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Abstract
Spin relaxation parameters, although difficult to interpret, are attracting interest in NMR as these parameters are capable of yielding both structural and dynamic information. Cross-relaxation and cross-correlation parameters afford a non-ambiguous approach to molecular structure and dynamics although they require some special skills for their experimental determination and for their exploitation. This work will start with an introduction to nuclear spin cross-relaxation and cross-correlation phenomena in liquids then look in more detail at molecules in soft matter and large biomolecules. Providing a detailed, timely account, the authors are filling a gap in the present NMR literature for the analytical scientist.
Table of Contents
| Section Title | Page | Action | Price |
|---|---|---|---|
| Cover | Cover | ||
| Preface | v | ||
| Contents | vii | ||
| Chapter 1 Introduction to Nuclear Spin Cross-relaxation and Cross-correlation Phenomena in Liquids | 1 | ||
| 1.1 A Survey of Nuclear Spin Relaxation Mechanisms and the Concept of Spectral Densities | 2 | ||
| 1.1.1 Interaction with Local Randomly Fluctuating Magnetic Fields | 3 | ||
| 1.1.2 Dipolar Interactions | 6 | ||
| 1.1.3 Chemical Shift Anisotropy (CSA) | 8 | ||
| 1.1.4 The Spin-rotation Relaxation Mechanism | 9 | ||
| 1.1.5 Correlated Mechanisms | 10 | ||
| 1.2 An Introduction to Spin 1/2 Quantum Mechanics | 11 | ||
| 1.2.1 Operators for a Single Spin 1/2 | 11 | ||
| 1.2.2 Product-operators for a System Involving Several Spins 1/2 | 15 | ||
| 1.2.3 Product-operators for a Two Spin 1/2 System and Relevant Spin States | 16 | ||
| 1.2.4 The Density-matrix and the Density-operator | 20 | ||
| 1.3 Evolution Equations | 23 | ||
| 1.3.1 The Interaction Representation | 23 | ||
| 1.3.2 Solving the Density-operator Evolution Equation within the Bloch-Wangsness-Redfield Theory | 24 | ||
| 1.3.3 Evolution Equations of Quantities Associated with Product-operators | 26 | ||
| 1.4 Spin Relaxation in a Single Spin 1/2 System | 28 | ||
| 1.4.1 Relaxation by Random Fields | 28 | ||
| 1.4.2 Relaxation by Chemical Shift Anisotropy (CSA) | 29 | ||
| 1.5 Spin Relaxation in a Two Spin 1/2 System Involving Dipolar Interaction | 32 | ||
| 1.5.1 The Dipolar Relaxation Hamiltonian | 32 | ||
| 1.5.2 Longitudinal and Transverse Auto-relaxation Rates Including the Dipolar Contribution | 34 | ||
| 1.5.3 Cross-relaxation Rates | 36 | ||
| 1.5.4 Cross-correlation Rates | 37 | ||
| 1.6 The Fundamental Relaxation Equations in the Case of a Two-spin 1/2 System | 41 | ||
| 1.6.1 The Nuclear Overhauser Effect (nOe) and the Simple Solomon Equations | 41 | ||
| 1.6.2 The Extended Solomon Equations | 45 | ||
| 1.6.3 The Goldman Equations | 47 | ||
| 1.7 Multi-spin Systems. Occurrence of Dipolar-Dipolar Cross-correlation Rates | 48 | ||
| 1.7.1 Longitudinal Relaxation | 49 | ||
| 1.7.2 Transverse Relaxation | 52 | ||
| 1.8 Conclusion | 57 | ||
| References | 57 | ||
| Chapter 2 Homonuclear Cross-relaxation and Cross-correlation in Small Molecules and in Soft Matter | 61 | ||
| 2.1 Introduction | 61 | ||
| 2.2 One-dimensional Cross-relaxation Experiments in Homonuclear Systems | 62 | ||
| 2.2.1 Steady-state Nuclear Overhauser Enhancement | 62 | ||
| 2.2.2 Transient NOE Experiments | 63 | ||
| 2.2.3 2D Cross-relaxation Experiments in Homonuclear Systems | 71 | ||
| 2.2.4 Distance Measurements from NOE Experiments | 77 | ||
| 2.2.5 Selected Examples of the Usefulness of Cross-relaxation | 80 | ||
| 2.3 Experiments to Measure Cross-correlated Relaxation Rates | 94 | ||
| 2.3.1 Experimental Observation of Longitudinal Cross-correlations | 94 | ||
| 2.3.2 Experimental Observation of Transverse Cross-correlations | 105 | ||
| 2.3.3 Cross-correlations Under Spin-lock Conditions | 112 | ||
| 2.3.4 Experimental Dynamic Frequency Shifts | 116 | ||
| 2.3.5 Cross-correlations in Paramagnetic and Quadrupolar Systems | 121 | ||
| 2.4 Motional Models and Cross-correlated Spin Relaxation | 125 | ||
