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  • 1
    Online Resource
    Online Resource
    Newark :John Wiley & Sons, Incorporated,
    Keywords: Crystallography. ; Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (524 pages)
    Edition: 2nd ed.
    ISBN: 9781118587324
    Series Statement: EMagRes Bks.
    Language: English
    Note: Intro -- NMR Crystallography -- Contents -- Contributors -- Series Preface -- Volume Preface -- Part A Introduction -- 1 Crystallography & -- NMR: an Overview -- 1.1 Introduction -- 1.2 Limitations of Diffraction Techniques -- 1.3 NMR and its Crystallographic Significance -- 1.4 Required Information -- 1.5 Concluding Remarks -- References -- 2 Tensors in NMR -- 2.1 Introduction -- 2.2 Cartesian to Spherical Tensors -- 2.3 Hamiltonians in Terms of Spherical Tensors of Rank 0, 1, 2 -- 2.4 Matrix Elements for Spherical Tensors -- References -- 3 Computation of Magnetic Resonance Parameters for Crystalline Systems: Principles -- 3.1 Introduction -- 3.2 Overview of the Planewave-Pseudopotential Approach -- 3.3 Shielding in a Periodic System -- 3.4 Other Magnetic Resonance Parameters -- 3.5 Examples -- References -- 4 Experimental Characterization of Nuclear Spin Interaction Tensors -- 4.1 Introduction -- 4.2 Measurements from Wideline Spectra -- 4.3 Spinning Sideband Analysis -- 4.4 Single Crystals -- 4.5 Reliability -- 4.6 Conclusion -- References -- Part B Chemical Shifts -- 5 Magnetic Shielding & -- Chemical Shifts: Basics -- 5.1 Introduction -- 5.2 Symmetry Properties of the Shielding Tensor -- 5.3 Theory of Magnetic Shielding -- 5.4 Calculations of Magnetic Shielding -- References -- 6 Symmetry Effects at the Local Level -- 6.1 Introduction -- 6.2 Spin Systems and Interactions -- 6.3 Magnetic Shielding Tensors in Single Crystals -- 6.4 Magnetic Shielding Tensors in Polycrystalline Powders -- 6.5 Summary and Miscellaneous -- References -- 7 Chemical Shift Computations for Crystalline Molecular Systems: Practice* -- 7.1 Computational Details -- 7.2 General Aspects -- 7.3 Practical Uses of the Computations -- 7.4 Conclusions -- References -- 8 Chemical Shifts & -- Solid-state Molecular-level Structure -- 8.1 Introduction. , 8.2 Molecular Structure -- 8.3 Tautomeric Form -- 8.4 Bond Lengths -- 8.5 Bond Angles -- 8.6 Dihedral Angles -- 8.7 Steric Crowding -- 8.8 Concluding Remarks -- References -- 9 Chemical Shift Anisotropy & -- Asymmetry: Relationships to Crystal Structure -- 9.1 Introduction -- 9.2 Direct Encoding of Lattice Structure in Shift Tensors -- 9.3 Indirect Reflections of Lattice Structure in NMR Tensor Data -- 9.4 Refinement of Established Crystal Structures -- 9.5 Deriving Full Crystal Structures -- References -- Part C Coupling Interactions -- 10 Dipolar & -- Indirect Coupling: Basics -- 10.1 Introduction -- 10.2 Characterization of Indirect Spin-Spin Coupling Interactions in Solids -- 10.3 Characterization of Dipolar Spin-Spin Coupling Interactions in Solids -- 10.4 Conclusions -- References -- 11 Dipolar Recoupling: Heteronuclear -- 11.1 Introduction -- 11.2 MAS Hamiltonian -- 11.3 Heteronuclear Dipolar Recoupling in Spin Pairs -- 11.4 Heteronuclear Dipolar Recoupling in Multispin Systems -- 11.5 Conclusions -- References -- 12 Dipolar Recoupling: Homonuclear -- 12.1 Introduction -- 12.2 Theoretical Background and Notation -- 12.3 Dipolar