Table of Contents

Acknowledgments

Preface

Chapter 1: Classical NMR Spectroscopy

• 1.1 Nuclear magnetism
• 1.2 The Bloch equations
• 1.3 The one-pulse NMR experiment
• 1.4 Linewidth
• 1.5 Chemical shift
• 1.6 Scalar coupling and limitations of the Bloch equations

Chapter 2: Theoretical Description of NMR Spectroscopy

• 2.1 Postulates of quantum mechanics
  • 2.1.1 The Schrödinger equation
  • 2.1.2 Eigenvalue equations
  • 2.1.3 Simultaneous eigenfunctions
  • 2.1.4 Expectation value of the magnetic moment
• 2.2 The density matrix
  • 2.2.1 Dirac notation
  • 2.2.2 Quantum statistical mechanics
  • 2.2.3 The Liouville-von Neumann equation
  • 2.2.4 The rotating frame transformation
  • 2.2.5 Matrix representations of the spin operators
• 2.3 Pulses and rotation operators
• 2.4 Quantum mechanical NMR spectroscopy
  • 2.4.1 Equilibrium and observation operators
  • 2.4.2 The one-pulse experiment
• 2.5 Quantum mechanics of multi-spin systems
  • 2.5.1 Direct product spaces
  • 2.5.2 Scalar coupling Hamiltonian
  • 2.5.3 Rotations in product spaces
  • 2.5.4 One-pulse experiment for a two-spin system
• 2.6 Coherence
• 2.7 Product Operator Formalism
  • 2.7.1 Operator spaces
  • 2.7.2 Basis operators
  • 2.7.3 Evolution in the product operator formalism
    • 2.7.3.1 Free precession
    • 2.7.3.2 Pulses
    • 2.7.3.3 Practical Points
  • 2.7.4 Single quantum coherence and observable operators
  • 2.7.5 Multiple quantum coherence
  • 2.7.6 Coherence transfer and multiple quantum coherence
  • 2.7.7 Examples of product operator calculations
    • 2.7.7.1 The spin-echo
    • 2.7.7.2 INEPT
    • 2.7.7.3 Refocussed INEPT

Chapter 3: Experimental Aspects of NMR Spectroscopy

• 3.1 NMR instrumentation
• 3.2 Data acquisition
  • 3.2.1 Sampling
  • 3.2.2 Quadrature detection
• 3.3 Data Processing
  • 3.3.1 Fourier transformation
  • 3.3.2 Data manipulations
    • 3.3.2.1 Zero-filling
    • 3.3.2.2 Apodization
    • 3.3.2.3 Phasing
  • 3.3.3 Signal-to-noise ratio
  • 3.3.4 Alternatives to Fourier transformation
    • 3.3.4.1 Linear prediction
    • 3.3.4.2 Maximum entropy reconstruction
• 3.4 Pulse techniques
  • 3.4.1 Off-resonance effects
  • 3.4.2 Composite pulses
  • 3.4.3 Spin decoupling
  • 3.4.4 Selective pulses
• 3.5 Water suppression techniques
  • 3.5.1 Presaturation
  • 3.5.2 Jump-return and binomial sequences
  • 3.5.3 Spin lock and gradient pulses
  • 3.5.4 Post-acquisition signal processing
• 3.6 One-dimensional proton NMR spectroscopy
  • 3.6.1 Sample preparation
  • 3.6.2 Instrument setup
    • 3.6.2.1 Tuning
    • 3.6.2.2 Shimming
    • 3.6.2.3 Temperature calibration
    • 3.6.2.4 Pulse width calibration
    • 3.6.2.5 Recycle delay
  • 3.6.3 Referencing
  • 3.6.4 Acquisition and data processing
    • 3.6.4.1 One-pulse experiment
    • 3.6.4.2 Hahn-echo experiment

