Principles of Nuclear Magnetic Resonance in One and Two Dimensions

Transcription

1 Principles of Nuclear Magnetic Resonance in One and Two Dimensions Richard R. Ernst, Geoffrey Bodenhausen, and Alexander Wokaun Laboratorium für Physikalische Chemie Eidgenössische Technische Hochschule Zürich CLARENDON PRESS OXFORD

2 CONTENTS SYMBOLS, TRANSFORMATIONS, AND ABBREVIATIONS xix 1. INTRODUCTION 1 2. THE DYNAMICS OF NUCLEAR SPIN SYSTEMS Equation of motion Density operator Density operator equation Expectation values Schrödinger and Heisenberg representation Reduced spin density operator Explicit matrix representation of the master equations Liouville operator space Superoperators Commutator superoperators Unitary transformation superoperators Projection superoperators General representation of superoperators Matrix representation of a superoperator Eigenvalues and eigenoperators of superoperators Superoperator algebra Products of Cartesian spin operators Systems of spins l = \ Systems containing spins S > \ Products involving shift operators Polarization operators Cartesian single-transition operators Single-transition shift operators Irreducible tensor operators Coherence transfer The nuclear spin Hamiltonian Interactions of nuclear spins Interactions linear in the spin operators Interactions bilinear in the spin operators Interactions quadratic in the spin operators The relaxation superoperator Semi-classical relaxation theory Restriction to secular contributions Extreme narrowing Matrix representation of the relaxation superoperator Specific relaxation mechanisms First-rank relaxation mechanisms Second-rank relaxation mechanisms Spin dynamics due to chemical reactions Description of reaction networks in classical kinetics 58

3 Xll CONTENTS Exchange in systems without spin-spin couplings Modified Bloch equations for first-order reactions Higher-order reactions for spin systems without spin-spin couplings Density operator description of exchanging systems with spin-spin couplings Density operator equation and exchange superoperator for first-order reactions MANIPULATION OF NUCLEAR SPIN HAMILTONIANS The tools for manipulations Average Hamiltonian theory _ Exact calculation of Ж Cumulant expansion of the propagator Averaging by time-dependent perturbations Truncation of internal Hamiltonians Floquet theory Average Hamiltonian due to aperiodic perturbations General condition for an average Hamiltonian Average Hamiltonian in spin-echo experiments Cancellation of irrelevant terms ONE-DIMENSIONAL FOURIER SPECTROSCOPY Response theory Linear response theory Time and frequency domains Linear data-processing Apodization Resolution enhancement Non-linear response theory Quantum-mechanical response theory Stochastic response theory Classical description of Fourier spectroscopy Bloch equations in the rotating frame Ideal pulse experiment Off-resonance effects due to finite pulse amplitude Longitudinal interference in repetitive pulse experiments Transverse interference in repetitive pulse experiments Remedies for phase and intensity anomalies due to transverse interference Quenching of transverse magnetization by magnetic field gradient pulses Scrambling of transverse interference by random pulse intervals Quadriga Fourier spectroscopy Four-phase Fourier spectroscopy Phase-alternated pulse sequences 133

4 CONTENTS хш Remedies for anomalies due to non-ideal pulses: composite pulses Minimum residual M z component after а лг/2- pulse Minimum phase dispersion of transverse magnetization after a лг/2-pulse Accurate inversion: sequences optimized by calculation of trajectories Recursive expansion procedures Accurate refocusing Composite z-pulses Cyclic composite pulses Sensitivity of Fourier spectroscopy Signal-to-noise ratio of Fourier spectra The signal The noise The sensitivity Optimization of the weighting function Optimization of the signal energy Signal-to-noise ratio in slow-passage spectra Sensitivity comparison of Fourier and slow-passage experiments Sensitivity enhancement by recycling of magnetization Quantum-mechanical description of Fourier spectroscopy Density operator formalism applied to Fourier spectroscopy Equivalence of slow-passage and Fourier spectroscopy Fourier spectroscopy Slow-passage spectroscopy Comparison of Fourier and slow-passage spectra Fourier spectroscopy of non-equilibrium systems Selective and semi-selective pulses Identification of the terms in the density operator Composite rotations Intervals with a central refocusing pulse Bilinear rotations with transverse components Sequences without 'sandwich symmetry' Phase cycles Phase shifts and r.f. rotation angles Heteronuclear systems Heteronuclear polarization transfer Transfer of spin order Polarization transfer by nuclear Overhauser effect Cross-polarization in the rotating frame Adiabatic polarization transfer Polarization transfer by radio-frequency pulses Editing procedures based on polarization transfer Investigation of dynamic processes, relaxation, and chemical exchange 201