Recoupling by RF Pulses Alone -- 12.4 Chemical-Shift-Dependent Dipolar Recoupling -- 12.5 Symmetry Principles in Homonuclear Dipolar Recoupling -- 12.6 Frequency-Selective Homonuclear Dipolar Recoupling -- 12.7 Other Recent Developments -- References -- 13 Dipolar Coupling: Molecular-level Mobility -- 13.1 Introduction -- 13.2 Basics -- 13.3 Averaged Dipolar Couplings-Fast Motions -- 13.4 Dynamic Lineshape-Intermediate Motions -- 13.5 Site-Resolved Heteronuclear and Homonuclear Dipolar Couplings -- 13.6 Double-Quantum Experiments -- 13.7 Dipolar Exchange NMR-Slow Motions -- 13.8 Summary -- References -- 14 Spin Diffusion in Crystalline Solids -- 14.1 Introduction -- 14.2 The Mechanism of Spin Diffusion. , 14.3 Experiments to Measure Spin Diffusion -- 14.4 Modeling Spin Diffusion -- 14.5 Applications of Spin Diffusion to NMR Crystallography -- 14.6 Conclusion -- References -- 15 Indirect Coupling & -- Connectivity -- 15.1 Introduction -- 15.2 Homonuclear Through-Bond Correlation Spectroscopy -- 15.3 Heteronuclear Through-Bond Correlation Spectroscopy -- 15.4 Conclusions -- References -- 16 Nuclear Quadrupole Coupling: An Introduction & -- Crystallographic Aspects -- 16.1 Introduction -- 16.2 Theory of Quadrupolar Coupling -- 16.3 Computation of Quadrupolar Parameters -- 16.4 Effect on NMR Spectra -- 16.5 Measurement by NMR -- 16.6 Use in NMR Crystallography -- 16.7 Conclusions -- References -- Part D Crystal Structure Determination using NMR -- 17 Fundamental Principles of NMR Crystallography -- 17.1 Introduction -- 17.2 NMR Physical Measurements -- 17.3 Resolving Structures by NMR -- 17.4 NMR Crystallography and Beyond Periodic Structures -- References -- 18 Interplay between NMR & -- Single-crystal X-ray Diffraction -- 18.1 Introduction -- 18.2 Background Concepts -- 18.3 Solid-State NMR and X-Ray Diffraction -- 18.4 Examples -- 18.5 Conclusion -- References -- 19 Combined Analysis of NMR & -- Powder Diffraction Data -- 19.1 Introduction -- 19.2 Introduction to Structure Determination from Powder Diffraction Data -- 19.3 Structure Determination from Powder Diffraction Data Augmented by Information from Solid-State NMR -- 19.4 Structure Determination Directly from Solid-State NMR Data -- References -- 20 Tensor Interplay -- 20.1 Introduction -- 20.2 Tensor Interplay -- 20.3 Concluding Remarks -- References -- Part E Properties of the Crystalline State -- 21 Intermolecular Interactions & -- Structural Motifs -- 21.1 Introduction -- 21.2 Host-Guest Interactions: Zeolites -- 21.3 Aromatic π-π Stacking and Ring-Current Effects. , 21.4 Interactions in Nanostructures -- 21.5 Polymorphs -- 21.6 Ab Initio Calculations -- 21.7 Conclusion -- References -- 22 Hydrogen Bonding in Crystalline Organic Solids -- 22.1 Introduction -- 22.2 NMR Chemical Shifts -- 22.3 Dipolar Couplings -- 22.4 Hydrogen Bond-Mediated J Couplings -- 22.5 Hydrogen-Bond Dynamics -- 22.6 Outlook -- References -- 23 Inorganic Non-stoichiometric Crystalline Systems & -- Atomic Ordering -- 23.1 Introduction -- 23.2 NMR Interactions and Data Analysis -- 23.3 Example Applications -- 23.4 Conclusions -- References -- 24 Rotational & -- Translational Dynamics -- 24.1 Introduction -- 24.2 NMR and Dynamics -- 24.3 Rotational Barriers and Symmetry -- 24.4 Dynamics and Dipolar Coupling -- 24.5 Deuterium NMR Lineshapes -- 24.6 Shielding and Dynamics -- 24.7 