Spin Dynamics Basics of Nuclear Magnetic Resonance. Malcolm H. Levitt
|
|
- Gabriel Matthews
- 5 years ago
- Views:
Transcription
1 Spin Dynamics Basics of Nuclear Magnetic Resonance Second edition Malcolm H. Levitt The University of Southampton, UK John Wiley &. Sons, Ltd
2 Preface xxi Preface to the First Edition xxiii Introduction 1 Part 1 Nuclear Magnetism 3 1 Matter Atoms and Nuclei Spin Classical angular momentum Quantum angular momentum Spin angular momentum Combining angular momenta The Pauli Principle Nuclei The fundamental particles Neutrons and protons Isotopes Nuclear Spin Nuclear spin states Nuclear Zeeman splitting Zero-spin nuclei Spin-1/2 nuclei Quadrupolar nuclei with integer spin Quadrupolar nuclei with half-integer spin Atomic and Molecular Structure Atoms Molecules States of Matter Gases Liquids Solids 19
3 viii 2 Magnetism The Electromagnetic Field Macroscopic Magnetism Microscopic Magnetism Spin Precession Larmor Frequency Spin Lattice Relaxation: Nuclear Paramagnetism Transverse Magnetization and Transverse Relaxation NMR Signal Electronic Magnetism 36 3 NMR Spectroscopy A Simple Pulse Sequence A Simple Spectrum Isotopomeric Spectra Relative Spectral Frequencies: Case of Positive Gyromagnetic Ratio Relative Spectral Frequencies: Case of Negative Gyromagnetic Ratio Inhomogeneous Broadening Chemical Shifts J-Coupling Multiplets Heteronuclear Decoupling 59 Part 2 The NMR Experiment 63 4 The NMR Spectrometer The Magnet The Transmitter Section The synthesizer: radio-frequency phase shifts The pulse gate: radio-frequency pulses Radio-frequency amplifier The Duplexer The Probe The Receiver Section Signal preamplifier The quadrature receiver Analogue digital conversion Signal phase shifting Overview of the Radio-Frequency Section Pulsed Field Gradients Magnetic field gradients Field gradient coils Field gradient control 80
4 5 Fourier Transform NMR A Single-Pulse Experiment Signal Averaging Multiple-Pulse Experiments: Phase Cycling Heteronuclear Experiments Pulsed Field Gradient Sequences Arrayed Experiments NMR Signal NMR Spectrum Fourier transformation Lorentzians Explanation of Fourier transformation Spectral phase shifts Frequency-dependent phase correction Two-Dimensional Spectroscopy Two-dimensional signal surface Two-dimensional Fourier transformation Phase twist peaks Pure absorption two-dimensional spectra Three-Dimensional Spectroscopy 114 Part 3 Quantum Mechanics Mathematical Techniques Functions Continuous functions Normalization Orthogonal and orthonormal functions Dirac notation Vector representation of functions Operators Commutation Matrix representations Diagonal matrices Block diagonal matrices Inverse Adjoint Hermitian operators Unitary operators Eigenfunctions, Eigenvalues and Eigenvectors Eigenequations Degeneracy Eigenfunctions and eigenvalues of Hermitian operators Eigenfunctions of commuting operators: non-degenerate case Eigenfunctions of commuting operators: degenerate case Eigenfunctions of commuting operators: summary Eigenvectors 134
5 x 6.4 Diagonalization Diagonalization of Hermitian or unitary matrices Exponential Operators Powers of operators Exponentials of operators Exponentials of unity and null operators Products of exponential operators Inverses of exponential operators Complex exponentials of operators Exponentials of small operators Matrix representations of exponential operators Cyclic Commutation Definition of cyclic commutation Sandwich formula 139 Review of Quantum Mechanics Spinless Quantum Mechanics The state of the particle The equation of motion Experimental observations Energy Levels Natural Units Superposition States and Stationary States Conservation Laws Angular Momentum Angular momentum operators Rotation operators Rotation sandwiches Angular momentum eigenstates and eigenvalues The angular momentum eigenstates Shift operators Matrix representations of the angular momentum operators Spin Spin angular momentum operators Spin rotation operators Spin Zeeman basis Trace Spin-1/ Zeeman eigenstates Angular momentum operators Spin-1/2 rotation operators Unity Operator Shift operators Projection operators Ket-bra notation Higher Spin Spin 1= Spin 1 = 3/ Higher spins 165
