J. Schaefer and E. 0. Stejskal, J. Am. Chem. SOC., 1976, 98, 1031. 8 E. Lippmaa, M. Alla and T. Tuherm, Proc. 19th Congress Ampere, Heidelberg, 1976. 9 J. Herzfeld and A. E. Berger, J. Chem. Phys., 1980, 73, 6021. Selective Averaging (Academic Press, New York, 1976). 10 M. Munowitz, R. G. Griffin, G. Bodenhausen and T. H. Huang, J. Am. Chem. SOC., 1981, 103, 2529. 11 M. G. Munowitz and R. G. Griffin, J. Chem. Phys., 1982, 76, 2848. 12 J. E. Roberts, S. Vega and R. G. Griffin, J. Am. Chem. SOC., 1984, 106, 2506. 13 Y. Yarim-Agaev, P. M. Tutunjian and J. S. Waugh, J. Magn. Reson., 1982, 47, 51. 14 A. Bax, N. M. Szeverenyi and G. M. Maciel, J. Magn. Reson., 1983, 51, 400. 15 G. E. Maciel, N. M. Szeverenyi and M. Sardashti, J. Magn. Reson., 1985,54, 365; T. Terao, H. Miura 16 T. G. Oas, R. G. Griffin and M. H. Levitt, J. Chem. Phys., submitted for publication. 17 D. P. Raleigh, M. H. Levitt and R. G. Griffin, Chem. Phys. Lett., 1988, 146, 71. 18 E. R. Andrew, A. Bradbury, R. G. Eades and V. T. Winn, Phys. Lett., 1963, 4, 99. 19 E. R. Andrew, S. Clough, L. J. Farnell, T. D. Giedhill and I. Roberts, Phys. Lett., 1966, 21, 505. 20 A. Abragam, Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961), p. 135. 21 E. T. Olejniczak, S. Vega and R. G. Griffin, J. Chem. Phys., 1984, 81,4804. 22 D. P. Raleigh, E. T. Olejniczak and R. G. Griffin, J. Chem. Phys., accepted for publication. 23 A. C. Kolbert, D. P. Raleigh, M. H. Levitt and R. G. Griffin, to be published. 24 W. T. Dixon, J. Chem. Phys., 1982, 77, 1800. 25 D. P. Raleigh, E. T. Olejniczak, S. Vega and R. G. Griffin, J. Magn. Reson., 1987, 72, 238. 26 G. Bodenhausen, S. P. Kempsell, R. Freeman and H. D. W. Hill, J. Magn. Reson., 1979, 35, 337. 27 J. E. Roberts, G. S. Harbison, M. G. Munowitz, J. Herzfeld and R. G. Griffin, J. Am. Chem. SOC., 28 E. 0. Stejskal, J. Schaefer and J. S. Waugh, J. Magn. Reson., 1977, 28, 105. 29 A. G. Redfield, Phys. Rev., 1955, 98, 1787. 30 D. P. Raleigh, G. S. Harbison, T. G. Neiss, J. E. Roberts and R. G. Griffin, Chem. Phys. Lett., 1987, 31 M. H. Levitt, D. P. Raleigh and R. G. Griffin, to be published. 32 B. H. Meier and W. L. Earl, J. Am. Chem. SOC., 1987, 109, 7937. 33 A. Schmidt and S. Vega, personal communication. 34 T. Barbara and G. S. Harbison, personal communication. 35 W. V. Veeman, Prog. Nucl. Magn. Reson. Spectrosc., 1984, 16, 193. 36 J. N. Van Niekeck, F. R. L. Schoening and J. H. Talbot, Acta Crystallogr., 1953, 6, 720. 37 W. K. Rhim, D. D. Elleman, L. B. Schreibier and R. W. Vaughan, J. Chem. Phys., 1974,60, 4595. 38 R. W. Vaughan, D. D. Elleman, L. M. Stacey, W. K. Rhim and J. W. Lee, Rev. Sci. Instr., 1977, 43, and A. Saika, J. Chem. Phys., 1986, 85, 3816. 1987, 109,4163. 138, 285. 1356.D. P . Raleigh, A . C. Kolbert, T. G. Oas, M. H . Levitt and R. G. Grifin 371 1 39 P. Caravatti, G. Bodenhausen and R. R. Ernst, J . Magn. Reson., 1983, 55, 88. 40 A. Bax, Two-dimensional NMR in Liquids (Reidel, Boston, 1984). 41 H. W. Spiess, in NMR Basic Principles and Progress, ed. D. Diehl, E. Fluck and R. Kosfield (Springer- Verlag, Berlin, 1978).. Paper 8/OI474D; Received 15th April, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403691

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I , 1988, 84(11), 3713-3730 Spectral Spin Diffusion in Polycrystalline Solids under Magic-angle Spinning Atsushi Kubo and Charles A. McDowell" 2036 Main Mall, Department of Chemistry, University of British Columbia, Vancouver, B.C. V6T I Y6, Canada Spectral spin diffusion in 13C NMR of double 13C-labelled sodium acetate trihydrate (SAC), and in 31P NMR of zinc(I1) bis(0,O'-diethyldithio- phosphate) (ZNP) has been studied under magic-angle spinning conditions. Spin-diffusion time constants, qD, were determined from the intensities of the spinning sidebands in experiments using rotation-synchronized DANTE pulse sequences, at several different spinning frequencies. The theory of Suter and Ernst, developed for spectral spin diffusion in single crystals, was extended to the case of polycrystalline samples rotating under magic-angle spinning conditions.We considered two mechanisms for the spin diffusion, i.e. dipolar interaction and J-coupling. The spin-diffusion time constants, qT), were related to the zero-quantum lineshape functions in a manner similar to the theory of Suter and Ernst. The zero-quantum lineshape functions were estimated from the observed single-quantum lineshape functions. In the present studies the dependence of the experimental values for T,, on the rotational frequency v, are in good agreement with those calculated from the theory based on the dipolar interaction mechanism. The values of T,, for SAC showed a deep minimum at Am z 2m,, and a shallow minimum at Am z 3m,. This phenomenon is rotational relaxation resonance.1. Introduction A major development in solid-state nuclear magnetic resonance spectroscopy occurred with the introduction of magic-angle spinning (MAS) of samples.'. Because MAS imposes a time dependence on all nuclear anisotropic interactions, this causes the averaging of inhomogeneous interactions and yields well-resolved NMR spectra of amorphous and polycrystalline solids. Later, when combined with cross-p~larization,~ and high-power proton decoupling,** it led to modern high-resolution solid-state NMR spectroscopy.6 It was early observed that in addition to the narrow central line there appeared satellite lines, or sidebands, on either side at integral multiples of the rotation frequency.'. Subsequently it was shown that when the spinning frequency is comparable to, or less than, the chemical-shift anisotropy, information on the anisotropy and orientations of chemical shift tensor can be obtained by appropriate mathematical analysis.'-' The combination of two-dimensional methods with the MAS technique has recently led to important developments whereby accurate and detailed information can be obtained not only about the anisotropies of chemical shifts, but also direct and indirect dipolar couplings, and slow molecular orientations, from the appropriate analysis of the rotational sideband patterns. Spin diffusion between nuclei with different chemical shifts (spectral spin diffusion) has recently been studied by the combination of two-dimensional NMR exchange techniques,l0' 22 or by the application of selective pulse excitation Since spin diffusion is largely induced by homonuclear dipolar interaction, it is possible to determine the strength of the dipolar interaction, or the internuclear distance, from the 37133714 Spin Digusion in Solids under MAS observed spin-diffusion time constants.Several applications of spectral spin-diffusion measurements based on these ideas have recently been reported. 26-32 Theoretical analyses of spectral spin diffusion have recently been reported by Suter and Ernst22 and by Henrichs et al.,33 both using different approaches to analyse spin- diffusion rates. We have reported our detailed studies of 31P spectral spin diffusion in single crystals of dipotassium a-D-glucopyranose- 1 -phosphate dihydrate, and also triphenyl phosphine, and have assessed the above theories as to their applicability to the 31P NMR spectral spin-diffusion rates in single In this publication we report the results of an MAS study of 13C doubly labelled sodium acetate (SAC), and zinc(rr) bis(0,O’-diethyldithiophosphate) (ZNP) under MAS conditions.One aspect of this paper is the study of the effect of spinning frequency on the spin-diffusion time constant ( qD). There are few studies on spin diffusion which have paid attention to the effect of the spinning f r e q ~ e n c y . ~ ~ . ~ ~ Another important matter is the contribution of the homonuclear J coupling to spectral spin diffusion. The Hamiltonian of the homonuclear J coupling also includes the so-called flip-flop term, although it is often much smaller than the homonuclear dipolar coupling.Under MAS conditions, the J coupling Hamiltonian included the static part, while the dipolar interaction is modulated by co, and 2cou,, where u), is the spinning angular frequency. In favourable cases it may be possible to measure these different contributions to the spin diffusion process. 2. Theoretical 2.1. Nuclear Relaxation under Modulation of the Hamiltonian Under MAS conditions, many terms in the Hamiltonian become time-dependent. Modulation of the Hamiltonian also can be introduced by applying a radio-frequency (r.f.) magnetic field, or by the use of various multiple-pulse experiments. Haeberlen and W a ~ g h ~ ~ discussed spin-lattice relaxation phenomena in periodically perturbed systems.They started from the following equation of motion of the density matrix p given by Abragam : 38 dp = - dT(W*(t), W * ( t - r), p 1 L . (1) - dt s:; In this paper we use a slightly different method to calculate the relaxation times; our method is probably easier to understand. The time-dependent Hamiltonian is generally written as %(I) = a#) T,+a2(t) q+ ... +a,(t) T, (2) where the a,(t) coefficients are time-dependent. The q terms are nuclear spin operators. The time-evolution operator, U(t), is given by U(t) = Texp( -i [ dtl.hY(tl)) where T is Dyson’s time-ordering operator. We assume the observable B does not commute with & but commutes with q, k # 1, because we can often find such cases. We divide the Hamiltonian into two parts, .hY1(t) and S 0 ( t ) , as defined by the following equations:A .Kubo and C. A . McDowell The time-evolution operator Uo(t) of the Hamiltonian So(?) is given by the equation 3715 Uo(t) = Texp -i dt, Zo(tl) . ( s , 1 Since Uo(t) commutes with B it does not affect the motion of the quantity B. following equation : By differentiating both sides of eqn (6) we obtain The time-evolution operator U*( t ) in the interaction representation is given by the (6) U*(t) = U&-’ U(t). (7 4 where Zl*(t) = Uo(t)-l A?#) q)(t). (7 b) (8) d - U*(t) = -iX,*(t) U*(t) dt Integrating this equation we obtain We define the decay function of the quantity B by the following equation: Tr{BU(t)-l BU(t)} Tr { B2} JB(t> = (9) On expanding the exponential in eqn (9) we obtain the result that The first-order term in eqn (10) is zero, because Tr{ABC) = Tr{CAB): The second-order term includes the two-times correlation function GBt(t), of the quantity B = i/d[T,, B], namely Tr { B’ &( t)-l B’ &( t)} Tr {(B’)21 G,,(t) = The factor, d, is defined as Tr(S2} = Tr{B2} and this relation is fulfilled, so that d is given by Thus second-order term in eqn (10) may now be written as The higher-order terms in eqn (10) consist of the more than two-times correlation function of the quantity c(t) = U;’(t) &(t).When X,*(t) is a random function of t, and the time-correlation functions of X:(t) have much shorter correlation times than the relaxation time &(I), it is often found experimentally that jB(t) is an exponential ... . (14) j B ( t ) = exp(-t/T,) = I--+-- function of t, i.e.t t2 TB 2! T i The relaxation time T, can be obtained when we compare eqn (12) or (1 3) with eqn (14) under the assumption that G,,(t) has a shorter correlation time than TB.3716 Spin Difiusion in Solids under MAS We write al(tl) as the sum of its Fourier components: al(t) = C A(w) exp(iwt). W Eqn (13) can thus be rewritten as - d2 2 A(w) A(w') f dt, r' dz exp [i(u + w') T3] GBf(z) exp (- iw'z) (16) w , 0, J o J o since G,,(t) vanishes in a much shorter time than TB, and because we are interested in the behaviour of j,(t) on the timescale of TB the upper limit of the second integral can be replaced by infinity. The terms w+w' = 0 give a contribution which is proportional to t. The other terms give rise to an oscillating term with frequency w + w'.The relaxation time TB is therefore given by (17) 0 1 - = d2 Ts A(w) A( - w) dz G,,(z) exp (- iwz). This equation can also be derived from eqn (1) by replacing Z * ( t ) by H,*(t) defined by eqn (7). Note that the time dependence of the terms of the Hamiltonian other than the perturbation term Zl(t) are included in the time-evolution operator Uo(t) given by eqn (5). The conditions which are necessary for eqn (17) to apply are that TB % 27r/w,, zB,, where w, is the frequency at which the Hamiltonian is modulated, and zB, is the correlation time of G,,(t). The following conditions have been fulfilled for the second condition TB % zBf to be satisfied; (1) 0, zBr -g 1 ; d << l/zB,. (2) If w, zB, 2 1, d << urn. 2.2. Hamiltonian under MAS Under MAS conditions, the secular Hamiltonian in the high magnetic-field region may be written as where Ttm are irreducible spherical tensor components of the nuclear spin operators.A represents the various types of interactions ; 2 (Zeeman interaction), Cx (chemical-shift interaction of the X spin), D,, (dipolar interaction between the X and Y spins) and J (J-coupling between the S , and S, spins). The list of the coupling parameters C', R', d' and T,I' is given by Spie~s,~' and we reproduce in table 1 the spin operators TAo, Tio and Tio. The second term, which represents the antisymmetric part of the interaction, differs from zero, only for the case involving J-coupling. The time-dependent factors cJ(t) are given by 1 Zy = C'( TAo R' + T;, E'( t ) + Tio d$ d' ti( t)) (18) ~ ~ ( t ) = C DL exp (imco, t ) (194 (19@ m--1 1 05 = - [P'l, %30(W + P A %(Q') + P L 9:1o(Q')l d3 where and pfo = -iy'2p&, pfil = p:zfip& and 9k,(n) are components of the Wigner rotation matrix.a' represents the Euler angles, which define the transformation from the principal-axes system of the interaction 3, to the rotor-fixed axes system. We used the same definition of the Euler angles as Spie~s.