Noninteger Quadrupolar Dynamic Averaging -- 24.8 Concluding Remarks -- References -- 25 Intramolecular Motion in Crystalline Organic Solids -- 25.1 Introduction -- 25.2 Dynamics and Structure -- 25.3 Effects of Dynamics on NMR Spectra -- 25.4 Characterization of Dynamics in Solids -- 25.5 Overview -- References -- 26 Structural Phase Transitions -- 26.1 Introduction -- 26.2 The Classification of Phase Transitions -- 26.3 NMR Identification of Phase Changes -- 26.4 The Landau Theory -- 26.5 Pure Quadrupole Resonance -- 26.6 Dynamics at Structural Phase Transitions -- 26.7 Summary -- References -- Part F Applications of NMR to Crystalline Solids -- 27 Structural Biology -- 27.1 Introduction -- 27.2 Sample Preparation -- 27.3 Assignment Strategies -- 27.4 Structural Restraints -- 27.5 Alternative Isotope Labeling Patterns -- 27.6 Structure Calculation and Refinement -- 27.7 Dynamics -- 27.8 Prospects -- References -- 28 Organic & -- Pharmaceutical Chemistry -- 28.1 Introduction. , 28.2 Search for the Stereochemistry of Organic Compounds and Pharmaceuticals in the Solid State by Means of XRD and SSNMR -- 28.3 Polymorphism of Organic Compounds and Pharmaceuticals -- 28.4 Molecular Disorder -- 28.5 Cryocrystallography and Solid-State NMR -- 28.6 Conclusions -- References -- 29 Inorganic & -- Materials Chemistry -- 29.1 Introduction -- 29.2 Space-Group Assignment -- 29.3 Toward Full Structural Determination using NMR -- References -- 30 Geochemistry -- 30.1 Introduction -- 30.2 Al, Si Order/Disorder -- 30.3 Al Coordination in Minerals -- 30.4 Anion Order/Disorder in Minerals -- 30.5 Order/Disorder of Cations Other than Al, Si -- 30.6 Vacancy Defects -- 30.7 Speciation and the Structural Role of H -- 30.8 Structural Environment of other Minor Components -- 30.9 Potential Future Applications -- References -- Index -- NMR Abbreviations and Acronyms.
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  • 2
    Online Resource
    Online Resource
    Newark :John Wiley & Sons, Incorporated,
    Keywords: Solids -- Analysis. ; Electronic books.
    Type of Medium: Online Resource
    Pages: 1 online resource (557 pages)
    Edition: 1st ed.
    ISBN: 9781118588857
    Series Statement: EMagRes Bks.
    DDC: 538/.362
    Language: English
    Note: Cover -- Title Page -- Copyright Page -- Contents -- Contributors -- Series Preface -- Volume Preface -- Part A: Basic Principles -- 1 Quadrupolar Interactions -- 1.1 Introduction -- 1.2 Quadrupolar Hamiltonian in a Uniform Space -- 1.3 Spherical Tensor Representation for the Quadrupolar Hamiltonian -- 1.4 Quadrupolar Interaction as a Perturbation of Zeeman Interaction -- 1.5 Energy Levels and the Spectrum of a Single Crystal -- 1.6 Powder Spectrum -- 1.7 Appendix -- References -- 2 Quadrupolar Nuclei in Solids -- 2.1 Introduction -- 2.2 Basic Spin Properties -- 2.3 Interaction with Radiofrequency Fields -- 2.4 Experimental Methods -- 2.5 Theory -- References -- 3 Quadrupolar Coupling: An Introduction and Crystallographic Aspects -- 3.1 Introduction -- 3.2 Theory of Quadrupolar Coupling -- 3.3 Computation of Quadrupolar Parameters -- 3.4 Effect on NMR Spectra -- 3.5 Measurement by NMR -- 3.6 Use in NMR Crystallography -- 3.7 Conclusions -- References -- 4 Quadrupolar Nuclei in Solids: Influence of Different Interactions on Spectra -- 4.1 Introduction -- 4.2 Rules of Thumb