6 Part 4 Nuclear Spin Interactions Nuclear Spin Hamiltonian Spin Hamiltonian Hypothesis Electromagnetic Interactions Electric spin Hamiltonian Magnetic spin interactions External and Internal Spin Interactions Spin interactions: summary External Magnetic Fields Static field Radio-frequency field Gradient field External spin interactions: summary Internal Spin Hamiltonian The internal spin interactions Simplification of the internal Hamiltonian Motional Averaging Modes of molecular motion Molecular rotations Molecular translations Intramolecular and intermolecular spin interactions Summary of motional averaging Internat Spin Interactions Chemical Shift Chemical shift tensor Principal axes Principal values Isotropic chemical shift Chemical shift anisotropy (CSA) Chemical shift for an arbitrary molecular orientation Chemical shift frequency Chemical shift interaction in isotropic liquids Chemical shift interaction in anisotropic liquids Chemical shift interaction in solids Chemical shift interaction: summary Electric Quadrupole Coupling Electric field gradient tensor Nuclear quadrupole Hamiltonian Isotropic liquids Anisotropic liquids Solids Quadrupole interaction: summary Direct Dipole Dipole Coupling Secular dipole dipole coupling Dipole dipole coupling in isotropic liquids 215
7 xii Dipole dipole coupling in liquid crystals Dipole dipole coupling in solids Dipole dipole interaction: summary 9.4 J-Coupling Isotropic J-coupling Liquid crystals and solids Mechanism of the J-coupling J-coupling: summary 9.5 Spin Rotation Interaction 9.6 Summary of the Spin Hamiltonian Terms Part 5 Uncoupled Spins Single Spin-1/ Zeeman Eigenstates Measurement of Angular Momentum: Quantum Indeterminacy Energy Levels Superposition States General spin states Vector notation Some particular states Phase factors Spin Precession Dynamics of the eigenstates Dynamics of the superposition states Rotating Frame Precession in the Rotating Frame Radio-frequency Pulse Rotating-frame Hamiltonian x-pulse Nutation Pulse of general phase Off-resonance effects 253 Ensemble of Spins-1/ Spin Density Operator Populations and Coherences Density matrix Box notation Balls and arrows Orders of coherence Relationships between populations and coherences Physical interpretation of the populations Physical interpretation of the coherences Thermal Equilibrium Rotating-Frame Density Operator 268
8 xiii 11.5 Magnetization Vector Strong Radio-Frequency Pulse Excitation of coherence Population inversion Cycle of states Stimulated absorption and emission Free Precession Without Relaxation Operator Transformations Pulse of phase Op = Pulse of phase (Pp = 7r/ Pulse of phase rbp = n Pulse of phase = 37r/ Pulse of general phase (b p Free precession for an interval r Free Evolution with Relaxation Transverse relaxation Longitudinal relaxation Magnetization Vector Trajectories NMR Signal and NMR Spectrum Single-Pulse Spectra Experiments an Non-Interacting Spins-1/ Inversion Recovery: Measurement of T Spin Echoes: Measurement of 7' Homogenous and inhomogenenous broadening Inhomogenenous broadening in the time domain Spin echo pulse sequence Refocusing Coherence interpretation Coherence transfer pathway Spin Locking: Measurement of T1p Gradient Echoes Slice Selection NMR Imaging Quadrupolar Nuclei Spin I = Spin-1 states Spin-1 energy levels Spin-1 density matrix Coherence evolution Observable coherences and NMR spectrum Thermal equilibrium Strong radio-frequency pulse Excitation of coherence NMR spectrum Quadrupolar echo 331