5 XIV CONTENTS Longitudinal relaxation Inversion recovery methods Saturation recovery methods Progressive saturation Selective perturbations Transverse relaxation Chemical reactions and exchange processes One-sided first-order reaction Two-sided first-order reaction Transient chemical reactions with coupled spin systems Experimental preparation of chemical nonequilibrium states Fourier double resonance Theoretical formulation of Fourier double resonance Double-resonance irradiation during detection Continuous Fourier double resonance Fourier double resonance of two coupled spins 7=1/ Strong coupling Weak coupling Spin tickling Spin decoupling treated by average Hamiltonian theory Heteronuclear spin decoupling Off-resonance decoupling Time-shared decoupling Broadband decoupling and scaling of heteronuclear interactions Multiple-pulse decoupling techniques Scaling of heteronuclear couplings Illusions of decoupling MULTIPLE-QUANTUM TRANSITIONS Number of transitions Detection of multiple-quantum transitions by continuous-wave NMR " Intensity of multiple-quantum transitions Saturation of multiple-quantum transitions Level shift of multiple-quantum transitions Line-widths of multiple-quantum transitions Applications of CW multiple-quantum NMR Time-domain multiple-quantum spectroscopy Excitation and detection of multiple-quantum coherence Non-selective pulses Selective single-quantum pulses Selective multiple-quantum pulses Spin-connectivity selective excitation Selective excitation of specific orders Offset-dependence of multiple-quantum frequencies and separation of orders Structure of multiple-quantum spectra Multiple-quantum double resonance 273

6 CONTENTS xv 5.4. Relaxation of multiple-quantum coherence Correlated external random fields Quadrupolar relaxation Measurement of multiple-quantum relaxation rates and effects of magnetic field inhomogeneity 278 TWO-DIMENSIONAL FOURIER SPECTROSCOPY Basic principles Formal theory of two-dimensional spectroscopy Explicit matrix representation Expansion of the density operator in single-transition operators Coherence transfer pathways Selection of pathways Multiple transfer Two-dimensional Fourier transformation Properties of the complex two-dimensional Fourier transformation Vector notation Similarity theorem Convolution theorem Power theorem Projection cross-section theorem Kramers-Kronig relations in two dimensions Hypercomplex two-dimensional Fourier transformation Peak shapes in two-dimensional spectra Basic peakshapes Inhomogeneous broadening and interference of neighbouring peaks Techniques for obtaining pure two-dimensional absorption peaks Real Fourier transformation in г, Time-reversal in a complementary experiment Combination of two experiments in quadrature Absolute-value spectra Projections of two-dimensional spectra Two-dimensional filtering Matched filter Lorentz-Gauss transformation Pseudo-echo transformation Manipulations of two-dimensional spectra Shearing transformations Delayed acquisition Time-proportional phase increments Symmetrization Pattern recognition Single-channel detection Operator terms and multiplet structures in two-dimensional spectra Sensitivity of two-dimensional spectra The signal envelope 349