for Interpreting the Solid-State NMR Spectra of Quadrupolar Nuclei -- 4.3 Influence of the Magnetic Shielding Interaction on Solid-State NMR Spectra of Quadrupolar Nuclei -- 4.4 Influence of Spin-Spin Coupling Interactions on Solid-State NMR Spectra of Quadrupolar Nuclei -- 4.5 Conclusions -- References -- Part B: Advanced Techniques -- 5 Acquisition of Wideline Solid-State NMR Spectra of Quadrupolar Nuclei -- 5.1 Introduction -- 5.2 Systems for Study by Ultra-Wideline NMR Spectroscopy -- 5.3 Methodologies for Acquisition of Ultra-wideline NMR Spectra -- 5.4 Applications of UW SSNMR -- 5.5 Conclusions -- References -- 6 Sensitivity and Resolution Enhancement of Half-Integer Quadrupolar Nuclei in Solid-State NMR -- 6.1 Introduction. , 6.2 Single-Crystal Energy Levels, Populations, and Detection -- 6.3 Methods of Altering Populations -- 6.4 From Single Crystals to Powders -- 6.5 Sensitivity Enhancement for Powdered Samples -- 6.6 Application of Hyperbolic Secant Pulses in Resolution Enhancement -- 6.7 Concluding Remarks -- References -- 7 Quadrupolar Nutation Spectroscopy -- 7.1 Introduction -- 7.2 Spin Hamiltonians and Density Matrix -- 7.3 Practical Considerations -- 7.4 Applications of Nutation NMR Spectroscopy -- 7.5 Quantitative Spectra and Nutation-Based Filtering -- References -- 8 Dynamic Angle Spinning -- 8.1 Introduction -- 8.2 Basic Principles -- 8.3 Implementation -- 8.4 Applications -- References -- 9 Double Rotation (DOR) NMR -- 9.1 Introduction -- 9.2 Information from One Dimensional DOR Experiments -- 9.3 Two Dimensional DOR Experiments -- 9.4 Concluding Remarks -- References -- 10 MQMAS NMR: Experimental Strategies -- 10.1 Introduction -- 10.2 Theoretical Background -- 10.3 Detection of Pure-Phase Spectra -- 10.4 Processing and Interpretation of MQMAS Spectra -- 10.5 Measurements of Heteronuclear Correlations -- 10.6 Sensitivity Enhancement via CPMG -- 10.7 Conclusion -- References -- 11 STMAS NMR: Experimental Advances -- 11.1 Introduction -- 11.2 Theoretical Background -- 11.3 Experimental Implementation -- 11.4 Double-Quantum Filtered STMAS (DQF-STMAS) -- 11.5 STMAS with Self-Compensation for Angle Misset (SCAM-STMAS) -- 11.6 STARTMAS and Other "Ultrafast" Methods -- 11.7 Motional Broadening in STMAS -- 11.8 Higher-Order Interactions in STMAS -- 11.9 Applications of STMAS -- 11.10 Conclusions -- References -- 12 Correlation Experiments Involving Half-Integer Quadrupolar Nuclei -- 12.1 Introduction -- 12.2 The Special Case of Quadrupolar Nuclei -- 12.3 J-Coupling and Residual Splitting -- 12.4 Experiments using J-Couplings -- 12.5 Dipolar Couplings. , 12.6 Conclusion -- References -- 13 Computing Electric Field Gradient Tensors -- 13.1 Introduction -- 13.2 Models of the Charge Distribution -- 13.3 Summary and Conclusions -- References -- Part C: Applications -- 14 Quadrupolar NMR to Investigate Dynamics in Solid Materials -- 14.1 Introduction -- 14.2 Deuterium -- 14.3 Nitrogen-14 -- 14.4 Oxygen-17 -- 14.5 Lithium -- 14.6 Multiple-Quantum Experiments -- 14.7 Concluding Remarks -- References -- 15 Alkali Metal NMR of Biological Molecules -- 15.1 Introduction -- 15.2 Solid-State NMR for Alkali Metal Ions -- 15.3 Detection of Alkali Metal Ions in Biological Molecules -- 15.4 Concluding Remarks -- References -- 16 Nitrogen-14 NMR Studies of Biological Systems -- 16.1 Introduction -- 16.2 