9 xiv 13.2 Spin 1= 3/ Spin-312 energy levels Populations and coherences NMR signal Single pulse spectrum Spin-3/2 spectra for small quadrupole couplings Second-order quadrupole couplings Central transition excitation Central transition echo Spin I = 5/ Spins I = 7/ Spins I = 9/2 350 Part 6 Coupled Spins Spin-1/2 Pairs Coupling Regimes Zeeman Product States and Superposition States Spin-Pair Hamiltonian Pairs of Magnetically Equivalent Spins Singlets and triplets Energy levels NMR spectra Dipolar echo Weakly Coupled Spin Pairs Weak coupling AX spin systems Energy levels AX spectrum Heteronuclear spin pairs Homonuclear AX System Eigenstates and Energy Levels Density Operator Rotating Frame Free Evolution Evolution of a spin pair Evolution of the coherences Spectrum of the AX System: Spin Spin Splitting Product Operators Construction of product operators Populations and coherences Spin orientations Thermal Equilibrium Radio-Frequency Pulses Rotations of a single spin pair Rotations of the spin density Operator 393
10 Operator transformations Free Evolution of the Product Operators Chemical shift evolution J-coupling evolution Relaxation Spin Echo Sandwich Experiments an AX Systems COSY The assignment problem COSY pulse sequence Theory of COSY: coherence interpretation Product Operator interpretation Experimental examples INADEQUATE C isotopomers Pulse sequence Theory of INADEQUATE Coherence transfer pathways and phase cycling Two-dimensional INADEQUATE INEPT The sensitivity of nuclear isotopes INEPT pulse sequence Refocused INEPT Residual Dipolar Couplings Angular information Spin Hamiltonian Orienting media Doublet splittings Many-Spin Systems Molecular Spin System Spin Ensemble Motionally Suppressed J-Couplings Chemical Equivalence Magnetic Equivalence Weak Coupling Heteronuclear Spin Systems Alphabet Notation Spin Coupling Topologies Many-Spin Dynamics Spin Hamiltonian Energy Eigenstates 468
11 xvi 18.3 Superposition States Spin Density Operator Populations and Coherences Coherence orders Combination coherences and simple coherences Coherence frequencies Degenerate coherences Observable coherences NMR Spectra Many-Spin Product Operators Construction of product operators Populations and coherences Physical interpretation of product operators Thermal Equilibrium Radio-Frequency Pulses Free Precession Chemical shift evolution J-coupling evolution Relaxation Spin Echo Sandwiches INEPT in an /2 S System COSY in Multiple-Spin Systems AMX spectrum Active and passive spins Cross-peak multiplets Diagonal peaks Linear spin systems TOCSY The ambiguity of COSY spectra TOCSY pulse sequence Theory of TOCSY 499 Part 7 Motion and Relaxation Motion Motional Processes Molecular vibrations Local rotations of molecular groups Molecular flexibility Chemical exchange Molecular rotations Translational motion Mechanical motion Motional Time-Scales Motional Effects Motional Averaging Motional Lineshapes and Two-Site Exchange 516