~' Another time-dependent factor <'( t), is given by c'(t) = At exp (iw, t ) + dl exp ( - iw, t ) + A; exp (2iw, t ) + A!, exp ( - 2iw, t ) (20a)A . Kubo and C. A . McDowell 3717 Table 1. Spin-dependent operators Ti,,, in laboratory-axes systema ~~ ~ a This table is based on information in ref. (39). 2.3. Spin Diffusion under MAS We consider the case of spectral spin diffusion between two spins S = + in the presence of abundant I spins.The commutation relations of the Hamiltonian are discussed in detail by Suter and Ernst.22 The observable of the spin diffusion process B = Sl2--S2,. The operator corresponds to the z component of the zero-quantum transition We introduce the following zero-quantum transition operators : R, = %SI+ s2+ + SI- s2+> (21 4 Rz = ;(slz-s2z). (21 c ) The Hamiltonian of the dipolar interaction between the S, and S, spins is expressed (22) The term Sl,S2, commutes with the observable of the spin diffusion R,, and does not affect the spin diffusion between the S , and S, spins. We can choose r: fir;: R, yDs,sz(t) as Xl(t). The spin-diffusion time constant due to the dipolar interaction T& is given by the following equation : by using the zero-quantum transition operators as shown in the following equation: H;((t) = -7; Ar1,3(2S1, S2, - R,) yDsisz(t).C A S l s z A”;TrSz dz GRY(z) exp (- imwr 7). (23) som - = d2 1 T:D m-*1, k2 We introduce the zero-quantum lineshape function KR,(w), defined by KRY(w) = som dz G,$z) exp (- iwz). Eqn (23) can now be rewritten as 1 -- - d2{A~slszA”~~P[KRy(OT) + K R y ( - ~ , ) ] + A f s , s , A_D,s1s2[K420r)+ KRI(-2mr)]}. (25) GI, For powder samples, a distribution of T& can exist, if A f s , s , ADf,s, or Afs,s2 ADglse have strong angular dependences. However, if spin diffusion between polycrystallites3718 Spin Digusion in Solids under MAS is fast enough to maintain a uniform spin temperature over the sample, the sample can still have a single spin-diffusion time constant, which is calculated by integrating eqn (25) over OD.We thus obtain the equation We ignore the orientation dependence of the zero-quantum lineshape function KRy(co). The Hamiltonian for the case with J-coupling is given by The spin-diffusion time constant due to J-coupling, cD, is By taking the powder average, c,, is calculated as It is noteworthy that eqn (29) includes the KRy(0), co = 0, component of the zero-quantum lineshape function, while that term is absent from eqn (26). Eqn (26) and (29) are similar to the equation which Suter and Ernst,22 Henrichs et al.33 and Kubo and M ~ D o w e l l ~ ~ derived for qD, the spin-diffusion rate in single crystals. The corresponding equation for the single-crystal case only contains the KRy(0) term.If we wish to obtain information about the strength of the dipolar interaction, or of the J-coupling, we need to know the zero-quantum lineshape function.' 2.4. The Estimation of the Zero-quantum Lineshape Function from the Single-quantum Lineshape Functions Henrichs et al.33 proposed a method to estimate the zero-quantum lineshape function, KR (co), from the single-quantum lineshape functions measured without the application of 1 spin decoupling. In another p ~ b l i c a t i o n ~ ~ we have discussed in detail the limitations of this method. At first we assume that the decay function of the zero-quantum coherence is given (30) where Il is the intensity of the lth sideband of the zero-quantum line, TR is the linewidth of each zero-quantum line.The Fourier component is given by by GRY(t) = exp (- t / TR) f I,{[exp - i(co, I + Aco) t ] + exp [i(co, I + Am) t]> 1 KRy(?i'lcU,) = d t GRV( t ) eXp ( - imo, t ) T R ). (31) TR JI = ' I' (1 +i[co,(l+m)+Aco] TR+ 1 -i[co,(l-m)+dco] TRA . Kubo and C. A . McDowell 3719 If two spins S, and S , are far from each other, and the correlation of the dipolar fields at the S , nucleus and the S, nucleus produced by I spins can be ignored, &(t) can be written as the product of the two evolution operators, U f ) ( t ) Uf)(t). Note that Ut)(t) includes the Siz and I spin operators, referring to nuclei which are close to the Si spin. The following commutations for interaction relations are satisfied : [ UP)(t), Uf’(t)] = [ UF)(t), S,,] = [Uf’(t) S,,] = 0.(32) By using these operators the zero-quantum lineshape function can be rewritten as We now introduce the decay functions of the single quantum coherence, L By using eqn (34), we can write eqn (33) as GR(t) = $~y)(t)~?’(t) +j?’(t)~y’(t)]. We approximate the single-quantum lineshape function by (35) J‘,“)( - t ) = C 4”) exp [ T i(w, I + w(”) t] exp ( - t/ F,”)) (36) 1 where 4k) is intensity of the lth sideband of the spectrum of the Sk spin, a(”) is the angular frequency of the isotropic peak of the spectrum of the Sk spin. The term l/Tik) is the width of each sideband of the spectrum of the Sk spin. Eqn (35) can be rewritten by using eqn (36) to yield the expression x (exp {i[w,(l- m) + dl) - d2)] t } + exp { - i[w,(l- m) + - d2)] t}). (37) By comparing eqn (37) and (30) we obtain the relations 1 1 1 - _ --+- TR Tf) T p Am = ~ ( 1 ) -w(2) For powder samples we must take the average over all possible orientations of the crystallites; thus we obtain the result3720 Spin Difusion in Solids under MAS where ( }powder means the powder average.However, from the single-quantum spectra, we can only observe (j'~)(t)}powde. - and (~'~)(t)),owder. - We approximate eqn (39) by writing (GRy(t))powder i[(j:)('))powder (jy2)(t))powder + <jy)(t))powder (j:2)(t))powderl' (40) Eqn (38) can be applied to powder samples by using this approximation. 2.5. Calculation of the Zero-quantum Lineshape Function The calculation of the zero-quantum lineshape function for single-crystal samples is discussed in detail in our other publication^.^' We now outline the theory needed to calculate the zero-quantum lineshape function for rotating samples under the MAS condition.We shall try to show which factors contribute to the sideband intensities or the widths of the zero-quantum lines. To derive the time dependence of the zero-quantum coherence, the relevant terms of the Hamiltonian ' Z 0 ( t ) needed are given by the equation rA?o(t) = 7, B,,{o:;: - 0:;: + f[Ad"~"~i(t) - AcT'"~"s~(~)]> R, where b:: = ys y I h ( ~ - t ; ) - ~ . (41 b) r:: is the internuclear distance between the Si and the Ik spins. This Hamiltonian can be related to the relevant Hamiltonian of the single-quantum coherence Sxi if we replace the chemical-shift term oi:;+$Adi) ecsi(t) in eqn (1 1) by the difference of the chemical shift: in eqn (41a), and the dipolar coupling b,S,'cDsiik(t) by the difference of the dipolar couplings bs,' cDslzk(f) - bti <Ds2z,(t).Thus we see that the difference of chemical-shift anisotropies, and the difference of the dipolar interactions, contribute to the rotational sidebands of the zero-quantum spectra. Since <"s,(t) and eCs2(t) are functions of the two different Euler angles, Q"s,(t) and QCs2(t), the difference of the chemical-shift anisotropies $[Ad') cCsl(t) - A d 2 ) 5cs2(t)] is not zero, when the chemical shielding tensors of S, and S, spins have the same principal values, but different orientations. The third term in eqn (41), & , l Z k r I (t), is the dipolar interaction between the I spins. This term commutes with the obskivable R,, and the first term in eqn (41a), but does not commute with the second term, -a:,": + $[Ao"' cCsl(t) - Ad2) ccs2(t)] y, Bo{oi;: - CT~;; + $[Ad1) ccsl(t) - Ad2) cCs2(t)]> R, - 2 Ikz[bf: c D s i r k ( t ) - bt: cDsZrk(t)] R,.k This dependence is expected to broaden the zero-quantum lines, and changes the sideband intensities in a similar way as slow molecular motions change the shape of the single-quantum MAS To simplify the problem, we ignore the third term, and calculate the sideband intensities due to the difference of the chemical-shift anisotropies, and the difference in the static heteronuclear dipole interactions. We also assume that there is only one kind of I spin. If we introduce the operators R+, defined by the decay function of the zero-quantum coherence can be written as - R, - = Rx+iR, (42)A .Kubo and C. A . McDowell where Uo(t) is given by Uo(t) = exp - i 'X;(tl) dt, ( s : 3721 (44) and we have 'X;(t,) = 7, B0{ai;; - 0;;; + :[Ad1) r c s i ( t ) - A d 2 ) c"sz(t)]} R, -21,[bf' cDsir(t) - biI c " s z r ( t ) ] R,. (45) By calculating the trace over R and Z, eqn (43) can be rewritten as where ACO = y s B0(&; - CT~:;) (47) c'f ( t ) = ;[Ad1' tcsi( t ) - Ad*) 5"sz(t)] y s Bo f [bf' t"si I ( t ) - bfI <"sir( t)] (48) cT - ( t ) = Cf+ cos w, t + Sf* sin w, t + Cf* cos ~ C O , t + Sf* sin 2w, t. <",t) can be changed into the same form given by Maricq and Waughs or Herzfeld and Berger,g namely (49) exp ( + i [ <:(tl)dtl) can be expressed as the sum of the sideband terms: exp (i S, t:(tl) dt1) + exp (i S, dt1) = c I m exp (imw, t ) (50) where Im is the intensity of the mth sideband.We do not calculate the explicit forms of I m . Eqn (46) can now be written as (51) Multiplying eqn ( 5 1 ) by the relaxation factor exp (- t / q ) there results an expression which corresponds to eqn (30). As discussed el~ewhere,~~ the heteronuclear dipolar interactions Xtsirk are sometimes comparable to the homonuclear dipolar interactions X t r r l . In this situation the relaxation theory described in subsection 2.1 can be applied to calculate the linewidth, if the spinning speed is high enough to satisfy the condition w, % lXts I. We now calculate the width of the zero-quantum lines with this condition, i.e. at 6iih rotation speeds. Xl(t) and Xo(t) in eqn (4a) and (4b) can be chosen as m GRY(t) = C Zm {exp [i(mm, + A o ) t] + exp [ - i(mw, + Am) t]}.m The linewidth, l/TR, is calculated to be 1 - = C (b:: Azirx - bil A2zIk) TR k ; l ; m - * , f Z x (b::fA"$rk-bi: A!%'r) dtGIkIi(t) exp(-imco,.t) (54) 1: where GI, is the two-spin correlation function, given by I , ( ? ) = 4(Tr { 'I)-' Tr {rk Uo(t)-l rl Uo(t))* ( 5 5 )3722 Spin Diffusion in Solids under MAS Fig. 1. A rotationally synchronized DANTE sequence. This pulse sequence is similar to that used by Caravatti et al.,25 except that the sign of the last 13C or 31P 90" pulse is altered, instead of the first 'H 90" pulse. We approximate this function by writing where z, is the correlation time of the flip-flop transitions of the I spins. Eqn (54) can now be rewritten as (57) 2% - = 2 2 1 TR m-1,2 k 1 + (mu, zJ2 * Eqn (57) can be applied only when w, % IJFOO,,, I.Under the slow-spinning condition co, % lX$s,Ikl the lineshape of the zero-quantug line can be calculated from Floquet Hamiltonih t h e ~ r y , ~ ~ , ~ ~ which has been applied to describe the effect of the molecular motion on lineshapes in MAS 54, 55 3. Experimental 13C doubly labelled sodium acetate (SAC) was purchased from MSD Isotopes, Montreal, Canada, and used without further purification. Zinc(I1) bis(0,O'-diethyl- dithiophosphate), Zn[S,P(OC,H,),], (ZNP) was ~ynthesized~~ by mixing concentrated aqueous solutions of zinc sulphate (BDH Chemicals) and ammonium diethyldithio- phosphate (Aldrich) in a molar ratio of 1 : 2. The precipitate was purified by repeated recrystallization from acetone solutions.The chemical analysis results were : C, found 22.2Y0, calculated 22.1 YO; H, found 4.7'/0, calculated 4.6%. All the NMR experiments were carried out by using a Bruker CXP200 FTNMR spectrometer with operating resonance frequencies of 50.30 MHz for 13C, 80.98 MHz for 31P and 200.0MHz for lH, respectively. The MAS double air-bearing probe was purchased from Doty Scientific Inc., Columbia, South Carolina. The spinning frequency was controlled within f 50 Hz during each experiment by supplying a constant N, gas flow. The magic angle was adjusted using the 79Br resonance from solid KBr.49 (fig. 1) was used to determine the spin-diffusion time constant GD. However, we reversed the signs of the last 13C, 31P 90" pulse, instead of the first 'H 90" pulse. 2-6 transients were collected by using 6 ,us ;n/2 pulses, 1 ms contact time and 8-20 s recycling times.The carrier frequency was set to one of the isotropic peaks. The time duration between the short pulses, t,, was set equal to l / v r , where v, is the rotor spinning frequency. The rotationally synchronized DANTEA . Kubo and C. A . McDowell 3723 For slow spinning speeds, t, becomes long. Loss of magnetization and 'H r.f. power may occur during this time period and these cannot be ignored. The number of short pulses, N , and the lengths of these pulses, t,, were adjusted to obtain the maximum intensity of one of the sideband groups, while keeping the 7r/2 pulse condition Nt, z 6ps. Examples of the values of N and t, used are: (1) 12, 0 .5 ~ ~ ; (2) 10, 1.Ops and (3) 4, The 13C NMR spectra of SAC without lH decoupling were recorded by using a standard single contact lH-13C cross-polarization pulse sequence. Since the two 31P resonance frequencies of ZNP are very close together, the 31P NMR spectra without 'H decoupling for ZNP were observed after eliminating one group of the sidebands by employing the rotationally synchronized DANTE sequence. More than 30 transients were accumulated. 