| 2.4.1 Spectral Densities for Different Types of Motion | 125 | ||
| 2.4.2 Interpretation of Cross-correlation Motional Parameters | 134 | ||
| 2.5 Molecular Information from Cross-Correlated Spin Relaxation | 135 | ||
| 2.5.1 Structural Parameters from Cross-correlations | 135 | ||
| 2.5.2 Estimating the CSA Tensor | 136 | ||
| 2.5.3 Information about Carbohydrates and Nucleotides from Cross-correlations | 137 | ||
| 2.5.4 Information about Small Ligand Conformations from Binding Studies using Cross-correlations | 140 | ||
| 2.5.5 Motional Information from Cross-correlation Rates | 145 | ||
| 2.6 Conclusions | 148 | ||
| Acknowledgments | 149 | ||
| References | 149 | ||
| Chapter 3 Heteronuclear Cross-relaxation | 166 | ||
| 3.1 Introduction and Basic Concepts | 166 | ||
| 3.2 The Heteronuclear Overhauser Effect (HOE) | 170 | ||
| 3.3 HOE's Measurements and the Information they Provide | 174 | ||
| 3.4 2D Heteronuclear Overhauser Spectroscopy (HOESY) | 179 | ||
| 3.5 The 1D HOESY Experiment | 187 | ||
| 3.6 An Improved HOESY Experiment: The P.HOESY Sequence | 188 | ||
| 3.7 Inverse HOESY Experiments | 190 | ||
| 3.8 Filtered-HOESY Experiments | 192 | ||
| 3.9 1D HOE and 2D HOESY in Intermolecular Interactions | 193 | ||
| 3.10 Using Intermolecular HOESY in Chemistry and Biology | 198 | ||
| 3.10.1 Chemical Structure, Reactivity and Chiral Recognition | 198 | ||
| 3.10.2 Solute-Solvent Interactions | 200 | ||
| 3.10.3 Ion Pairs and Ionic Liquids | 206 | ||
| 3.10.4 Metallic Bonds and Aggregates | 214 | ||
| 3.10.5 Biology | 217 | ||
| 3.11 Conclusion | 220 | ||
| Acknowledgments | 221 | ||
| References | 221 | ||
| Chapter 4 Cross-correlation in Biomolecules | 239 | ||
| 4.1 Introduction | 239 | ||
| 4.1.1 Definitions | 240 | ||
| 4.1.2 Span of Uses | 240 | ||
| 4.1.3 Presentation of This Chapter | 241 | ||
| 4.2 Theory | 241 | ||
| 4.2.1 The Homogeneous Master Equation | 241 | ||
| 4.2.2 Frame Transformations of Liouvillian Superoperators | 243 | ||
| 4.2.3 Average Liouvillian Theory: Discrete Averaging | 244 | ||
| 4.2.4 Application of Discrete ALT: Measurement of CSA/DD CCCR Rates | 246 | ||
| 4.2.5 Average Liouvillian Theory: Continuous Averaging | 246 | ||
| 4.2.6 Application of Continuous ALT: Measurement of CSA/DD CCCR Rates | 248 | ||
| 4.2.7 Note on the Secular Approximation | 249 | ||
| 4.3 Measurements of Cross-relaxation at the Steady-state Effects | 249 | ||
| 4.4 HSQC-type Experiments to Measure Cross-correlated Cross-relaxation Rates | 253 | ||
| 4.4.1 Measuring CSA-Dipolar Cross-correlation (1D Experiments) | 253 | ||
| 4.4.2 2D Experiments to Measure CSA-Dipolar Cross-correlations | 254 | ||
| 4.4.3 Multi-dimensional Experiments to Measure Dipole-Dipole Cross-correlations | 269 | ||
| 4.4.4 2D Experiments for Measuring CSA-CSA Cross-correlations | 271 | ||
| 4.5 Motional Models and Cross-correlated Spin Relaxation | 274 | ||
| 4.5.1 Model-free Formalism and Large Biomolecules | 275 | ||
| 4.5.2 Dipole-Dipole Cross-correlation in Biomolecules | 278 | ||
| 4.5.3 Correlated Internal Motions | 280 | ||
| 4.5.4 3D Gaussian Axial Fluctuations Model | 281 | ||
| 4.5.5 Extraction of Cross-correlation Parameters From Dynamics | 284 | ||
| 4.5.6 Motional Information From Cross-correlation Rate | 285 | ||
| 4.6 Local Chemical Properties of Biomolecules | 286 | ||
| 4.6.1 Estimating the CSA Tensor | 286 | ||
| 4.6.2 Hydrogen Bonds and Cross-correlated Cross-relaxation | 290 | ||
| 4.7 Chemical Exchange and Cross-correlations | 292 | ||
| 4.8 Information About RNA and DNA Nucleic Acids from Cross-correlations | 296 | ||
| 4.9 Ligand-binding Studies Using Cross-correlations | 303 | ||
| 4.10 Transverse Relaxation Optimized Spectroscopy: Tailoring Auto-relaxation with Cross-correlated Relaxation | 304 | ||
| 4.10.1 Interference Between Relaxation Mechanisms | 304 | ||
| 4.10.2 TROSY From CSA-DD Cross-correlated Relaxation | 305 | ||
| 4.10.3 TROSY From DD-DD Cross-correlated Relaxation | 307 | ||
| References | 310 | ||
| Subject Index | 316 |