12 Slow intermediate exchange and motional broadening Fast intermediate exchange and motional narrowing Averaging of J-splittings Asymmetric two-site exchange Knight shift Paramagnetic shifts Sample Spinning Longitudinal Magnetization Exchange Two-dimensional exchange spectroscopy Theory Motional regimes Diffusion Relaxation Types of Relaxation Relaxation Mechanisms Random Field Relaxation Autocorrelation functions and correlation times Spectral density Normalized spectral density Transition probabilities Thermally corrected transition probabilities Spin lattice relaxation Dipole Dipole Relaxation Rotational correlation time Transition probabilities Solomon equations Longitudinal relaxation Transverse relaxation Steady-State Nuclear Overhauser Effect NOESY NOESY pulse sequence NOESY signal NOESY spectra NOESY and chemical exchange Molecular structure determination ROESY Transverse cross-relaxation Spin locking Transverse Solomon equations ROESY spectra ROESY and chemical exchange ROESY and TOCSY Cross-Correlated Relaxation Cross-correlation Cross-correlation of spin interactions Dipole dipole cross-correlation and angular estimations TROSY 590
13 XVlli Part 8 Appendices 597 Appendix A: Supplementary Material 599 A.1 Euler Angles and Frame Transformations 599 A.1.1 Definition of the Euler angles 599 A.1.2 Euler rotations: first scheme 599 A.1.3 Euler rotations: second scheme 600 A.1.4 Euler rotation matrices 601 A.1.5 Reference-frame orientations 601 A.1.6 Consecutive reference-frame transformations 602 A.1.7 Passive rotations 602 A.1.8 Tensor transformations 603 A.1.9 Intermediate reference frames 604 A.2 Rotations and Cyclic Commutation 604 A.3 Rotation Sandwiches 605 A.4 Spin-1/2 Rotation Operators 606 A.5 Quadrature Detection and Spin Coherences 608 A.6 Secular Approximation 611 A.7 Quadrupolar Interaction 614 A.7.1 Full quadrupolar interaction 614 A.7.2 First-order quadrupolar interaction 614 A.7.3 Higher-order quadrupolar interactions 615 A.8 Strong Coupling 615 A.8.1 Strongly-coupled Spin-1/2 pairs 615 A.8.2 General strongly coupled systems 620 A.9 J-Couplings and Magnetic Equivalence 621 A.10 Spin Echo Sandwiches 623 A.10.1 Short-duration limit 625 A.10.2 Long-duration limit 625 A.10.3 Two spin echo sequences 626 A.10.4 Heteronuclear spin echo sequences 627 A.11 Phase Cycling 629 A.11.1 Coherence transfer pathways 629 A.11.2 Coherence transfer amplitudes 630 A.11.3 Coherence orders and phase shifts 631 A.11.4 The pathway phase 632 A.11.5 A sum theorem 633 A.11.6 Pathway selection I 634 A.11.7 Pathway selection II 635 A.11.8 Pathway selection III 637 A.11.9 Selection of a single pathway I 638 A Selection of a single pathway II 639 A Dual pathway selection 640 A Internal phases I 641 A Internal phases II 642 A Nested phase cycles I 644 A Nested phase cycles II 645 A Different ways of constructing phase cycles 648
14 xix A.12 Coherence Selection by Pulsed Field Gradients 649 A.12.1 Field gradient dephasing 649 A.12.2 Pathway phase 651 A.12.3 Coherence transfer echoes 652 A.12.4 Pathway selection 652 A.12.5 Heteronuclear coherence transfer echoes 652 A.13 Bloch Equations 653 A.14 Chemical Exchange 654 A.14.1 The incoherent dynamics 655 A.14.2 The coherent dynamics 655 A.14.3 The spectrum 656 A.14.4 Longitudinal magnetization exchange 658 A.15 Solomon Equations 660 A.16 Cross-Relaxation Dynamics 662 Appendix B: Symbols and Abbreviations 665 Answers to the Exercises 681 Index 693
PROTEIN NMR SPECTROSCOPY
List of Figures List of Tables xvii xxvi 1. NMR SPECTROSCOPY 1 1.1 Introduction to NMR Spectroscopy 2 1.2 One Dimensional NMR Spectroscopy 3 1.2.1 Classical Description of NMR Spectroscopy 3 1.2.2 Nuclear
More informationMagnetic Resonance Spectroscopy
INTRODUCTION TO Magnetic Resonance Spectroscopy ESR, NMR, NQR D. N. SATHYANARAYANA Formerly, Chairman Department of Inorganic and Physical Chemistry Indian Institute of Science, Bangalore % I.K. International