4. Results and Discussion The 13C CP-MAS spectra of SAC resembled those reported by Raleigh et aL50 We also observed the 23 Hz splittings of both the methyl and carboxy isotropic peaks which are due to the 13C-13C J-coupling. The 31P CP-MAS spectra of ZNP consist of two isotropic peaks at < = 95.5 ppm and a! = 99.5 ppm from the corresponding resonance for 85 % H3P0,, which was used as a standard.The same procedure as described by Conner et aL5' was used to determine the spin- diffusion time constant &,. The ratios r' of the intensities of the two isotropic peaks were measured as a function of the mixing time t,, and were normalized by the equilibrium value r& measured under the condition that t , + GD; r(t,) = r'(tm)/rLq, where r(t,) is the normalized value. The values of In [ 1 + r(t,)/ 1 - r(t,)] were plotted against t,. If the sample has a single-spin diffusion time constant &,, this plot becomes a straight line described by the equation I .5 p s . &, is obtained from the gradient of this line. Fig. 2 shows the v, dependence of TsD for SAC.The spin-diffusion process is well described by a single time constant T,,, except when v, > 4.9 kHz. For these regions of u,, significant deviations from eqn (58) were observed (fig. 3). The average value 7'& was determined by using the equation Fig. 2 displays the data with error bars which express the distribution of the relaxation times. &, exhibits a deep minimum around v, = 3.9 kHz, and a shallow minimum around v, = 2.7 kHz. These frequencies correspond to and 5 of the frequency difference between the carboxy and methyl resonance lines. In fig. 4 we show the v, dependence of the T,, values for ZNP. The plots of In {[ 1 + r(tm)]/[ 1 - r(t,)]} us. t, are explained well by eqn (58) over the whole range of v,. The q,, values for ZNP decrease monotonically as v, increases.Fig. 5 shows the 13C NMR spectrum of SAC and the 31P NMR spectrum of ZNP without 'H decoupling. Each sideband resembles a Lorentzian shape. The widths at half- height, Av;, of the isotropic peaks and the sideband intensities were read from the spectra. The widths Av; decrease monotonically when v, increases (fig. 6). The v, dependences of T,, were analysed in terms of the theory proposed in section 2. We consider only the dipolar mechanism here, because the J-coupling is expected to be much smaller than the dipolar interaction for both the compounds studied. Since3724 Spin Diflusion in Solids under MAS 10 1 0.5 1.0 3.0 5.0 vr /kHz Fig. 2. The rotational frequency v, dependence of the spin-diffusion time constant T,, of SAC.The closed and open circles show the experimental and the calculated values, respectively. The exchange of the magnetization cannot be described by a single spin-diffusion time constant T,, above 4.9 kHz. The average values T,, were determined by the method described in the text and are shown with error bars. 0 tm 5 - 2.0 n I 4 v \ n + d v 4 I .o 0 10 20 30 cm /ms Fig. 3. The mixing time I,, dependence of In (I+ r ) / ( I - r), where r represents the normalized ratios of the intensities of the two isotropic peaks. The data for v, = 5480+20 Hz show deviation from the linear dependence given by eqn (58).A . Kubo and C. A . McDowell (4 I 3725 ZNP vr = 4120k20Hz O O k 50 I I I I I ZNP 0 80 0 0 eo I .o 5.0 v, IkHz Fig. 4. The rotational frequency v, dependence of the spin-diffusion time constant T,, of ZNP.The closed and open circles show the experimental and calculated values, respectively. I I 1 -5 0 5 vr = 4720220Hz 1 . -10 0 10 V k H Z Fig. 5. The 13C NMR spectrum of SAC (a) and 31P NMR spectrum of ZNP (b) without 'H decoupling condition. there is more than one pair of S spins interacting with each other in the crystals, the strength of the dipolar interaction d2 in eqn (23) should be replaced by the lattice sum k k where rik is the internuclear distance between ith S , spin and the kth S, spin. The values of x k dik were calculated from the known crystal-structural data.*** 51 The +or and f 2 0 r components of the zero-quantum spectra, KR*(+or) and3726 1 .o Spin Diffusion in Solids under MAS 2.0 5.0 v, /kHz Fig.6. The rotational frequency v, dependence of the widths at half-height Av; for each of the two resonance lines, in 13C NMR spectrum of SAC and in 31P NMR spectrum of ZNP. The solid circles (0) and the open circles (0) are the widths of the carboxyl and the methyl isotropic peaks of the 13C NMR spectrum of SAC. The solid triangles (A) and the open triangles (A) are the widths of the 95.5 and 99.5 ppm peaks of the 31P NMR spectrum of ZNP, respectively. KR,( & 2wr), were calculated from the observed single-quantum spectra using eqn (38). The calculated rotational frequency v, dependences of T,, are shown in fig. 2 and 4 by open circles. The calculated T,, values for SAC show a similar v, dependence as the experimental T,, values. The calculated T,D values for ZNP are in good agreement with the experimental values.When the spinning frequency is increased, the width of the zero-quantum line, 27r/TR, is expected to decrease in the same manner as the width of the single quantum line measured without 'H decoupling. If 2n/T, becomes much smaller than or, only specific sidebands of the zero-quantum line can contribute to spin diffusion. We discuss the two cases; (1) A o z 0, w, % 27c/TR and ( 2 ) A o = no,, or % 27r/TR. ZNP is an example of the first case, while SAC corresponds to the second one. In the first case Am z 0, the spin-diffusion time constant due to the dipolar coupling is given by (60) 1 d2 TR - = - (Il + I-1 + ;I2 + ;Ip2) TFD 15 1 +Aw2Tk' When the spinning speed is increased, all the sideband intensities In where n # 0, and the widths 2n/TR of the zero-quantum lines, decrease.If A o # 0, the condition A o > 27r/TR is satisfied at high spinning speeds. Eqn (60) can be rewritten as 1 d2 1 - = - ( I l + L 1 + ; I 2 + L I )- T:,, 15 -' Ao2TR' In this equation the two effects, the decrease of the sideband intensities and the decrease of the width, act in the same direction. Spin diffusion between spins with Ao # 0 can be suppressed at the high spinning speed limit. If, however, A o = 0, eqn (60) becomesA . Kubo and C. A . McDowell 3727 In this case the two effects consequent on increasing the spinning speed may cancel each other. It may, however, be possible to observe spin diffusion even in the high spinning- speed limit. We also have to distinguish between two possibilities for the spin pair with the same principal values of the chemical shielding tensors, because they may or may not have the same orientations.In the former case only, the dipolar interactions can contribute to the spin diffusion. It would be interesting to see if there is a difference in the w, dependence of T,, in both cases. When Aco % 0, LO, 9 2;n/TR, the spin-diffusion time constant due to J-coupling, G,, is given by 1 (zl+I-l++12++I-2) ) 1 +:E2Tk' (63) From comparison with eqn (60), the symmetric part of the J-coupling can contribute spin diffusion only when A J 2 - (1 +$) - d 2 . 9 This mechanism is limited to heavy atoms. The isotropic part, or the antisymmetric part, can be observed if d 2 15 Ji",, I, - - (Il + I-, + + iI-2) or Since the ratio (Il+Z-J/I0 decreases as the spinning frequency is increased, it is not impossible to observe these mechanisms in the high-speed spinning experiments.It is also possible to observe these mechanisms selectively if a train of the ;n-pulses is applied to the S spin system during the mixing time to eliminate the sidebands from the zero- quantum spectra. In the second case when Aw = n q , the spin diffusion time constant cD due to the dipolar interaction is given by If' n = 1 or k2, spin diffusion is expected to be greatly enhanced, because eqn (64) includes the isotropic peak intensity I,. The experimental values of T,, for SAC (fig. 2) show a deep minimum at Aco 2co, and a shallow minimum at ALO % 3~0,. The latter minimum is caused by the first and second sidebands of the zero-quantum line.A similar observation and explanation have been reported by Andrew et a1.46747 for 31P spin diffusion in a rotating sample of polycrystalline phosphorus pentachloride ; this phenomenon is rotational relaxation r e s ~ n a n c e . ~ ~ Another interpretation of this phenomenon is also possible. From eqn (10) T,, may be written as Eqn (65) consists of the time correlation function of XT(t), i.e. the flip-flop term of the3728 Spin Diffusion in Solids under MAS dipolar or the J-coupling Hamiltonian expressed in the interaction representation. This equation corresponds to the o = 0 Fourier component of the correlation function The quasi-static term of X,*(t) determines the spin-diffusion time constant qD. This concept may be useful for the interpretation of other phenomena observed with rotating samples under MAS conditions, such as the dipolar lineshapes** 4 7 9 50 and the excitation of the multiquantum coherence under MAS conditions. We consider the case where there are dipolar SD? s2 and chemical-shift interactions SC,,, S c S 2 .The time dependence of the dipolar Hamiltonian expressed in the interaction representation is given by 53 2S,, S,, - isl+ S,- exp - is,- S,, exp [ - i (Aot + [ tR(tl) dt,)]} tDsls2(t) = - d ( 2S1, S,, A$,s2 exp (imm, t ) m - + l , + 2 - _ 2 c S,, S,- A s l s 2 Il exp {i[(m + I ) or + Am] t> m - * l , * 2 1 S,-S,+ A$ls2Z, exp{i[(m-I)w,-Ao] t } m - r t l , + Z 1 The Hamiltonian can be truncated in the same way as we truncate the dipolar or the quadrupolar Hamiltonian, when we need to calculate the lineshape in a high magnetic field.If n o , + A o z 0, the truncated Hamiltonian tX* ( t ) is given by D s l S 2 c S,, Sz- A$,s2 In-m exp [i(no, + Am) t] d “X;, ( t ) = -- 2 m - + l , + 2 1 2 2 S,- S,, A$,s2 Zm+n exp [ - i(no, + Ao)t]. (68) d -- 2 m - + l , + 2 The time dependence of the operator B can be calculated from the expression Tr {BtU0(t)-lp(O) Wo(t)). Here Uo(t) is the time-evolution operator of the truncated Hamiltonian : and p(0) is the initial density matrix. From this equation it is clear that there are still quasi-static terms of the dipolar interactions even under MAS conditions. For example, when Am = 0, the truncated Hamiltonian becomes C S1- S,, A21s2Zm. (70) d d ( t ) = -- C S,, Sz- A>isz Im -- 1 2 2 m-+1, + 2 2 m - - + l , + 2A .Kubo and C. A . McDowell 3729 The second moment of the S, resonance line can be calculated from the expression This concept may also be useful in the following new experiment. Further modulation , of the spin Hamiltonian can be introduced by applying special r.f. pulses or multiple pulses. It is then possible to create the quasistatic Hamiltonian from the non-secular terms. For example, the flip-flop term S , I- can become the quasistatic Hamiltonian if we apply the r.f. field from the z direction with the frequency cu,-cus. The time dependence of the term S+I- in the interaction representation is given by Uo(t)-l S+ I- Uo(t) = S+ I- exp i (cus -coo,) t + (cu,, - q,) cos (a, -us) t , df,)] (72) where cu,, = ys H,,, and cu,, = y, Hl,.H,, is the amplitude of the r.f. magnetic field applied from the z direction. We can rewrite eqn (72) by using the Bessel functions of the mth kind, Jm(x), as [ ( s: The term m = - 1 in eqn (73) is the static term. Since S, and I, do not commute with S+ I-, the interaction S+ I- may be observable by monitoring the change of S, or I, after applying r.f. irradiation from the z direction. We thank the Natural Sciences and Engineering Research Foundation of Canada for grants to C.A.McD. Also A.K. thanks the Killam Foundation for the award of a postdoctoral fellowship. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 E. R. Andrew, A. Bradbury and R. G. Eades, Nature (London), 1959, 162, 1659. I. J. Lowe, Phys. Rev. Lett., 1959, 2, 285. S. R. Hartmann and E.L. Hahn, Phys. Rev., 1962, 128, 2042. A. Pines, M. G. Gibby and J. S. Waugh, J. Chem. Phys., 1973, 59, 569. J. Schaefer and E. 0. Stejskal, J. Am. Chem. SOC., 1976, 100, 1031. C. A. Fyfe, Solid State NMR for Chemists, (C.F.C. Press, Guelph, 1983). E. Lippmaa, M. Alla and T. Turherm, Proc. Of 19th Congr. Ampere (Groupement Ampere, Heidelberg, 1976), p. 113. M. M. Maricq and J. S. Waugh, J. Chem. Phys., 1979, 70, 3300. J. Herzfeld and A. E. Berger, J. Chem. Phys., 1980, 73, 6201. J. Jenner, B. H. Meier, P. Bachman and R. R. Ernst, J. Chem. Phys., 1979, 71, 4546. M. G. Munowitz, R. G. Griffith, G. Bodenhausen and T. W. Hwang, J. Am. Chem. SOC., 1981, 103, 2529. M. Munowitz and R. R. Griffith, J. Chem. Phys., 1982, 76, 2848. M. Munowitz, W. P. Aue and R. G.Griffith, J. Chem. Phys., 1982, 77, 1686. W. P. Aue, D. J. Ruben and R. G. Griffin, J. Chem. Phys., 1984, 80, 1729. G. R. Harbison and H. W. Spiess, Chem. Phys. Lett., 1986, 124, 128. E. M. Menger, S. Vega and R. G. Griffith, J. Am. Chem. SOC., 1986, 108, 2215. J. Herzfeld, J. E. Roberts and R. G. Griffin, J. Chem. Phys., 1987, 86, 597. G. S. Harbison, V. D. Vogt and H. W. Spiess, J. Chem. Phys., 1987, 86, 1206. Y. Yang, M. Schuster, B. Blumich and H. W. Spiess, Chem. Phys. Lett., 1987, 139, 239. A. E. DeJong, A. P. M. Kentgens and V. S. Veeman, Chem. Phys. Lett., 1984, 109, 337. H. Miura, T. Terao and A. Saika, J. Chem. Phys., 1986, 85, 2458.3730 Spin Diflusion in Solids under MAS 22 (a) D. Suter and R. R. Ernst, Phys. Rev. B, 1982, 25, 6038; (b) D. Suter and R.R 23 G. Bodenhausen, R. Freeman and G. A. Morris, J . Magn. Heson., 1976, 23, 17 24 P. Caravatti, G. Bodenhausen and R. R. Ernst, J . Magn. Reson., 1983. 55, 88. 25 P. Caravatti, M. H. Levitt and R. R. Ernst, J . Magn. Reson., 1986, 68, 323. 32, 5608. R. Freeman, J. Magn. Reson., 1978, 29, 433. Ernst, Phys. Rev. B, ; G. A. Morris and 26 N. M. Szeverenyi, M. J. Sullivan and G. E. Maciel, J. Magn. Reson., 1982, 47, 462. 27 T. A. Cross, M. H. Frey and S. J. Opella, J . Am. Chem. Soc., 1983, 105, 7471. 