7 XVI CONTENTS Thermal noise and fj-noise Sensitivity Comparison of the sensitivities of one- and twodimensional experiments Optimization of two-dimensional experiments Low resolution in the (Wj-domain High resolution in the»^domain Practical recommendations 357 TWO-DIMENSIONAL SEPARATION OF INTERACTIONS Basic principles Separation of chemical shifts and scalar couplings in isotropic phase Homonuclear systems Two-dimensional separation in heteronuclear systems Separation of 5-spin multiplets and 5-spin chemical shifts Removal of the chemical shifts from the (о г - domain by shearing of the two-dimensional spectrum Separation of 5-spin multiplets vs. 5-spin chemical shifts by refocusing and gated coupling Separation of 5-spin multiplets vs. 5-spin chemical shifts by refocusing and inversion of / nuclei Separation of 5-spin multiplets due to coupling to a selected /-spin vs. 5-spin chemical shifts Separation of long-range IS couplings vs. 5-spin chemical shifts 370 7'.2.2.7'. Separation of one-bond IS couplings vs. 5-spin chemical shifts Artefacts Pure two-dimensional absorption Strong coupling effects in refocusing experiments Echo modulation by non-resonant nuclei Separation of chemical shifts and dipolar couplings in oriented phase Homonuclear separated local field spectra Heteronuclear separated local field spectra Correlation of chemical shielding and dipolar coupling tensors in static powders Full simulation of powder spectra Ridge plots Separation of Ж 15 and Ж 25 under magic-angle spinning conditions Separation of isotropic and anisotropic chemical shifts Rotation-synchronized pulses Synchronous sampling with scaling Magic-angle flipping Magic-angle hopping 399

8 CONTENTS xvii TWO-DIMENSIONAL CORRELATION METHODS BASED ON COHERENCE TRANSFER Coherence transfer in two-dimensional correlation spectroscopy: amplitudes and selection rules Homonuclear two-dimensional correlation spectroscopy Weakly coupled two-spin systems Applications to complicated spectra Connectivity and multiplet effects in weakly coupled systems Strong coupling in two-dimensional correlation spectroscopy Magnetic equivalence Modified two-dimensional correlation experiments Delayed acquisition: spin-echo correlation spectroscopy Constant-time correlation spectroscopy: (^-decoupling Filtering and editing Multiple-quantum filtering p-spin-filters Filtering according to coupling network connectivity Relayed coherence transfer Coherence transfer by an average Hamiltonian in total correlation spectroscopy Homonuclear two-dimensional multiple-quantum spectroscopy Excitation and detection of multiple-quantum coherence Double-quantum spectra of two-spin systems Multiple-quantum spectra of scalar-coupled networks in isotropic phase Multiple-quantum spectra of dipole-coupled nuclei in anisotropic phase Double-quantum spectra of quadrupolar nuclei with 5 = 1 in anisotropic phase Heteronuclear coherence transfer Sensitivity considerations Coherence transfer pathways Heteronuclear two-dimensional correlation spectroscopy in isotropic phase Transfer of in-phase magnetization Broadband decoupling Decoupling by refocusing pulses Bilinear rotation decoupling Editing of heteronuclear correlation spectra Relayed heteronuclear correlation spectroscopy Heteronuclear correlation experiments involving double transfer Heteronuclear correlation in solids 485 DYNAMIC PROCESSES STUDIED BY TWO-DIMENSIONAL EXCHANGE SPECTROSCOPY Polarization transfer in one- and two-dimensional methods Selection of coherence transfer pathways 494

9 XVUl CONTENTS 9.3. Cross-relaxation and exchange in systems without resolved couplings Slow exchange Two-site systems Multiple-site exchange Two-dimensional exchange spectroscopy in coupled spin systems Density operator treatment Zero-quantum interference Longitudinal scalar or dipolar order Suppression of J cross-peaks Two-dimensional exchange difference spectroscopy Determination of rate constants by 'accordion' spectroscopy Cross-relaxation and nuclear Overhauser effects Intramolecular cross-relaxation Intramolecular cross-relaxation in a two-spin system Intramolecular cross-relaxation in a system with equivalent spins Intermolecular cross-relaxation Cross-relaxation in the slow-motion limit: applications to macromolecules Chemical exchange Indirect detection of longitudinal relaxation in multilevel spin systems Dynamic processes in solids NUCLEAR MAGNETIC RESONANCE IMAGING Classification of imaging techniques Sequential point techniques Sensitive point technique Field focusing NMR (FONAR) and topical NMR Sequential line technique Sensitive line or multiple sensitive point method Line scan technique Echo line imaging Sequential plane technique Projection-reconstruction technique Fourier imaging Spin-warp imaging Rotating-frame imaging Planar and multiplanar imaging Echo planar imaging Comparison of sensitivity and performance time of various imaging techniques Sensitivity Performance time 563 REFERENCES 565 INDEX 597