More informationHigh-Resolutio n NMR Techniques i n Organic Chemistry TIMOTHY D W CLARIDGE
High-Resolutio n NMR Techniques i n Organic Chemistry TIMOTHY D W CLARIDGE Foreword Preface Acknowledgements V VI I X Chapter 1. Introduction 1.1. The development of high-resolution NMR 1 1.2. Modern
More informationPrinciples of Nuclear Magnetic Resonance in One and Two Dimensions
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
More informationCONTENTS. 2 CLASSICAL DESCRIPTION 2.1 The resonance phenomenon 2.2 The vector picture for pulse EPR experiments 2.3 Relaxation and the Bloch equations
CONTENTS Preface Acknowledgements Symbols Abbreviations 1 INTRODUCTION 1.1 Scope of pulse EPR 1.2 A short history of pulse EPR 1.3 Examples of Applications 2 CLASSICAL DESCRIPTION 2.1 The resonance phenomenon
More informationTHEORY OF MAGNETIC RESONANCE
THEORY OF MAGNETIC RESONANCE Second Edition Charles P. Poole, Jr., and Horacio A. Farach Department of Physics University of South Carolina, Columbia A Wiley-lnterscience Publication JOHN WILEY & SONS
More informationELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications
ELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications Second Edition JOHN A. WElL Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan, S7N OWO Canada JAMES
More informationSpin Relaxation and NOEs BCMB/CHEM 8190
Spin Relaxation and NOEs BCMB/CHEM 8190 T 1, T 2 (reminder), NOE T 1 is the time constant for longitudinal relaxation - the process of re-establishing the Boltzmann distribution of the energy level populations
More informationT 1, T 2, NOE (reminder)
T 1, T 2, NOE (reminder) T 1 is the time constant for longitudinal relaxation - the process of re-establishing the Boltzmann distribution of the energy level populations of the system following perturbation
More informationPrinciples of Magnetic Resonance
С. Р. Slichter Principles of Magnetic Resonance Third Enlarged and Updated Edition With 185 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Contents 1. Elements of Resonance
More informationPrinciples of Nuclear Magnetic Resonance Microscopy
Principles of Nuclear Magnetic Resonance Microscopy Paul T. Callaghan Department of Physics and Biophysics Massey University New Zealand CLARENDON PRESS OXFORD CONTENTS 1 PRINCIPLES OF IMAGING 1 1.1 Introduction
More informationONE AND TWO DIMENSIONAL NMR SPECTROSCOPY
ONE AND TWO DIMENSIONAL NMR SPECTROSCOPY Atta-ur-Rahman H.E.J. Research Institute of Chemistry, University ofkarachi, Karachi 32, Pakistan ELSEVIER Amsterdam Oxford New York Tokyo 1989 IX CONTENTS Chapter-l
More informationSpectroscopy of Polymers
Spectroscopy of Polymers Jack L. Koenig Case Western Reserve University WOMACS Professional Reference Book American Chemical Society, Washington, DC 1992 Contents Preface m xiii Theory of Polymer Characterization
More informationBasic One- and Two-Dimensional NMR Spectroscopy
Horst Friebolin Basic One- and Two-Dimensional NMR Spectroscopy Third Revised Edition Translated by Jack K. Becconsall WILEY-VCH Weinheim New York Chichester Brisbane Singapore Toronto Contents XV 1 The
More informationClassical behavior of magnetic dipole vector. P. J. Grandinetti
Classical behavior of magnetic dipole vector Z μ Y X Z μ Y X Quantum behavior of magnetic dipole vector Random sample of spin 1/2 nuclei measure μ z μ z = + γ h/2 group μ z = γ h/2 group Quantum behavior
More informationSuperoperators for NMR Quantum Information Processing. Osama Usman June 15, 2012
Superoperators for NMR Quantum Information Processing Osama Usman June 15, 2012 Outline 1 Prerequisites 2 Relaxation and spin Echo 3 Spherical Tensor Operators 4 Superoperators 5 My research work 6 References.