28 H. T. Edzes and J. P. C. Bernards, J. Am. Chem. Soc., 1984, 106, 1515. 29 P. Caravatti, P. Neuenschwander and R. R. Ernst, Macromolecules, 1986, 19, 1889. 30 P. Caravatti, J.A. Deli, G. Bodenhausen and R. R. Ernst, J . Am. Chem. SOC., 1982, 104, 5506. 31 M. Linder, P. M. Henrichs, J. M. Hewitt and D. J. Massa, J . Chem. Phys., 1985, 82, 1585. 32 K. Takegoshi and C. A. McDowell, J. Chem. Phys., 1986, 84, 2084. 33 P. M. Henrichs, M. Linder and J. M. Hewitt, J . Chem. Phys., 1986, 85, 7077. 34 A. Kubo and C. A. McDowell, J . Chem. Phys., 1988, 89, 63. 35 N. J. Clayden, J . Magn. Reson., 1986, 68, 360. 36 H. Kessemeier and R. E. Norberg, Phys. Rev., 1967, 155, 321. 37 V. Haeberlen and J. S. Waugh, Phys. Rev., 1969, 185, 420. 38 A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, New York, 1961) chap. 39 H. W. Spiess, in NMR, Basic Principles and Progress (Springer, Berlin, 1978), vol. 15. 40 0. W. Sorensen, G. W. Eich, M. H. Levitt, G. Bodenhausen and R. R. Ernst, Progr. NMR Spectrosc, 41 W. P. Rothwell and J. S. Waugh, J . Chem. Phys., 1981, 74, 2721. 42 D. Suwelack, W. P. Rothwell and J. S. Waugh, J. Chem. Phys., 1981, 73, 2559. 43 A. Schmidt, S. 0. Smith, D. P. Raleigh, J. E. Roberts, R. G. Griffin and S. Vega, J . Chem. Phys., 1986, 44 J. H. Shirley, Phys. Rev. B, 1965, 138, 979. 45 D. R. Dion and J. 0. Hirschfelder, in Adv. Chem. Phys. ed. I. Prigogine and S. Rice (Wiley, New York, 46 E. R. Andrew, A. Bradbury, R. G. Eades and V. T. Wynn, Phys. Lett., 1963, 4, 99. 47 E. R. Andrew, S. Clough, L. F. Farnell, T. D. Gledhill and I. Roberts, Phys. Lett., 1966, 21, 505. 48 T. Ito, T. Igarashi and H. Hagihara, Acta. Crystallogr., Sect. B, 1969, 25, 2303. 49 J. S. Frye and G. E. Maciel, J . Magn. Reson., 1982, 48, 125. 50 D. P. Raleigh, G. S. Harbison, T. G. Neiss, J. E. Roberts and R. G. Griffin, Chem. Phys. Lett., 1987, 51 T. S. Cameron, Kh. M. Mannan and Md. Obaidur Rahman, Acta. Crystallogr., Sect. B, 1976, 32, 52 C. Connor, A. Naito, K. Takegoshi and C. A. McDowell, Chem. Phys. Lett., 1985, 113, 123. 53 B. H. Meier and W. L. Earl, J . Chem. Phys., 1986, 85, 4905. 54 S. Vega, E. T. Olejniczak and R. G. Griffin, J . Chem. Phys., 1984, 80, 4832. 55 A. Schmidt and S. Vega, J . Chem. Phys., 1987, 87, 6875. VIII, eqn (33). 1983, 16, 163. 85, 4248. 1976), vol. 35. 138, 285. 87. Paper 8/0055 1 F ; Received 9th February, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403713

出版商:RSC    

年代:1988

数据来源: RSC

摘要:

J . Chem. SOC., Furuduy Trans. 1, 1988, 84(11), 3731-3745 The Nuclear Magnetic Resonance of 129Xe trapped in Clathrates and some other Solids J. A. Ripmeester,* C. I. Ratcliffe and J. S. Tse Division of Chemistry, National Research Council of Canada, Ottawa, Ontario KIA OR6, Canada lZ9Xe NMR spectra were obtained for xenon trapped in the cages of clathrate hydrates and a clathrasil sample. The data, together with shift data for solid xenon, have yielded a linear correlation between the radius of the free space available to the xenon atom and the chemical shift. This observation cannot be rationalized by using simple binary collision theory. In order to account for the observation of anisotropic chemical shifts for xenon trapped in non-spherical environments a simple multiple-site model was developed.Several applications of 129Xe NMR spectroscopy are also presented. These include the identification of new clathrate hydrates, the use of '*'Xe NMR to follow changes in site symmetry in a clathrasil and a cyclodextrin inclusion compound, and the observation of trapping sites in crystalline and amorphous solids. Atomic 12'Xe, owing to its large polarizable electron cloud, has chemical shifts which are extremely sensitive to the physical surroundings of the xenon nucleus.1v2 The low- temperature solid has its resonance ca. 300 ppm downfield from the dilute gas. "'Xe NMR chemical shifts have been measured in binary mixtures of gases,3 and in dilute systems these can be understood in terms of a pairwise interaction model. More empirical approaches have been used in attempts to understand the chemical shifts of xenon dissolved in condensed phase^.^-^ For liquids, an approach based on a continuum model for the condensed phase has been used with some S U C C ~ S S .~ Several approaches have been formulated to account for the chemical shifts of xenon trapped in ze01ites.~'~ One of these correlates the chemical shift with the mean free path of the xenon atom,5 the other with the degree of curvature of the interacting surface.' However, detailed correlations of chemical shifts with structure are not well understood. Zeolites are not ideal materials to follow such correlation~,~-~~ as they are made up out of interconnected channels and cages, often with the locations of the exchange cations unknown.Also, the presence of diffusion is a complicating factor. Materials which appear to be ideally suited to test shift-structure relationships are the clathrates, where a xenon guest atom is located in a crystalline host lattice and localized in a well defined ~age.~O-'~ The clathrate hydrates15* l6 and the structurally related cIathrasilsl7 are particularly convenient host systems, as their structures have several types of cage which are not too far from being spherical. Past on the NMR of xenon trapped in the two types of cages of its structure I hydrate showed a downfield shift for xenon in the smaller cage. Also, there was a correlation of the cage shape with the observation of an anisotropic chemical shift. In this contribution, we further explore the relationship between cage size and shape and the chemical shift of the trapped xenon.Then the state of theory available for 12%e chemical-shift calculations will be reviewed, and finally several applications of 12'Xe NMR will be presented. 373 13732 NMR Study of 12’Xe in Solids Experimental In this section we will briefly mention some of the factors which influence the ease with which 12’Xe NMR signals can be obtained. The 12’Xe isotope, with 26.44% natural abundance and gyromagnetic ratio close to that of 13C, should be an excellent nucleus for NMR observation. One factor which rules against this is the absence of efficient spin-lattice relaxation mechanisms, so that for trapped xenon atoms relaxation times of 5-20 min can easily result. In polycrystalline solids where there is an anisotropic chemical shift, and therefore, considerable line broadening, this can lead to intolerably long acquisition times in order to attain a sufficient signal-to-noise ratio.However, in solids the possibility of using polarization transfer techniqueslg becomes an attractive possibility if an abundant nucleus such as the proton is present. The cross- polarization technique, as almost universally practiced today uses matching of the rare- spin and abundant-spin energy levels in the rotating reference frame (Hartmann-Hahn matching). This requires the presence of nuclear dipolar coupling between the abundant and rare spins. For quantitative work the relationship between spectral line intensities and the cross-polarization time must also be explored.In the case of rigidly held directly bonded nuclei, cross-polarization can be complete in times the order of 1 ms or less.2o However, in the case of 12’Xe, where abundant nuclei (protons) are always at least ca. 0.3 nm away, the cross-polarization process takes some tens of ms.lS One interesting advantage of the cross-polarization techniques is that it provides a way of discriminating against the signal from bulk xenon, since the signal can only arise from Xe atoms near to the protons. 12’Xe NMR spectra were obtained on a Bruker CXP-180 NMR spectrometer at a frequency of 49.8 MHz. In cross-polarization experiments, single contacts were used with r.f. field amplitudes of 3&60 kHz. Experiments at 77 K were performed by immersion of the sample directly in liquid nitrogen.Other temperatures were achieved with a conventional gas-flow system and a Bruker BVT- 1000 temperature controller. Magic-angle spinning experiments at room temperature were carried out with a probe utilizing Andrew-Beams spinners. Spinning experiments at low temperatures were performed by using a Chemagnetics probe and temperature controller. The preparation of hydrate,2’ clathrasil17 and cyclodextrin22 samples has been described previously. Results and Discussion Chemical-shift Correlations Isotropic Shifts For the sake of completeness, fig. 1 shows the previously reported 12’Xe NMR spectrum of the type I xenon hydrate,l3? la in addition to spectra of other xenon containing hydrate structures. The low-field, isotropic line of the type I spectrum can be assigned to xenon in the small cage, whereas the high-field line characteristic of an axially symmetric shielding tensor can be assigned to xenon in the more abundant type I large cages.Since the stability of clathrate hydrates depends on non-specific interactions between guest and host, the larger species in a mixture of guests usually determines the structure type due to efficient space-filling of the larger cages. Distribution of guests over the available sites then is determined by the appropriate Langmuir constants and the activities of the guests. The NMR spectrum of 12’Xe in type I1 hydrate was obtained for a mixed xenon-propane hydrate with most of the large cages filled with propane. The signal at high field can be assigned to large cage xenon, whereas the low-field signal, with a pronounced anisotropic chemical shift, can be assigned to xenon in the small type I1J. A .Ripmeester, C. I. Ratelife and J . S. Tse 12 - hedr al 14-hedral 12-hedral 16- hedral 12-hedral A 12-hedral I 100 ppm I 3733 Fig. 1. lz9Xe NMR spectra obtained at 77 K with cross-polarization of (a) Xe type I hydrate. (b) Xe-propane type I1 hydrate and ( c ) Xe-methylcyclohexane type H hydrate. cage. As a general rule, the lineshapes are isotropic for Xe in cages of cubic symmetry, otherwise they show various degrees of anisotropy and asymmetry. If the cage has a unique symmetry axis, an axially symmetric lineshape can be expected. The clathrasil dodecasil-3C in its high-temperature cubic phase is isostructural with type I1 hydrate,23 and as such provides two cages of similar shape and size as type I1 hydrate, but with a SiO, host lattice.The I2’Xe NMR spectrum of a dodecasil-3C sample with tetrahydrofuran and xenon as the main guests is shown later in fig. 6(a), and is reasonably similar to that of type I1 hydrate. The low-field line, due to xenon in the small cages, has the same sign of chemical-shift anisotropy with Aa of 44.9 ppm. The high-field line due to xenon in the spherical large cages has no noticeable anisotropy. Table 1 lists the clathrate types, the cages which occur, their symmetries and free van der Waals’ radii. The latter parameters were derived from the known structures by locating the cage atoms (0 for the hydrates, Si for the clathrasil), calculating th: mean radius .Of the cage, then subtracting the cage atom van der Waals’ radius (1.40 A for 0, 1.96 A for Si).The correlation between chemical shift and van der Waals’ radius of the trapping site is shown in fig. 2. Some additional data at the low-field end of the scale can be obtained by considering solid xenon itself. From the known xenon lattice parameters2* 9nd a xenon van der Waals’ radius derived from the structure determined at 4 K (2.167 A) the radius of the free space available to a xenon atom can be calculated. The overall correlation of the mean free radius of the space available to a xenon atom with the isotrqpic chemical shift is remarkably close to linear, with a slope of - 5.147 x A (ppm)-’. This observation is perhaps surprising in view of the very different interactions that the Xe atom experiences in the different structures.3734 NMR Study of IzgXe in Solids -300 -250 -200 - 150 - 100 - 50 0 (7 (PPm) Fig.2. Correlation of 129Xe isotropic NMR chemical shifts with the free-space radius available to the xenon atom: (1) solid Xe, 21 K; (2) solid Xe, 160 K; (3) dodecasil-3C, small; (4) structure I, small; ( 5 ) structure I, large; (6) structure 11, large; (7) dodecasil-3C, large. Table 1. Summary of cage characteristics and chemical-shift data 0xe(iSO) A o X e structure cage type" symmetry r,/Ab (pprnlc (ppm) hydrate type I hydrate type I hydrate type I1 hydrate type I1 hydrate type H hydrate type H hydrate type H clathrasil dodecasil-3C clathrasil dodecasil-3C m3 42m 3m 43m mrnm 62m 6/mm m3 43m - - 2.50 - 242 2.93 - 152 2.50 - 225 3.28 - 80 2.50 - 232 - -215 2.46 - 253 3.35 -81 - - 0 32 18 0 ca.