Chapter 4: Multi-dimensional NMR Spectroscopy

• 4.1 Two-dimensional NMR spectroscopy
• 4.2 Coherence transfer and mixing
  • 4.2.1 Through-bond coherence transfer
    • 4.2.1.1 COSY-type coherence transfer
    • 4.2.1.2 TOCSY transfer through bonds
  • 4.2.2 Through space coherence transfer
  • 4.2.3 Heteronuclear coherence transfer
• 4.3 Coherence selection, phase cycling and field gradients
  • 4.3.1 Coherence level diagrams
  • 4.3.2 Phase cycles
    • 4.3.2.1 Selection of a coherence transfer pathway
    • 4.3.2.2 Saving time
    • 4.3.2.3 Artifact suppression
    • 4.3.2.4 Limitations of phase cycling
  • 4.3.3 Pulsed field gradients
    • 4.3.3.1 Selection of a coherence transfer pathway
    • 4.3.3.2 Artifact suppression
    • 4.3.3.3 Limitations of pulsed field gradients
  • 4.3.4 Frequency discrimination
    • 4.3.4.1 Frequency discrimination by phase cycling
    • 4.3.4.2 Frequency discrimination by pulsed field gradients
    • 4.3.4.3 Aliasing and folding in multi-dimensional NMR spectroscopy
• 4.4 Resolution and sensitivity
• 4.6 Three and Four dimensional NMR Spectroscopy

Chapter 5: Relaxation and Dynamic Processes

• 5.1 Introduction and survey of theoretical approaches
  • 5.1.2 Relaxation in the Bloch equations
  • 5.1.2 The Solomon Equations
  • 5.1.3 Bloch, Wangsness and Redfield Theory
• 5.2 The Master Equation
  • 5.2.1 Interference Effects
  • 5.2.2 Like and Unlike Spins
  • 5.2.3 Relaxation in the Rotating Frame
• 5.3 Spectral Density Functions
• 5.4 Relaxation Mechanisms
  • 5.4.1 Intramolecular Dipolar Relaxation for IS spin system
  • 5.4.2 Intramolecular dipolar relaxation for scalar coupled IS spin system
  • 5.4.3 Intramolecular dipolar relaxation for IS spin system in the rotating frame
  • 5.4.4 Chemical shift anisotropy and quadrupolar relaxation
  • 5.4.5 Scalar relaxation
• 5.5 Nuclear Overhauser Effect
• 5.6 Chemical Exchange Effects in NMR Spectroscopy
  • 5.6.1 Chemical exchange for isolated spins
  • 5.6.2 Qualitative effects of chemical exchange in scalar coupled systems

Chapter 6: Experimental 1H NMR Methods

• 6.1 Assessment of the 1D 1H Spectrum
• 6.2 COSY-type experiments
  • 6.2.1 COSY
    • 6.2.1.1 Product operator analysis.
    • 6.2.1.2 Experimental protocol
    • 6.2.1.3 Processing
    • 6.2.1.4 Information content
    • 6.2.1.5 Quantitation of scalar coupling constants in COSY spectra
    • 6.2.1.6 Experimental variants
  • 6.2.2 Relayed COSY
    • 6.2.2.1 Product operator analysis.
    • 6.2.2.2 Experimental protocol
    • 6.2.2.3 Processing.
    • 6.2.2.4 Information content.
  • 6.2.3 Double-relayed COSY
• 6.3 Multiple Quantum Filtered COSY
  • 6.3.1 2QF-COSY
    • 6.3.1.1 Product operator analysis.
    • 6.3.1.2 Experimental protocol
    • 6.3.1.3 Processing.
    • 6.3.1.4 Information content
  • 6.3.2 3QF-COSY
    • 6.3.2.1 Product operator analysis
    • 6.3.2.2 Experimental protocol and processing
    • 6.3.2.3 Information content
  • 6.3.3 E-COSY
    • 6.3.3.1 Product operator analysis
    • 6.3.3.2 Experimental protocol
    • 6.3.3.3 Processing
    • 6.3.3.4 Information content
    • 6.3.3.5 Experimental variants
• 6.4 Multiple Quantum Spectroscopy
  • 6.4.1 2Q spectroscopy
    • 6.4.1.1 Product operator analysis
    • 6.4.1.2 Experimental protocol
    • 6.4.1.3 Processing
    • 6.4.1.4 Information content
  • 6.4.2 3Q spectroscopy
    • 6.4.2.1 Product operator analysis
    • 6.4.2.2 Experimental protocol and processing
    • 6.4.2.3 Information content
• 6.5 TOCSY
  • 6.5.1 Product operator analysis
  • 6.5.2 Experimental protocol
  • 6.5.3 Processing
  • 6.5.4 Information content
  • 6.5.5 Experimental variants
• 6.6 Cross-relaxation NMR experiments
  • 6.6.1 NOESY
    • 6.6.1.1 Product operator analysis.
    • 6.6.1.2 Experimental protocol
    • 6.6.1.3 Processing.
    • 6.6.1.4 Information content.
    • 6.6.1.5 Experimental variants.
  • 6.6.2 ROESY
    • 6.6.2.1 Product operator analysis
    • 6.6.2.2 Experimental protocol and processing
    • 6.6.2.3 Information content
    • 6.6.2.5 Experimental variants
• 6.7 1H 3D experiments
  • 6.7.1 Experimental protocol
  • 6.7.2 Processing
  • 6.7.3 Information content
  • 6.7.4 Experimental variants