More informationGeneral NMR basics. Solid State NMR workshop 2011: An introduction to Solid State NMR spectroscopy. # nuclei
: An introduction to Solid State NMR spectroscopy Dr. Susanne Causemann (Solid State NMR specialist/ researcher) Interaction between nuclear spins and applied magnetic fields B 0 application of a static
More informationAn introduction to Solid State NMR and its Interactions
An introduction to Solid State NMR and its Interactions From tensor to NMR spectra CECAM Tutorial September 9 Calculation of Solid-State NMR Parameters Using the GIPAW Method Thibault Charpentier - CEA
More informationTHE NUCLEAR OVERHAUSER EFFECT IN STRUCTURAL AND CONFORMATIONAL ANALYSIS
THE NUCLEAR OVERHAUSER EFFECT IN STRUCTURAL AND CONFORMATIONAL ANALYSIS David Neuhaus and Michael P. Williamson VCH CONTENTS Preface v Acknowledgments vii Symbols, Abbreviations, and Units xvii Introduction
More informationNMR Spectroscopy: A Quantum Phenomena
NMR Spectroscopy: A Quantum Phenomena Pascale Legault Département de Biochimie Université de Montréal Outline 1) Energy Diagrams and Vector Diagrams 2) Simple 1D Spectra 3) Beyond Simple 1D Spectra 4)
More informationNuclear Magnetic Resonance Imaging
Nuclear Magnetic Resonance Imaging Simon Lacoste-Julien Electromagnetic Theory Project 198-562B Department of Physics McGill University April 21 2003 Abstract This paper gives an elementary introduction
More informationNuclear magnetic resonance in condensed matter
University of Ljubljana Faculty of mathematics and physics Physics department SEMINAR Nuclear magnetic resonance in condensed matter Author: Miha Bratkovič Mentor: prof. dr. Janez Dolinšek Ljubljana, October
More informationMR Fundamentals. 26 October Mitglied der Helmholtz-Gemeinschaft
MR Fundamentals 26 October 2010 Mitglied der Helmholtz-Gemeinschaft Mitglied der Helmholtz-Gemeinschaft Nuclear Spin Nuclear Spin Nuclear magnetic resonance is observed in atoms with odd number of protons
More informationThe Raman Effect. A Unified Treatment of the Theory of Raman Scattering by Molecules. DerekA. Long
The Raman Effect A Unified Treatment of the Theory of Raman Scattering by Molecules DerekA. Long Emeritus Professor ofstructural Chemistry University of Bradford Bradford, UK JOHN WILEY & SONS, LTD Vll
More informationSpectral Broadening Mechanisms
Spectral Broadening Mechanisms Lorentzian broadening (Homogeneous) Gaussian broadening (Inhomogeneous, Inertial) Doppler broadening (special case for gas phase) The Fourier Transform NC State University
More informationChapter 7. Nuclear Magnetic Resonance Spectroscopy
Chapter 7 Nuclear Magnetic Resonance Spectroscopy I. Introduction 1924, W. Pauli proposed that certain atomic nuclei have spin and magnetic moment and exposure to magnetic field would lead to energy level
More informationDirect dipolar interaction - utilization
Direct dipolar interaction - utilization Two main uses: I: magnetization transfer II: probing internuclear distances Direct dipolar interaction - utilization Probing internuclear distances ˆ hetero D d
More informationNMR, the vector model and the relaxation
NMR, the vector model and the relaxation Reading/Books: One and two dimensional NMR spectroscopy, VCH, Friebolin Spin Dynamics, Basics of NMR, Wiley, Levitt Molecular Quantum Mechanics, Oxford Univ. Press,
More informationIntroduction to Relaxation Theory James Keeler
EUROMAR Zürich, 24 Introduction to Relaxation Theory James Keeler University of Cambridge Department of Chemistry What is relaxation? Why might it be interesting? relaxation is the process which drives
More informationIII.4 Nuclear Magnetic Resonance
III.4 Nuclear Magnetic Resonance Radiofrequency (rf) spectroscopy on nuclear spin states in a uniaxial constant magnetic field B = B 0 z (III.4.1) B 0 is on the order of 1-25 T The rf frequencies vary