-= 5 ca. 40 45 0 - " 51262 means that there are 12 pentagonal and 2 hexagonal faces. Mean free radius. Measurements for hydrates made in 200-240 K range for clathrasils at room temperature. Anisotropic Sh ijts All experiments to date indicate that the smaller the cavity in which the Xe atom sits the further downfield is the isotropic chemical shift. The Xe chemical-shift anisotropy tensors for cages which have a unique symmetry axis are found to be axial (see table 1). This requires the oZz component of the tensor to be aligned parallel to the unique symmetry axis. Naively one might expect that if the symmetry axis were also the shortest axis of the cage then B,, would be the low-field component (i.e.anisotropy negative) and vice versa if the symmetry axis were the longest. The results show the exact opposite: Xe in oblate cavities (e.g. structure I hydrate, large cage, and structure I1 hydrate, small cage) shows axial tensors with positive anisotropy, and in prolate cavities (e.g. phenol and P-quinol clathrates)". l4 shows axial tensors with negative anisotropy. [We initiallyJ . A . Ripmeester, C . I . Ratclifle and J . S. Tse 3735 had doubts about whether Xe-P-quinol fit into this pattern, since the cage in P-quinol clathrates has often been described as spherical. However, based on the X-ray diffraction structure of H,S-P-quinol (since the cell for Xe-P-quinol is not known) some simple calculations based on van der Waals’ contacts clearly indicated that the Xe would have more freedom along the three-fold axis of the cage, i.e.the cavity is prolate for Xe.] We are thus faced with the problem of explaining this apparent paradox between the cavity shape/anisotropy sign and the size/shift correlations. One simple model is as follows. Instead of regarding the tensor as that of a static Xe atom at the cage centre, assume that it is an average tensor arising from motion of the Xe atom over the surface of the cavity. This is inherently more plausible than a static Xe atom, since calculations using van der Waals’ hard-sphere contacts indicate that there is room for motion. We have also carried out Lennard-Jones potential calculations for Xe in hydrate cages and find that for large cages the minimum potential is not at the cage centre, and for smaller cages, where the minimum is at the centre, the potential remains quite low for modest excursions from the centre.It is assumed that at any particular site on the inner surface the chemical-shift tensor is axial and has a fixed anisotropy (which we will refer to as the static anisotropy). Further it is assumed that this tensor is oriented such that its o,, component is normal to the surface of the cavity. We know that the observed tensor must be oriented with its o;, along the unique axis of the cage (the prime notation is used to refer to the averaged tensor component). Consequently if we set up the description of the static tensor for any site in terms of this particular cage-fixed coordinate system and then average over all sites the resultant tensor will be diagonal.Furthermore, since the symmetry about this axis is greater than two-fold the averaged tensor must also be axial. We can also apply the axial symmetry to simplify the calculations, since for any particular site which has o,, oriented at an angle a with respect to the cage fixed z axis we can apply axial averaging among that and all other sites at an angle P around the cage axis. The result for such axial averaging at a particular angle is well known for three-fold reorientation of such groups as -CH, or -NHl, although this all follows from standard procedures as outlined by others:25 A 0 2 AoaV = -(3 COS~P- 1) where Aoav is the anisotropy of the averaged tensor at angle p and Ao is the static anisotropy.We must then calculate the population-weighted average over all values of B to obtain the averaged tensor anisotropy for the whole cavity: where PI( is the population at Pi. A simple approximation for is to equate it to the surface area for the element at pi. It is trivial to apply this model to a few simple cavity shapes which have only one or two types of angle populations. A cube, a regular octahedron or a cylinder with height equal to its diameter all give averaged anisotropies of zero. However, if stretched along their axes they all give negative anisotropies, and if compressed they give positive anisotropies. One finds a similar picture for ellipsoidal cavities, although the calculation is not so trivial. A sphere gives zero anisotropy (as it should) and a compression (oblate ellipsoid) produces a positive anisotropy .So the general pattern emerging from this3736 NMR Study of 12’Xe in Solids model is that prolate cavities give negative anisotropy and oblate ones give positive anisotropy. Provided we recognise and accept the implicit assumption that the static tensor has positive anisotropy, this can therefore explain the observed relationship between anisotropy and cavity shape. However, having derived this, one should reflect on the assumptions which have been made. The most serious of these are probably the ones concerning the static tensor, i.e. it is not likely that the static tensor will be strictly axial nor is it likely that it will be identical at every site. However, small divergences may not have a large effect on the calculated average.Theoretical Considerations According to Ramsey’s theory,26 the magnetic shielding of a nucleus can be divided into two components : the diamagnetic term and the paramagnetic term. The diamagnetic term is largely dominated by the contribution from the core electrons. Since the interactions between a free xenon and other molecules are dispersive, there is apparently no need to invoke covalancy in order to rationalize the variation of magnetic shielding in Xe.27 In addition, it is unlikely that the diamagnetic term will be sensitive to the environment. In contrast, the paramagnetic term is related to the induced excitations of the valence electrons into empty and continuum levels by the magnetic field, and it is the dominant contribution to the nuclear shielding for heavy elements. Therefore, the change in the paramagnetic term is mostly responsible for the variation of the 12’Xe nuclear shielding in different physical environments. The variation of the 12’Xe chemical shift in gaseous Xe under pressure has been studied in A virial expansion was used to analyse the experimental results. It was shown28 that at low pressure the chemical shift varies linearly with the pressure.This result suggests that binary collisions (or more exactly, two- body interactions) are the dominant processes at low pressure. At high pressure, higher-order terms (such as three- body interactions etc.) have to be taken into account. In mathematical terms the 12’Xe chemical shielding as a function of the density of the gas can be expressed as a(T,p) = a0+pa,(T,p)+p2a,(T,p)+ * .. * (3) The coefficients of the virial expansion an may be obtained by fitting the experimental data to eqn (3). According to statistical mechanics8 the first virial coefficient a1 can be written as the thermodynamic average of the two-body interactions : q(T, P ) = apW exp [ - W / k T I dr (4) s where a,(r) is the 12’Xe chemical shift when Xe interacts with another molecule at separation r and U(r) is the interaction potential. In principle, if both functions are known eqn (4) can be solved by Monte Carlo simulation and a comparison with experiment can be made. Unfortunately, in reality, an accurate interaction potential is very difficult to construct and knowledge of ap(r) is even scarce^.^' So far, there is no satisfactory theory which describes the nature of the two-body chemical-shift function although several approximate forms have been ~uggested.~’ Some models only consider the contribution from the diamagnetic term and evidently these will not be applicable to Recently, through the studies of “’Xe chemical shifts in different cages in the it was advocated that if the binary collision model is correct, the 12’Xe chemical shielding should be proportional to the number of collisions between the xenon and the atoms forming the cages.5 This conjecture was later tested in a series of calculations and it was found empirically that the chemical shift is inversely proportional to the ‘mean free path’ of Xe in the cage.This simple relationship, however, is not easily comprehended in view of the discussion presented above. Note that the binary collision 129Xe.30J. A . Ripmeester, C. I . Ratclifle and J . S. Tse 3737 model is only strictly valid for dilute gas interactions. Furthermore, the pairwise interaction chemical-shift function is weighted by the Boltzmann distribution which in turn is governed by the interaction potential. Also, this inverse relationship cannot account for the experimental observations presented here. It is informative, however, to analyse the two-body term of the virial expansion in detail. For xenon enclosed in a cage at moderate temperature (> 300 K), it can be assumed that the atom is situated at some equilibrium position from the cage wall. If we make the ansatz that the pairwise chemical shift can be replaced by an average value (op(0)), then eqn (4) can be written as ( 5 ) 01 = (o,(O)) I,.exp [- W l k T I dr- The volume integral in eqn ( 5 ) can be solved using the Lennard-Jones and Devonshire cell If the free volume in the encaged cavity is denoted by 6, then The chemical shift relative to the infinitely dilute Xe gas is where Kp,, is the volume of the cavity. Treating Xe as a hard sphere with radius a and where (R-a) can be identified as the ‘mean free path’ (0 of Xe in the cage. Note here that both (a,(O)) and (U(0)) are also dependent on the nature of the cavity. In the dilute Xe gas when the atoms are far apart (i.e. R $ a), (o,(O)) is very small and the shift from the free-atom value will also be small. Unfortunately, the cubic dependence predicted by eqn (8) does not agree with the correlation shown in fig. 2, where there is a linear correlation of with R.Evidently this empirical correlation requires more than a binary collision model, and we will not carry the analysis further. Another conclusion drawn from this theoretical analysis is that consideration of the binary collision term (two-body interactions) in the virial expansion alone should give the 12’Xe chemical shift approximately proportional to the third power of the ‘mean free path’ with a negative slope. This observation is at variance with the conjecture proposed ear lie^.^ In passing, we would like to point out that eqn (8) is an over-simplified solution to eqn (4). The limited experimental data prohibits a generalization of this relationship.However, any future serious calculations on chemical shielding should start with the full expression [eqn (4)]. To this end, ab initio quantum-mechanical calculations will be very useful in predicting the binary interaction chemical-shift function.12 So far only a few first-principle calculations have been performed. A more thorough theoretical investigation on a specific example will be desirable. Applications of Solid-state 12’Xe NMR Identijication of Hydrates Fig. 1 shows 12’Xe spectra obtained for the type 1,16 IF6 and H33 clathrate hydrates at 77 K. In this instance, our main interest is in the line positions rather than in line intensities. The main point is that each hydrate gives a unique pattern which is easily identified.When powdered ice and xenon are sealed together in a Pyrex tube, type I xenon hydrate forms readily on conditioning at 0 “C. In the presence of other potential guest molecules, type I hydrate reacts to form either type I1 or type H hydrates. This is3738 NMR Study of 129Xe in Solids \ ‘U A 1-100 ppm-i I \ Fig. 3. lz9Xe NMR spectra at 77 K of the reaction product of type I hydrate with tetramethylsilane to give a type H hydrate after storage in an ice-water bath for (a) 0, (b) 4, ( c ) 16, ( d ) 24 and (e) 40 h. illustrated in fig. 3 for a sample to which tetramethylsilane (TMS) has been added as potential guest material. The sample was stored in an ice-water bath, then, it was cooled to 77 K after various !engths of storage time, and the 12’Xe spectrum was obtained.It is quite clear that type I Xe hydrate reacts slowly with TMS to give type H hydrate, as witnessed by the pattern obtained after 40 h of reaction. The reaction rate depends largely on the vapour pressure of the reacting guest material in the sealed tube. For slow reaction rates it is not necessary to wait for the reaction to go to completion. In the case of adamantane guest material it was found that little or no reaction had taken place even after several days. However, it is possible to discriminate experimentally against observing the 12’Xe signal from type I hydrate by adjustment of the delay time while collecting data. The ‘H relaxation time of type I hydrate at 77 K is relatively long, at least several tens of seconds, as there are no efficient relaxation paths.On the other hand, hydrates with proton-containing guest molecules have intrinsic ‘H dipole-dipole relaxation processes because of relatively efficient molecular reorientation. Fig. 4(a) and (b) show 12’Xe spectra obtained for the reaction product of adamantane with type I xenon hydrate obtained with delay times of 60 and 2 s. When the type I Xe pattern is scaled and subtracted from the spectrum in fig. 4(b),J. A . Ripmeester, C. I. Ratclife and J . S. Tse 3739 Fig. 4. '29Xe NMR spectra of mixed type I Xe hydrate and type H Xe-adamantane hydrate : (a) taken with 60 s delay time, (b) taken with 2 s delay time and (c) difference spectrum obtained by subtraction of (b), scaled so as to reduce the Xe type I hydrate contribution to zero, from (a), leaving only the contribution from type H hydrate.I 100 ppm 1 L Fig. 5. '*'Xe NMR spectrum of type I Xe hydrate reacted incompletely with benzene to form a type I1 Xe-benzene hydrate. the remaining spectrum clearly shows the presence of an adamantane/Xe type H hydrate. In case the potential hydrate formers promote a type I1 hydrate, this can be seen right away by the appearance of the high-field line due to xenon in the type I1 large cage (fig. 5). FAR 84 I 2 33740 NMR Study of 12'Xe in Solids Fig. 6. 