Theoretical Background -- 16.3 14N Fingerprint in Spin S = 1/2 Spectra -- 16.4 Indirect Detection of 14N -- 16.5 Applications -- 16.6 Summary -- References -- 17 Oxygen-17 NMR Studies of Organic and Biological Molecules -- 17.1 Introduction -- 17.2 Solid-State 17O NMR Techniques -- 17.3 Characterization of 17O NMR Tensors in Organic Functional Groups -- 17.4 Recent Advances in 17O NMR of Large Biological Molecules -- 17.5 Concluding Remarks -- References -- 18 Oxygen-17 NMR of Inorganic Materials -- 18.1 General Introduction -- 18.2 Background and Technique Developments Enabling 17O NMR -- 18.3 Systems and Materials -- 18.4 Summary and Prospects -- References -- 19 Chlorine, Bromine, and Iodine Solid-State NMR -- 19.1 Introduction and NMR Properties of the Quadrupolar Halogens -- 19.2 Experimental Aspects -- 19.3 Representative Quadrupolar and Chemical Shift Data and Discussion of -- 19.4 Conclusions and Future Prospects -- References -- 20 Quadrupolar NMR of Ionic Conductors, Batteries, and other Energy-Related Materials -- 20.1 Introduction -- 20.2 Structure Determination -- 20.3 Dynamics -- 20.4 Summary. , References -- 21 Quadrupolar NMR of Nanoporous Materials -- 21.1 Introduction -- 21.2 Most Useful Nuclei -- 21.3 NMR Characterization Strategies for Nanoporous Materials -- 21.4 Conclusions -- References -- 22 Quadrupolar NMR in the Earth Sciences -- 22.1 Introduction -- 22.2 Minerals as Model Compounds -- 22.3 Site Occupancies in Disordered Crystalline Solid Solutions -- 22.4 Silicate Glasses and Melts -- 22.5 Dynamics and Kinetics -- 22.6 Minerals Containing Unpaired Electron Spins -- References -- 23 Quadrupolar NMR of Superconductors -- 23.1 Introduction -- 23.2 Quadrupolar Spectra -- 23.3 Spin-Lattice Relaxation in a Superconductor -- 23.4 NQR in Superconductors -- 23.5 Antiferromagnetism and Superconductivity -- 23.6 Charged Vortices in High-Temperature Superconductors -- 23.7 Summary and Future Directions -- References -- 24 Quadrupolar NMR of Semiconductors -- 24.1 Introduction -- 24.2 Background -- 24.3 NMR Spin Hamiltonian in Semiconductors -- 24.4 Spin-Lattice Relaxation of Quadrupolar Nuclei -- 24.5 Quadrupolar Interactions-Effects and Applications -- References -- 25 Quadrupolar NMR of Metal Nuclides in Biological Materials -- 25.1 Introduction -- 25.2 Experimental Approaches for Quadrupolar Metal NMR in Biological Systems -- 25.3 Interpretation of NMR Parameters in Terms of Molecular Structure: Quantum Chemical Calculations -- 25.4 Examples of Applications in Biological Systems -- 25.5 Conclusions -- References -- 26 Nuclear Waste Glasses: Insights from Solid-State NMR -- 26.1 Introduction -- 26.2 Nuclides of Interest in Nuclear Waste Glasses -- 26.3 Characterization of Nuclear Waste Glasses -- 26.4 Future Outlook and Challenges -- References -- 27 Quadrupolar Metal NMR of Oxide Materials Including Catalysts -- 27.1 Introduction -- 27.2 Metal Coordination Environment and NMR Parameters in Oxides -- 27.3 Ab Initio Calculations. , 27.4 Paramagnetic Effects -- 27.5 Examples of Quadrupolar Metal NMR in Materials Science -- 27.6 Applications in Glasses -- 27.7 Applications in HeterogeneousCatalysis -- References -- 28 Quadrupolar NMR of Intermetallic Compounds -- 28.1 Introduction -- 28.2 Background Concepts -- 28.3 Applications -- References -- Index -- Abbreviations and Acronyms -- EULA.