Chapter 7: Heteronuclear NMR Experiments

• 7.1 Heteronuclear correlation NMR spectroscopy
  • 7.1.1 Basic heteronuclear correlation experiments
    • 7.1.1.1 The HMQC experiment
    • 7.1.1.2 The HSQC experiment
    • 7.1.1.3 The decoupled HSQC experiment
    • 7.1.1.4 The constant-time HSQC experiment
  • 7.1.2 Additional considerations in HMQC and HSQC experiments
    • 7.1.2.1 Phase cycling and artifact suppression
    • 7.1.2.2 13C scalar coupling and multiplet structure
    • 7.1.2.3 Solvent suppression
    • 7.1.2.4 Relaxation during HMQC and HSQC experiments
    • 7.1.2.5 Folding and aliasing
    • 7.1.2.6 Processing HMQC and HSQC experiments
  • 7.1.3 Variant HSQC experiments
    • 7.1.3.1 The constant-time 1H-13C HSQC experiment
    • 7.1.3.2 Sensitivity improvement in heteronuclear correlation experiments
    • 7.1.3.3 Gradient enhanced HSQC NMR spectroscopy
• 7.2 Heteronuclear-edited NMR spectroscopy
  • 7.2.1 3D NOESY-HSQC spectroscopy
    • 7.2.1.1 3D 1H-15N NOESY-HSQC
    • 7.2.1.2 3D 1H-13C NOESY-HSQC
  • 7.2.2 3D TOCSY-HSQC spectroscopy
  • 7.2.3 3D HSQC-NOESY and HSQC-TOCSY experiments
  • 7.2.4 HMQC-NOESY-HMQC experiments
    • 7.2.4.1 3D 15N/15N HMQC-NOESY-HMQC
    • 7.2.4.2 4D 13C/15N HMQC-NOESY-HMQC
    • 7.2.4.3 4D 13C/13C HMQC-NOESY-HMQC
    • 7.2.4.4 Processing 4D HMQC-NOESY-HMQC spectra
  • 7.2.5 Relative merits of 3D and 4D heteronuclear-edited NOESY spectroscopy
• 7.3 13C-13C correlations: the HCCH-COSY and HCCH-TOCSY experiments
  • 7.3.1 HCCH-COSY
  • 7.3.2 Constant-time HCCH-COSY
  • 7.3.3 HCCH-TOCSY
• 7.4 3D Triple-resonance experiments
  • 7.4.1 A prototype triple resonance experiment: HNCA
    • 7.4.1.1 A simple HNCA experiment
    • 7.4.1.2 The CT-HNCA experiment
    • 7.4.1.3 The decoupled CT-HNCA experiment
    • 7.4.1.4 The gradient-enhanced HNCA experiment
  • 7.4.2 A complementary approach: the HN(CO)CA experiment
  • 7.4.3 A straight-through triple resonance experiment: H(CA)NH
  • 7.4.4 Other triple resonance experiments for backbone correlations
    • 7.4.4.1 HNCO
    • 7.4.4.2 HN(CA)CO
    • 7.4.4.3 HCACO
    • 7.4.4.4 HCA(CO)N
  • 7.4.5 Correlations with the Cb/Hb spins
    • 7.4.5.1 CBCA(CO)NH
    • 7.4.5.2 CBCANH
  • 7.4.6 Additional considerations for triple resonance experiments
• 7.5 Measurement of scalar coupling constants
  • 7.5.1 HNCA-J experiment
  • 7.5.2 HNHA experiment

Chapter 8: Sequential Assignment and Structure Calculations

• 8.1 Resonance assignment strategies
  • 8.1.1 1H resonance assignments
  • 8.1.2 Heteronuclear resonance assignments
• 8.2 Three dimensional solution structures
  • 8.2.1 NMR derived structural restraints
  • 8.2.2 Structure determination
• 8.3 Conclusion: Beyond structure