129Xe NMR spectra of clathrasil dodecasil-3C with Xe and THF as guests (a) 376, (b) 295, (c) 251 and ( d ) 220 K. Iz9Xe NMR and Site Symmetry The clathrasil dodecasil-3C is the structural analogue of type I1 clathrate hydrate.23 Recently it was shown that this clathrasil undergoes a number of phase transition^.^^ The highest temperature phase is cubic, space group Fd3, with 136 SiO, groups per unit cell.23 The large cage has point-group symmetry 43m, with the small-cage symmetry being m3.23 The 12'Xe NMR spectrum of a clathrasil sample with THF as the principal guest in the large cage is shown in fig. 6(a). In agreement with the spherical nature of the large cage, the 129Xe line for xenon in this cage shows no discernible anisotropic chemical shift. On the other hand, the signal for xenon in the small cage is characteristic of an axially symmetric shielding tensor with Ao = 44.9 ppm, in agreement with the cage having a threefold axis. The room-temperature phase of dodecasil-3C is known to be t e t r a g ~ n a l , ~ ~ although the detailed structure is not known.The xenon NMR spectrum, however, does give some indication as to the way the cage symmetries change on going from the cubic to the tetragonal phase. The line associated with xenon in the large cage changes little if at all, indicating the lack of a major change in large-cage symmetry. On the other hand, the line for xenon in the small cage, now has an additional shoulder characteristic of a non-axial shielding tensor (oZz = - 5 . I , oyy = - 29.1, o,, = 34.3 ppm), showing that the cage has been distorted from axial symmetry. Slightly below room temperature, at ca. 270 K, a phase transition to a third phase takes place which so far remains uncharacterized. In this phase the non-axial character of the powder pattern is greater than at room temperature, indicating further distortion of the cage.J .A . Ripmeester, C. I. Ratelife and J. S. Tse 3741 0 CH&H A Fig. 7. 13C and 12’Xe CP/MAS NMR spectra of a Xe a-cyclodextrin inclusion compound, obtained as a function of drying time. Finally, below ca. 240 K there is a third phase transition to a phase which is probably mon~clinic.~~ The 12’Xe powder pattern is now quite complicated, and no longer can it be analysed in terms of a single set of shielding parameters. Apparently this phase has more than one kind of small cage with different shielding parameters for the trapped xenon atoms. A second example of a change in I2’Xe NMR spectrum concomitant with a change in the sample condition is provided by the Xe-a-cydodextrin (aCd) inclusion compound.With small guest molecules an a-cyclodextrin macrocycle, consisting of six anhydro- glucose units bonded head to tail, forms well ordered orthorhombic crystals.22 Usually these materials are higher hydrates, the water molecules forming part of a hydrogen- bonded network which imposes both long-range and short-range order in the crystal. Fig. 7 ( a ) shows 13C as well as 12’Xe CP/MAS NMR spectra of a fully hydrated Xe- aCd inclusion compound. The 13C NMR spectrum is relatively well resolved, and is in agreement with there being one a-Cd molecule per symmetric unit in the crystal. The 12’Xe NMR spectrum consists of a single line ca. 192 ppm downfield from the infinitely dilute gas. For a static sample the 12’Xe NMR spectrum [fig. S(a)] consists of a powder pattern characteristic of an axially symmetric shielding tensor (ACT = 22.4 ppm).These 123-23742 NMR Study of "'Xe in Solids Fig. 8. lZ9Xe NMR powder patterns corresponding to the lZ9Xe CP/MAS NMR spectra shown in fig. 7(a) and (d). Fig. 9. lZ9Xe NMR spectra at 77 K of (a) solid xenon, (b) xenon trapped in solid H,S, (c) xenon trapped in solid tetramethylsilane and (d) xenon trapped in polystyrene. Spectra (b)-(d) were obtained with cross-polarization.J . A . Ripmeester, C . I. Ratclifle and J . S. Tse 3743 chemical-shift parameters are not too different from those for xenon in the small type I hydrate cage. When water is lost on drying of the sample, the 13C NMR spectrum changes markedly, individual lines becoming much less distinct [fig. 7(b)-(d)].This is consistent with a loss of short-range order in the sample. Initially the lz9Xe NMR line shifts to high field as water is lost, perhaps consistent with greater free space available to the xenon atom. Additional loss of water causes increased loss of resolution in the 13C NMR spectrum, although it is difficult to define the changes exactly. Interestingly enough, a second xenon line appears 7.0 ppm to low field of the initial Xe line, and eventually this becomes the only observable Xe line. These observations suggest that when the water content of the crystal is reduced below a certain critical level, the cyclodextrin macrocycle collapses around the xenon atom. The static sample 12’Xe NMR spectrum for the driest sample is shown in fig.8 (b), and is characteristic of a general shielding tensor with oSs = - 6.8, oYy = - 23.3 and ozz = 30.1 ppm. The free space available for the xenon atom, therefore, is smaller and of rather lower symmetry for the dry sample as compared to the hydrated sample. When the sample is rehydrated, the original spectra are again obtained. Xe trapped in Non-clathrate Solids Some exploratory studies were carried out on xenon trapped in solids which do not have distinct cages in order to see if the 12’Xe NMR spectrum could give some information on the trapping sites. Fig. 9 shows 12’Xe NMR spectra obtained for Xe trapped in solid H,S (ca. 5 mol %), tetramethylsilane and polystyrene at 77 K. For comparison purposes a spectrum of solid Xe is also shown. The xenon containing samples were quenched in dry ice-acetone, then cooled to 77 K before a spectrum was recorded.Since ‘H-12’Xe cross-polarization was used, [spectra (b)-(d)] the signal cannot originate from a bulk xenon phase. The 12’Xe signal of xenon trapped in solid H,S consists of a single line some 100 ppm to low field of the solid xenon signal. The correlation shown in fig. 2 then suggests that xenon trapped in H,S has rather less free space than xenon in the pure solid. This is understandable if xenon replaces H,S substitutionally in the lattice, as H,S is a slightly smaller species than xenon (both have f.c.c. structures, with lattice parameters 6.3472 A (Xe at 159 K)24 and 5.805 A (H,S at 142 K35 in its plastic phase)]. For the case of xenon in polystyrene [fig. 9(d)], a very wide line (ca.150 ppm width at half height) is obtained with a peak maximum some 80 ppm to high field of the solid xenon line. Evidently there is a large distribution in the type of site available for xenon in the non-crystalline polymer. Of course, it is not possible to say if part of the linewidth must be attributed to chemical shift anisotropy. On the whole, xenon is not nearly so tightly packed in the polystyrene as in solid xenon. The 12’Xe NMR signal obtained for xenon trapped in TMS shows that there are three different types of xenon site in the TMS lattice at 77 K. We have studied a closely related system, that of xenon in neopentane (ca. 5 mol%) in greater detail. Similar to the case of TMS, xenon trapped in quenched neopentane also shows the presence of three types of site [fig.lO(a)]. If, however, the neopentane-Xe solution is cooled slowly into the range of the neopentane plastic phase (163 K), a single line characteristic of axially symmetric shielding is obtained. This can occur only if the trapped xenon occupies an asymmetric site in an otherwise cubic crystal. For instance, it could replace a vacant methyl group site where a neopentane molecule is missing from the lattice. Further cooling into the region of the neopentane brittle phase (the phase transition in pure neopentane occurs at 140 K) produces a signal shifted slightly to higher field, with no sign of anisotropic shielding. In this phase xenon appears to take up a more central position perhaps at the centre of a vacant neopentane lattice site.The spectrum obtained by quenching the sample of neopentane-Xe to 77 K [fig. lO(a)]3744 NMR Study of lzgXe in Solids Fig. 10. lZ9Xe NMR spectra of xenon trapped in neopentane. (a) Sample quenched in liquid nitrogen, (b) sample slowly cooled to 163 K and ( c ) spectra for a slowly cooled sample in the region of the solid-solid phase transition. (i) 77, (ii) 163, (iii) 127, (iv) 129, (v) 131, (vi) 132 and (vii) 134 K. evidently consists of components attributable to both the plastic and brittle phases, as well as a third component. Conclusions We have shown that the chemical shift of xenon trapped in clathrate cages correlates linearly with the mean free radius of the cage: the smaller the cage, the larger the shift from the dilute gas value becomes, Simple theoretical considerations based on a binary collision model cannot account for this trend, predicting instead a cubic dependence on the cage radius.We have also accounted for the correlation of the anisotropic chemical shift with a deviation of the cage shape from spherical symmetry in terms of a simple model. A number of applications of 129Xe NMR spectroscopy have also been presented. For instance, it was shown that the NMR spectrum of Xe trapped in clathrate hydrates can be used to identify the structure of the hydrate. It was also illustrated that xenon can be used to probe structural changes in crystal lattices, e.g. in a clathrasils and a cyclodextrin inclusion compound. Also several examples were shown which suggest that 12'Xe NMR may have a place in identifying trapping sites in materials used for matrix isolation. References 1 D.Brinkman and H. Y. Carr, Phys. Rev., 1966, 150, 174. 2 C. J. Jameson, A. K. Jameson and S. M. Cohen, J. Chem. Phys., 1975, 62, 4224. 3 'C. J. Jameson, Bull. Magn. Reson., 1981, 3, 3. 4 K. W. Miller, N. V. Reo, A. J. M. SchootUiterkamp, D. P. Stengle, T. R. Stengle and K. L. 5 J. Demarquay and J. Fraissard, Chem. Phys. Lett., 1987, 136, 314. 6 E. G. Derouane and J. B. Nagy, Chem. Phys. Lett., 1987, 137, 341. 7 T. Ito and J. Fraissard, Proc. 5th Con$ Zeolites (Heyden, London, 1981), p. 510. 8 L. C. de Menorval and J. P. Fraissard, J. Chem. SOC., Faraday Trans. I , 1982, 78, 403. Williamson, Proc. Natl Acad. Sci. U.S.A., 1981, 78, 4946.J. A . Ripmeester, C . I. Ratclie and J. S .Tse 3745 9 T. Ito and J. Fraissard, J. Chem. Phys., 1982, 76, 5225. 10 J. A. Ripmeester, J. Am. Chem. Soc., 1982, 104, 209. 11 J. A. Ripmeester, J. Magn. Reson., 1984, 56, 247. 12 T. Ito, L. C. de Menorval, E. Guerrier and J. Fraissard, Chem. Phys. Lett., 1984, 111, 271. 13 J. A. Ripmeester and D. W. Davidson, J. Mol. Struct., 1981, 75, 67. 14 D. W. Davidson and J. A. Ripmeester, in Inclusion Compounds, ed. J. L. Atwood, J. E. D. Davies and 15 G. A. Jeffrey, in Inclusion Compounh, ed. J. L. Atwood, J. E. D. Davies and D. D. MacNicol 16 D. W. Davidson, in Water, A Comprehensive Treatise, ed. F. Franks (Plenum, New York, 1973), 17 H. Gies, F. Liebau and H. Gerke, Angew. Chem., 1982, 94, 214. 18 D. W. Davidson, Y. P. Handa and J. A. Ripmeester, J. Phys. Chem., 1986, 90, 6549. 19 A. Pines, M. C. Gibby and J. S. Waugh, J. Chem. Phys., 1973, 59, 569. 20 L. B. Alemany, D. M. Grant, R. J. Pugmire, T. D. Alger and K. W. Zilm, J. Chem. Soc., 1983, 105, 21 J. A. Ripmeester and D. W. Davidson, Mol. Cryst. Liq. Cryst., 1977, 43, 109. 22 W. Saenger, Angew. Chem., 1980, 19, 344. 23 H. Gies, 2. Kristallogr., 1984, 167, 73. 24 M. S. Anderson and C. A. Swenson, J. Phys. Chem. Solids, 1975, 36, 145. 25 R. J. Wittebort, E. T. Olejniczak and R. G. Griffin, J. Chem. Phys., 1987, 86, 5411. 26 N. F. Ramsey, Phys. Rev., 1950, 78, 699; 1952, 86, 243. 27 K. Yosida and T. Morya, J. Phys. Soc. Jpn, 1956, 14, 33. 28 A. K. Jameson, C. J. Jameson and H. S. Gutowsky, J. Chem. Phys., 1970, 53, 2310. 29 F. H. A. Rummens, Van der Waals Forces and Shielding Eflects (Springer, New York, 1975). 30 R. A. Kromhout and B. J. Linder, J. Magn. Reson., 1969, 1, 453. 3 1 R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, 32 J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley, 33 J. A. Ripmeester, J. S. Tse, C. I. Ratcliffe and B. M. Powell, Nature (London), 1987, 325, 135. 34 J. A. Ripmeester, M. A. Desando, Y. P. Handa and J. S. Tse, J. Chem. SOC., Chem. Commun., in 35 E. Sandor and S. 0. Ogunade, Nature (London), 1969, 224, 905. D. D. MacNicol (Academic Press, New York, 1984), vol. 3. (Academic Press, New York, 1984), vol. 1. vol. 2. 2133. Cambridge, 1952). New York, 1954). press. Paper 8/01 105B; Received 17th March, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403731

出版商:RSC    

年代:1988