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  • 3
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 1030-1037 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 4
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Journal of the American Chemical Society 116 (1994), S. 11129-11136 
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Inorganic chemistry 31 (1992), S. 145-148 
    ISSN: 1520-510X
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 85 (1986), S. 6240-6242 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The results of a deuterium NMR study of ND4SCN between 125 and 420 K are reported. The deuterium T1 data indicate phase transitions at 352 and 383 K, however no evidence was found for a recently reported reversible phase transition at 203 K in NH4SCN.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 3707-3708 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The 15N/14N isotope shift on the 15N chemical shielding in a mixture of 15N14N and 15N15N was found to be 0.0601±0.0022 ppm. Using a model developed by Jameson, the nuclear shielding derivative with respect to bond length was calculated from the measured isotope shift, [∂σ(15N)/∂r]e =−910±42 ppm/A(ring). This value is in excellent agreement with a value obtained from the temperature dependence of the shielding constant in the gas phase (at the zero pressure limit) and with a value determined from recent molecular orbital calculations. From relaxation measurements the scalar spin–spin coupling constant, 1J(14N,15N), in 14N15N was calculated to be 1.8±0.6 Hz which gives a reduced coupling constant, 1K(N,N)=2.0±0.7 (1020)m−2kg s−2 A(ring)−2. The magnitude of the reduced coupling constant is compared to that of other isoelectronic species and molecular orbital calculations.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 548-551 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Oxygen isotope shifts on the 13C chemical shifts and carbon isotope shifts on the 17O chemical shifts in carbon monoxide and carbon dioxide are reported. Using models developed by Jameson, shielding derivatives with respect to bond lengths can be calculated using the measured isotope shifts. For carbon monoxide, the derivatives were calculated to be [∂σ (13C)/∂r]e =−456±15 ppm/A(ring) and [∂σ (17O)/∂r]e =−1150±130 ppm/A(ring). Although earlier coupled Hartree–Fock calculations give a much lower value for [∂σ (17O)/∂r]e, recent ab initio calculations for carbon monoxide agree very well with our experimental results. Furthermore, the observed 18O/16O iostope shift is similar to values measured previously for a series of metal carbonyls. For carbon dioxide the iostope shift gives [∂σ (13C)/∂r]e =−214±17 ppm/A(ring) which is in excellent agreement with the value obtained from a recent variable temperature gas phase NMR study. In addition, scalar spin–spin coupling constants, 1J(13C,17O) were measured to be 16.4±0.1 Hz in carbon monoxide and 16.1±0.1 Hz in carbon dioxide. To our knowledge, these are the first directly measured carbon–oxygen coupling constants to be reported in the literature. From general trends in the periodic table, it seems likely that the sign of these coupling constants is positive.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 6321-6329 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra of second-order two-spin (AB) systems are investigated. Using average Hamiltonian theory (AHT), general expressions for the positions and relative intensities of the four allowed transitions are derived. In principle, correction terms to any order of the average Hamiltonian may be applied; however, terms up to and including third order appear to be adequate in reproducing the most important experimental features. In general, both the positions and relative intensities of the peaks are sensitive to the sample spinning frequency. Only at the high MAS frequency extreme do the MAS NMR spectra of two-spin (AB) systems in solids correspond to those predicted using formulas derived for solution samples. Under slow MAS conditions, MAS NMR spectra of AB spin systems deviate considerably from the corresponding AB spectra in solution NMR studies. Three general types of MAS NMR spectra are identified and their characteristic features are discussed. The theoretical expressions derived here are applied to reproduce the observed 31P MAS NMR spectra of a phosphole tetramer and cis-1,2-bis(diphenylphosphino)ethylene. It is shown that correction terms higher than first order must be considered in order to reproduce the anomalous spinning-frequency dependencies in MAS NMR spectra. The importance of carrying out measurements at two different applied fields is also demonstrated in the case of the phosphole tetramer.
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