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J . Chem. SOC., Faraday Trans. I, 1988, 84(11), 3747-3759 Quadrupole Nutation Nuclear Magnetic Resonance in Solids Ron Janssen and Wiebren S. Veeman" Laboratory of Molecular Spectroscopy, University of Nijmegen, 6525 ED Nijmegen, The Netherlands The theory of nutation NMR of quadrupolar nuclei with half-integer spin is treated for two different experimental situations. In the standard experiment, x nutation, the evolution of the spins is studied when subjected to a resonant r.f. pulse of phase x. It is shown that for a spin I = 3/2 the nutation of the magnetization is described by four separate oscillatory time- dependent terms. These four nutation frequencies are determined by transitions between the four eigenstates of the spin in the rotating frame. The nutation spectrum in many cases gives much more information than a normal NMR spectrum of the same nucleus.Unfortunately, however, the nutation spectrum is sometimes too complicated to interpret. Therefore a x, ---nutation experiment is investigated where the spins are subjected to a sequence of two pulses, one with phase x and the next one with phase - x. Again four nutation frequencies are found, but corresponding to different transitions in the rotating frame than in the x nutation experiment. The calculated nutation spectra for both situations are compared with experimental spectra of NaNO,. 1. Introduction Recently there has been much interest in the powder spectra of half-integer quadrupolar spins. In particular, NMR studies of zeolites, clays and ceramics have emphasized the need to obtain structural information from NM R spectra of half-integer quadrupolar spins such as 27Al and 23Na.In comparison with nuclear spins with spin quantum number I = 1/2, the NMR spectra of quadrupolar spins contain two new features : (1) several NMR transitions are possible within one spin multiplet and (2) the transition frequencies are not only determined by the interaction between the magnetic dipole moment of the nucleus and the external magnetic field, but also by the interaction between the nuclear electric quadrupole moment and the electric field gradient at the site of the nucleus. The information contained in an NMR spectrum from a quadrupolar spin is therefore not limited to the chemical shift, but such a spectrum can in principle also provide the parameters that describe the electric quadrupole interaction.Since these parameters depend on the local symmetry around the nucleus they can give direct structural information, usually in a more easily interpretable way than from chemical-shift parameters. Traditionally, quadrupole parameters can be determined by NQR, nuclear quadrupole resonance : usually no or only a weak magnetic field is present, and the nuclear spin levels are split mainly by the quadrupole interaction. The main disadvantage of NQR is its low sensitivity when the quadrupole interaction is small, a situation often encountered for many nuclei in many materials. The great advantage of NQR, at least when no magnetic field is used, is the absence of any external quantization axis and therefore the absence of anisotropic broadening in the spectrum.A recent technique which combines this advantage with the high sensitivity of high- field NMR is the zero-field NMR experiment, where the evolution of the spins is studied 37473748 Quadrupole Nutation NMR in Solids outside the magnet and the signal detected in the magnet.' The only disadvantage of this technique is the requirement that the nuclear spin-lattice relaxation time has to be at least of the same order of magnitude as the time it takes to shoot the sample in and out of the magnet (ca. 50 ms). For quadrupolar spins this condition is often not fulfilled. In a regular NMR experiment of a quadrupolar spin the high relative sensitivity is accompanied by more or less severe line broadening due to the anisotropy of the quadrupole interaction.Well-established line-narrowing techniques such as magic- or variable-angle spinning2 do narrow the quadrupole- broadened line, but for most practical cases do not completely remove the line broadening. When the quadrupole interaction is not very small, for half-integer spins usually only the (1/2, - 1 /2) transition is observed. The linewidth of this transition is inversely proportional to the magnetic field strength, and it is therefore advantageous to employ the highest field available. A factor that can limit the gain in resolution at higher magnetic fields is the line broadening due to chemical-shift anisotropy in the absence of magic-angle spinning or due to chemical-shift distribution with magic-angle spinning.For this situation nutation NMR can be helpful. In this two-dimensional experiment, introduced by Samoson and L i ~ p m a a , ~ the precession of the spins around the B, field in the rotating frame, the nutation, is Fourier-transformed to give the nutation spectrum. For spins I = 1/2 the nutation frequency is simply R,, = yB,, where y is the gyromagnetic ratio. For half- integer spins I = 3/2, 5 / 2 , 7/2 and 9/2 the situation is more complicated. For I = 3/2, for instance, four nutation frequencies are found which correspond to transitions between the eigenstates of the rotating frame Hamiltonian. These frequencies are complicated functions of the r.f. field strength and quadrupole intera~tion.~* For two extreme situations the four nutation frequencies merge into one frequency : when the quadrupole is negligibly small relative to the interaction of the spins with the r.f.field, the nutation frequency becomes R,, = yB,, and in the opposite case this frequency is given by (I+ i) Rrf. By measuring the nutation frequency one therefore obtains in a quick but qualitative way information about the size of the quadrupole interaction. Nutation NMR has been used in this way to study the effect of hydration on the local symmetry in zeolites.'-' For the intermediate case, when the quadrupole interaction is comparable to the r.f. field interaction, the nutation spectrum is much more complicated owing to the existence of several different nutation frequencies which give powder patterns (see below) which partly or strongly overlap in the nutation spectrum.In the original and most simple set- up of the nutation experiment the spins nutate around the B, field, which has a particular phase, say.x. We shall refer to this experiment as x nutation. Since the nutation spectrum that results from such an experiment may show many overlapping nutation lines, it is valuable to investigate whether nutation experiments can be designed which result in nutation spectra that are easier to interpret. In this paper we report theoretical and experimental results of an x, -x nutation experiment where the spins are subjected to a sequence of two pulses with phase x and -x. For the calculation of nutation spectra it is necessary to diagonalize the rotating- frame Hamiltonian, since nutation frequencies are eigenvalues of this Hamiltonian.In the past this has been done in three different ways : (1) analytically for spins I = 3/2,4 (2) with the fictitious spin formalism, also only for I = 3/2,' and (3) numerically for any half-integer spin.5 We limit ourselves here to spins with I = 3/2 and we use an exact analytical treatment, similar to that of Paney and hug he^,^ because in this situation there is no advantage in using the fictitious spin I = 1/2 formalism or the numerical procedure. In the first part of this paper the x nutation experiment is treated and compared with experimental results on 23NaN0,. The second part considers x, - x nutation.R. Janssen and W. S. Veeman 3749 X X tl r2 Fig. 1. Pulse schemes for the x nutation (a) and the x, --x nutation (b) experiments.t I . I , 200000 0 -200000 Hz Fig. 2. One-dimensional NMR spectrum for NaNO,. 2. Experimental The 23Na nutation spectra of NaNO, are determined by a two-dimensional experiment [Fig. 1 (a) for x nutation and fig. 1 (b) for x, --x nutation.] During the evolution period t , the spins nutate around the r.f. field, and during the detection period the resulting signal is detected. The nutation during t , is measured by increasing the length of t , in successive experiments, typically in steps of 2 ps. 256 t , values are taken, while for each value of t , 20 FIDS are added. The normal NMR spectrum of NaNO,, obtained with short r.f. pulses, is shown in fig. 2. Since the quadrupole interaction in NaNO, is small (e2@ = 336 kHz, q = 0)'' all three possible transitions (3/2,1/2), (1/2, - 1/2) and (- 1/2, - 3/2) are observed in the 23Na spectrum.3. Nutation 3.1. Theory During the evolution period in the two-dimensional NMR experiment of fig. 1 (a) the Hamiltonian for a spin I = 3/2 in the rotating frame is represented by: HY' = R, I, + R,(I," - 5/4) (h = 1) (1)3750 Quadrupole Nutation NMR in Solids where Rl = YB,, 0, = (e2qQ/8) (3 cos20- 1 + y ~ sin2 8 cos2qb) and 8 and qb define the orientation of the external magnetic field. Here it has been assumed that the spins are irradiated on resonance and that the quadrupole interaction, represented here by the parameter Qq, is small enough relative to the Zeeman interaction B, that the non-secular terms of the quadrupole interaction may be neglected. Also, possible dipolar interactions are ignored.The superscript (x) in HY) denotes the phase of the r.f. field, which is x for each t, value in the two-dimensional experiment. The nutation frequencies are determined by the eigenvalues of Hf). The transformation matrix, T, which diagonalizes HY) is given by Wokaun and Ernst,” but will be derived again here since it shows the way to a treatment of higher spins, at least to I = 5/2. The diagonalization of H’,”) is straightforward in the basis of eigenfunctions of I,, Im,), in the order 13/2), I - 1/2), I1/2) and I - 3/2). HY) is the basis represented by and can be diagonalized by means of the orthogonal transformation B: 0 cosp -sinB B = ( 0 0 sinp cosp 9 cosa -sina 0 sina cosa 0 where tan2a = -$~3i2q/(R1-;Rq) and tan2p = -f2/3Rq/(R1+$Rq). The eigenvalues of Ex = K1fl;)B are Ex, = $Rl+D- Ex2 = $2, - D- Ex3=-$R1+D+ (3) (4) Ex.= -$Ql - D, where D- = (Rt - R, Rq +a:); and D, = (a: + Q, aq + For a spin I = 5/2 a similar approach can be followed, and then the Hamiltonian blocks out in two 3 x 3 ma trices. Although the basis set Im,) is very convenient for diagonalizing Hf), this set does not form the best choice to calculate nutation spectra, since the transitions observed in the detection period are labelled by the quantum number m,, corresponding to eigenfunctions of I,. When A relates the two bases Im,) and Jm,): where 4 3 d3 1 A=#2/2 (1 \/3 -1 >:?) \/3 -1 d3 d 3 -1R. Janssen and W. S. Veeman then where /Cos& sine- cose, sine+\ sine- -cos& sine+ -cosO+ sine- -COS& -sine+ cose, \ cos e- sin 0- - cos 8, - sin o+/ cos 8- = cos a + 2/3 sin a sin 8- = 4 3 cos a - sin a cos0, = 43cosp+sinp sin t9+ = cosp- 4 3 sinp tan 28- = &'3i21/(i2q -@,) tan 28, = +43i21/(i2q ++a,).375 1 (7) Compared to the result of Wokaun and Ernstll our transformation matrix T differs in the signs of two columns owing to the choice of the matrix B. Our choice corresponds to a proper rotation, while Wokaun and Ernst used coscc sina 0 sincc -cosa 0 0 sinp -cosp These differences do not affect physical results. The NMR signal S(tl, t 2 ) can now be calculated with the density-matrix formalism: S(t1, t2) = Tr Mtl, t2) (I, - i1,)I (9) where p ( t l , t,) = exp ( -iH2 t,) exp (-iH:")t,) p(0) exp (iHF)t,) exp (iH, t,). H , represents the Hamiltonian during the detection period in the absence of any r.f.irradiation. The transitions between eigenstates of H,, ImJ, are labelled i2$) [(i,]) = (3/2,1/2), (1/2, - 1/2) or (- 1/2), - 3/2)]. Since to a good approximation we can observe these three NMR transitions separately (at least in principle), we can also observe the nutation spectrum in three ways via one of the possible transitions in t,. The signal due to the (i,j) transition in the detection period can then be written as S(tl, t,)ij K p(tl, t2)ii = p(tl, t, = O)ij exp (- ii2j;)t2) p(t,, t2 = O)ij = [exp (- iH?)t,) p(0) exp (iHF)t1)lij (10) (1 1) where represents the nutation spectrum detected via the ( i , ~ ) transition in t,. Since E, = T'S:)T, eqn (1 1) can be rewritten as p ( t l , t, = O)ij = [ T exp ( - iE, tl) T' p(O) T exp (iEz t l ) T'Iij where R,, = Ezk-Exz is one of the possible nutation frequencies and R(U),z = Gc q T ' P ( 0 ) TI,, (1 3) is the corresponding amplitude in the nutation spectrum.Note that the nutation frequencies are determined only by the eigenvalues of HF) and not by the transition (E'J) in t, via which the nutation signal is detected. The amplitudes R(& do depend on i and j .3152 Quadrupole Nutation NMR in Solids Table 1. The amplitudes R(ij)il and R(@il in units of yB,,/(16kB 7‘) of eqn (16) for the four different nutation frequencies in the x nutation spectrum of a spin I = 3/2 nutation frequency, i j transition in t , R(OX1 X I X t sin (0, - 0-) R, - 2 sin 0, sin 0- R, sin (0, - 0-) R, - cos (0, - 0-1 R, 2 cos 0, sin 0- R, - cos (0, - e-) R, cos (0, - 0-1 R, 2 sin 0, cos 0- R, cos (0, - 0-1 R, sin (0, - 0.J R, - 2 cos e- cos e, R, sin (0, - 0-) R, Because several elements [ T ’ p ( 0 ) TI,, are zero : where of the six possible nutation frequencies )52z)1 for a spin I = 3/2 only four amplitudes R(b]kz are non-zero, those corresponding to (kl) = (13), (14), (23) and (24). Since Szi:) = -Szg) we can combine the expressions for positive and negative nutation frequencies : R(i& exp (- iQkt)t,) + R(bIlk exp (iag)tl) = R(ij)i, cos (QL:)t,) + iR(ij)il sin (CIg)t,) (16) where As eqn (16) shows, the initial amplitude of the FID in t , is modulated by a cosine and sine term in ng)t,. The corresponding amplitudes R(i& and R(i~9;, are shown in table 1.The transitions LIE) with non-zero amplitudes are also indicated in the rotating- frame energy-level scheme for x nutation in fig.3(a). Clearly, two transitions, Q&) and a:), do not occur. The nutation signal detected via the transition i j in t , is now given S(tl, t2)ii = {Xkz[R(g)il cos (ng)t,) + iR(ij];, sin (ni:)t,)J> exp (- in{,”)t,). (17) by Although it is tempting to view the rotating-frame coherences as precessing spins I = i, eqn (17) and table 1 show that this cannot be correct. Clearly these spins would have a transverse magnetization component at t , = 0, at least when the (3/2,1/2) or (- 1/2, -3/2) transitions are detected, and this is not in agreement with the physical situationR. Janssen and W. S. Veeman 3753 1 3 2 4 Fig. 3. Energy levels in the rotating frame, indicating coherences during x nutation (a) and x, --x nutation (b).(4 (b) (4 0.0 6.0 10.0 16.0 20.0 26.0 30.0 36.0 Fig. 4. Simulated (1/2, - 1/2) x nutation spectra for NaNO,, showing separate powder lineshapes for each nutation frequency: (a) old, (b) o,,: (c) 024, (d) o,, and (e) total. The horizontal axis is in units of lo4 Hz. at t , = 0. Fortunately, when we add over all transitions kl, S(t,, Qij = 0 for t, = 0, as it should, because The effect of the presence of cos (aL:)t,) terms in eqn (1 7) is that the nutation spectra detected via the (3/2,1/2) and (- 1/2, - 3/2) satellite transitions are represented by superpositions of two-dimensional absorption and dispersion lineshapes. Since the nutation spectrum detected via the (1 /2, - 1 /2) transition can be properly phased, only these nutation spectra are considered here.The two-dimensional NMR spectrum for I = 3/2 is then given by the Fourier transform of C,, R(ij)i, = 0. (18) s(tl, t,);, -+ = @,, R(& - i)il sin (a&)] exp ( - i~4?it2). (19) 3.2. Comparison between Theory and Experiment With eqn (8), (1 5) and (19) and table 1 the nutation spectrum of a powdered sample can be calculated. Note that the orientation dependence of the nutation frequencies and amplitudes enters via Clq. Owing to this orientation dependence each nutation line kl must show a powder lineshape. Fig. 4 shows the powder lineshapes for all four nutation lines of the (1/2, - 1/2) nutation spectrum of NaNO, and also of the total nutation spectrum. The powder lineshapes for the various Di:) are quite different.Fig. 4 also shows how weak the ' triple' coherence flit) is. In this case three of the four nutation powder lineshapes overlap.3754 Quadrupole Nutation NMR in Solids Fig. 5. (a) Two-dimensional x nutation spectrum of NaNO,; the normal NMR spectrum is found along the horizontal axis, while the nutation spectrum is along the other axis. (b) Simulation of the (1/2, - 1/2) x nutation spectrum from the two-dimensional spectrum (a) (in units of lo4 Hz). Fig. 5(a) shows the total x nutation spectrum of NaNO,. Probably because of the superposition of absorption and dispersion lineshapes in the nutation spectrum detected uia the satellite transitions, the intensity of the satellites is rather weak. The (1/2, - 1/2) transition nutation spectrum, however, is clearly visible and agrees well with the simulated spectrum of fig. 5(b) when the total spectrum of fig.4 is convoluted with an appropriate line-broadening. The reason for the need of line-broadening will be discussed in section 5. 4. x, - x Nutation 4.1. Theory The next nutation experiment we will consider is depicted in fig. 1 (b). Here the nutation pulse, whose length t , is being stepped during the two-dimensional experiment, is splitR. Janssen and W. S. Veeman 3755 into two pulses with opposite phases x and --x. The Hamiltonians in the evolution period during the first and second half of t, are The density matrix at time t , = 22, t 2 = 0 is now given by p ( t l , t 2 = 0) = exp (-iHi-")z) exp (- iH?)z) p(0) exp (iHP)z) exp (iH:")z) = u exp ( - iE-, z) U-' T exp ( - iEx z) r1 p(0) T exp (iE, z) x T1 U exp (iRx z) U-' (22) where Ex = TIHF)T E-, = U - 1 H y u .(23) 1" is given by eqn (7) and U is obtained from T by changing the sign of R,. in t,, the nutation spectrum is proportional to When again we assume that we detect the nutation spectrum via the (i,j) transition Here p(l1, t 2 = O)ij = zkmnp uik-(u-lT)km LT1d0) T l ~ n ( T 1 u ) f l p uij x exp [ - i(RLiX) + RE;) z] - - z:kp, mn R ( g ) k p , mn exp ( - in?;, mn'). R&, mfl = ng) +RE; i-2:; = Ex, -Ex, R k p = E-xk - E-xp Ex, = +Rl + D- Ex. = $2, - 0- Ex3 = -inl + D+ E x4 =-la 2 1 -0 + E-,, = - $2, + 0, - -0, 2 1 EPx2 - EPx3 = illl + D- E-x4 = 5 'R 1 -0- Exr and EpX8 are the eigenvalues of HF) and Hi-,), respectively. nutation experiment and R ( ~ J ) ~ ~ , In eqn (24) RL:,mfl can be considered as the nutation frequency of the x, -x as the corresponding amplitude : R ( g ) k p , mn = Uik ujp( u-l T)km [Tip(o) Tlmfl ('-' ' ) n p ' cos ($- - 0J - sin ($- - 0-) 0 0 sin ($- - 0-) cos ($- - 0-) 0 (26) The matrix T ' p ( 0 ) T is given by eqn (14) and 0 ) (27) 0 0 cos ($+ - 0,) - sin (#+ - 8,) ( 0 0 cos (#+ - 0,) sin ($+ - 0,) U-'T = where tan2#+ = -f43R1/(R,-+R,) and tan2#- = -+43R,/(R,+&).Eqn (14) and (27) show that again only certain combinations of indices k, p , m and n can give non- zero amplitudes R(ij)kp, m y . In addition, some of the combinations kp, mn that give non- zero amplitudes result in zero nutation frequencies. Table 2 shows all k,p,m,n combinations that give non-zero R(iJkp, mfl with the corresponding nutation frequencies.From this table we find that besides nutation frequencies zero, only four different frequencies occur : ISzy'l = 20, = Rg)3756 Quadrupole Nutation NMR in Solids Table 2. The combinations of k, p, m and n indices that give non- zero amplitudes R(OIk,, mn in the x, -x nutation experiment 1 3 1 3 0 1 4 1 3 20- 1 3 1 4 20, 1 4 1 4 2(0,+D-) 1 3 2 3 - 20- 1 4 2 3 0 1 3 2 4 2(0+-D-) 2 3 1 3 - 20, 2 4 1 3 -2(D,-D-) 2 3 1 4 0 2 4 1 4 20- 2 3 2 3 -2(O,+D-) 2 4 2 3 -20, 2 3 2 4 -20- 2 4 2 4 0 1 4 2 4 20, 3 1 3 1 0 3 2 3 1 20, 3 1 3 2 20- 3 2 3 2 2(0,+D-) 3 1 4 1 -20, 3 2 4 1 0 3 1 4 2 -2(D,-D-) 3 2 4 2 20- 4 1 3 1 -20- 4 2 3 1 2(0,-D-) 4 1 3 2 0 4 1 4 1 -2(D++D-) 4 2 4 1 - 20- 4 1 4 2 -20, 4 2 4 2 0 4 2 3 2 20, Table 3. The amplitudes R(iJ3il and R(ij)ir in units of yB0/(64k,T) of eqn (29) for the four different nutation frequencies in the x7 - x nutation spectrum of a spin I = 3/2 nutation frequency, i j transition in t , R(OX 4 sin (48, + 48-) 0 - 4 sin (48, + 48-) 4 sin (48, + 48-) 0 - 4 sin (48, + 48-) - 4 sin (28, + 28-) - 2 sin (48,48-) 0 4 sin (28, + 28-) + 2 sin (48, + 48-) 4 sin (28, + 28-) - 2 sin (48, + 48-) 0 - 4 sin (28, + 20-) + 2 sin (48, + 48J - 8 cos 28- sin (28, + 28-) 4 sin 28- sin (28, + 28-) - 8 cos 28- sin (28, + 28J - 8 cos 28, sin (28, + 28-) 4 sin 28, sin (28, + 28-) - 8 cos 28, sin (28, + 28J 4 sin (28, + 28-) x (cos 28, + cos 2e-) 2 sin (28, + 28J 4 sin (28, + 28-) 4 sin (28, + 28J 2 sin (28, + 20-) 4 sin (28, + 28-) x (sin 28, - sin 28-) x (cos 28, + cos 2 e ~ x (cos 28, - cos 28-1 x (sin 28, +sin 28-) x (cos 28, - cos 2e-) When we compare these four frequencies with transitions in the energy-level scheme of HF) [see eqn (28) and fig.3(b)] we find that the possible nutation frequencies in the x, -x experiment can be expressed as functions of fig) and fig), the transitions that were missing in the x nutation experiment! When we add all R(OIkp, mn amplitudes that belong to a particular nutation frequencyR. Janssen and W. S. Veeman 3757 I 1 (4 1 1 1 1 1 1 1 1 1 1 1 0.0 6.0 10.0 16.0 20.0 26.0 30.0 36.0 40.0 46.0 60.0 Fig. 6. Simulated (1/2, - 1/2) x, --x nutation spectra for NaNO,, showing separate powder lineshapes for each nutation frequency : (a) w12 + w , ~ , (b) w12 (c) q2, (d) w34 and (e) total. The horizontal axis in in units of lo4 Hz.lap)[, resulting in a total amplitude R(ij)F) for the positive frequency a,(’) and in R(ij)L-) for the frequency --a:), we can write eqn (24) as p ( t l , t , = 0), = C, [R(ij)C) exp (-iR:)z) + R(iJ3,(-) exp (ia:’)z)] = Ea [R(i& cos (C2p)z) + iR(iJ3: sin (ap)z)] (29) where R(iJ3: = R(i~]r) + R(iJ3:-’ ; R(i39: = R(iJ3:’ - R(O’)L-). The amplitudes R(iJ3: and R(iJ3; and the corresponding frequencies SZp) are shown in table 3 . Again, just as in the case of x nutation, R(ij): = 0 only for the (1/2, - 1/2) transition. Although from table 3 it follows that C, R(ij]: # 0, this does not mean that a signal exists at time t , = 0, since the amplitudes R(iJ3: belonging to the non-zero nutation frequencies are cancelled at t , = 0 by the amplitudes of the terms with zero nutation frequencies. However, at times t , # 0 terms exist with zero nutation frequencies, in contrast to x nutation.Note that the zero nutation frequency mentioned here differs from the effects resulting from off-resonance as discussed previously. 4.2. Comparison between Theory and Experiment Fig. 6 shows the calculated [ ( i , ~ ] = (1/2, - 1/2)] nutation powder lineshapes for a x, - x nutation experiment on NaNO,. A careful comparison shows that now only two lineshapes overlap (a&) and a$)), but within one powder lineshape positive and negative amplitudes occur. The difference and sum frequency terms (a$) + a&) and S2g)-Q&)) are found at low and high frequencies. Fig. 7(a) and (b) display the experimental and simulated x, - x nutation spectra of NaNO,, where again for the simulated spectrum line broadening has been applied.In the simulated spectrum of fig. 7(b) the term with zero nutation frequency is left out, but it can be seen clearly in the experimental spectrum. The agreement between the simulated and experimental spectra is good except for the peak at ca. 75 kHz. This peak in the experimental spectrum is much stronger than follows from the simulation. The reason for this is not understood.37513 Quadrupole Nutation NMR in Solids Fig. 7. (a) Two-dimensional x, - x nutation spectrum of NaNO,; the normal NMR spectrum is found along the horizontal axis, while the nutation spectrum is along the other axis. (b) Simulation of the (1 /2, - 1 /2) x, - x nutation spectrum from the two-dimensional spectrum (a) (in units of lo4 Hz). 5.Line Broadening in Nutation Spectra At least four mechanisms can contribute to the width of lines in a nutation spectrum: dipolar interactions, distributions of the quadrupole parameters e2qQ and/or q, inhomogeneous r.f. field and relaxation effects. Although the chemical shift does not enter the Hamiltonian in the rotating frame and therefore is not included in the above list, it can still affect the quadrupole nutation spectrum via off-resonance effects. These, however, are neglected here. Also dipolar interactions are not considered here but should be taken into account in the rotating-frame Hamiltonian if present.12 It is not difficult to avoid broadening in the nutation spectrum by inhomogeneous r.f. fields, since the spectral width is so large compared to the usual r.f.inhomogeneity. Probably the two most important causes for the line broadening are the distribution of quadrupole parameters (static) and relaxation effects (dynamic). In many of our experiments on zeolites’. * we noticed a strong temperature-dependent line broadening in the 23Na nutation spectra, which we assign to relaxation effects. In many cases13 relaxation in the rotating frame becomes at certain temperatures so efficient that theR . Janssen and W. S. Veernan 3759 nutation spectrum broadens beyond detection. Since the splittings in the rotating frame are in our experiments ca. 100 kHz, efficient relaxation, causing ultra-short qp and I&,* can occur when the quadrupolar nucleus executes motions in this frequency range.The fluctuating electric field gradients then provide the relaxation channel. At this point it is not clear how much of the line broadening in the NaNO, spectra is due to relaxation or to a static distribution of quadrupole parameters. 6. Conclusions ’The x nutation experiment as originally proposed by Samoson and Lippmaa is the most ijimple version of a whole class of possible nutation experiments. The nutation frequencies for a spin I = 3 / 2 determined via the x nutation experiment can be classified according to the rotating-frame transitions as three ‘single’ and one ‘triple’ quantum coherences. Each nutation frequency yields a powder lineshape. For NaNO, three of these powder lineshapes in the nutation spectrum overlap. An investigation, theoretically and experimentally, of the x, - x nutation experiment on NaNO, shows that again four nutation frequencies occur, two of which can be assigned to ‘double quantum ’ coherences in the rotating-frame energy-level scheme, the other two being simply the sum and difference frequencies. Here two nutation frequency powder lineshapes overlap. Although the goal of this investigation, to find a composite nutation pulse that results in a simple nutation spectrum with preferably only one nutation frequency, has not yet been reached, this work shows the almost unlimited number of ways the nutation experiments can be executed. W. S. V. wants to acknowledge helpful discussions with Prof. M. Goldman (Saclay) and Prof. E. Belorizky (Grenoble). References 1 D. B. Zax, A. Bielecki, K. W. Zilm, A. Pines and D. P. Weitekamp, J . Chem. Phys., 82, 4877. 2 S. Ganapathy, S. Schramm and E. Oldfield, J. Chem. Phys., 1982, 77, 4360. 3 A. Samoson and E. Lippmaa, Chem. Phys. Lett., 1983, 100, 205. 4 L. Pandey, S. Towta and D. G. Hughes, J. Chem. Phys., 1986, 85, 6923. 5 A. P. M. Kentgens, J. J. M. Lemmens, F. M. M. Geurts and W. S. Veeman, J. Magn. Reson., 1987,71, 6 F. M. M. Geurts, A. P. M. Kentgens and W. S. Veeman, Chem. Phys. Lett., 1986, 120, 206. 7 G. A. H. Tijink, R. Janssen and W. S. Veeman, J . Am. Chem. SOC., 1987, 109, 7301. 8 R. Janssen, G. A. H. Tijink and W. S . Veeman, J. Chem. Phys., 1988, 88, 518. 9 P. P. Man, J. Magn. Reson., 1986, 67, 78. 62. 10 R. V. Pound, Phys. Rev., 1950, 79, 685. I 1 A. Wokaun and R. R. Ernst, J. Chem. Phys., 1977, 67, 1752. 12 D. Horne, R. D. Kendrick and C. S. Yannoni, J. Magn. Reson., 1983, 52, 299. 13 P. P. M. A. Dols, R. Janssen and W. S. Veeman, to be published. Paper 8/00696B ; Received 22nd February, 1988

ISSN:0300-9599    

DOI:10.1039/F19888403747

出版商:RSC    

年代:1988

数据来源: RSC