More informationBASIC NMR HANDBOOK Written by M. A. Eastman Copyright 1997, 2001, 2013, 2015, 2018
BASIC NMR HANDBOOK Written by M. A. Eastman Copyright 1997, 2001, 2013, 2015, 2018 Basic NMR Handbook Table of Contents: Preface ii viii PART 1 Chapter 1: Introduction to NMR 1 Why Study NMR? 1 The Magnetic
More informationSpectral Broadening Mechanisms. Broadening mechanisms. Lineshape functions. Spectral lifetime broadening
Spectral Broadening echanisms Lorentzian broadening (Homogeneous) Gaussian broadening (Inhomogeneous, Inertial) Doppler broadening (special case for gas phase) The Fourier Transform NC State University
More informationThe NMR Inverse Imaging Problem
The NMR Inverse Imaging Problem Nuclear Magnetic Resonance Protons and Neutrons have intrinsic angular momentum Atoms with an odd number of proton and/or odd number of neutrons have a net magnetic moment=>
More informationRelaxation, Multi pulse Experiments and 2D NMR
Relaxation, Multi pulse Experiments and 2D NMR To Do s Read Chapter 6 Complete the end of chapter problems; 6 1, 6 2, 6 3, 6 5, 6 9 and 6 10. Read Chapter 15 and do as many problems as you can. Relaxation
More informationQuantum Physics II (8.05) Fall 2002 Outline
Quantum Physics II (8.05) Fall 2002 Outline 1. General structure of quantum mechanics. 8.04 was based primarily on wave mechanics. We review that foundation with the intent to build a more formal basis
More informationP. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics THIRD EDITION
P. W. Atkins and R. S. Friedman Molecular Quantum Mechanics THIRD EDITION Oxford New York Tokyo OXFORD UNIVERSITY PRESS 1997 Introduction and orientation 1 Black-body radiation 1 Heat capacities 2 The
More informationQuantum Mechanics: Fundamentals
Kurt Gottfried Tung-Mow Yan Quantum Mechanics: Fundamentals Second Edition With 75 Figures Springer Preface vii Fundamental Concepts 1 1.1 Complementarity and Uncertainty 1 (a) Complementarity 2 (b) The
More informationDesign strategies for pulse sequences in multidimensional optical spectroscopies
JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 11 15 SEPTEMBER 2001 Design strategies for pulse sequences in multidimensional optical spectroscopies C. Scheurer a) and S. Mukamel b) Department of Chemistry,
More informationATOMIC AND LASER SPECTROSCOPY
ALAN CORNEY ATOMIC AND LASER SPECTROSCOPY CLARENDON PRESS OXFORD 1977 Contents 1. INTRODUCTION 1.1. Planck's radiation law. 1 1.2. The photoelectric effect 4 1.3. Early atomic spectroscopy 5 1.4. The postulates
More informationCross Polarization 53 53
Cross Polarization 53 Why don t we normally detect protons in the solid-state BPTI Strong couplings between protons ( >20kHz) Homogeneous interaction Not readily averaged at moderate spinning speeds Rhodopsin
More informationV27: RF Spectroscopy
Martin-Luther-Universität Halle-Wittenberg FB Physik Advanced Lab Course V27: RF Spectroscopy ) Electron spin resonance (ESR) Investigate the resonance behaviour of two coupled LC circuits (an active rf
More informationPRINCIPLES OF NONLINEAR OPTICAL SPECTROSCOPY
PRINCIPLES OF NONLINEAR OPTICAL SPECTROSCOPY Shaul Mukamel University of Rochester Rochester, New York New York Oxford OXFORD UNIVERSITY PRESS 1995 Contents 1. Introduction 3 Linear versus Nonlinear Spectroscopy
More informationFerdowsi University of Mashhad
Spectroscopy in Inorganic Chemistry Nuclear Magnetic Resonance Spectroscopy spin deuterium 2 helium 3 The neutron has 2 quarks with a -e/3 charge and one quark with a +2e/3 charge resulting in a total
More informationSolid-state NMR of spin > 1/2
Solid-state NMR of spin > 1/2 Nuclear spins with I > 1/2 possess an electrical quadrupole moment. Anisotropic Interactions Dipolar Interaction 1 H- 1 H, 1 H- 13 C: typically 50 khz Anisotropy of the chemical
More informationIntroduction to 1D and 2D NMR Spectroscopy (4) Vector Model and Relaxations
Introduction to 1D and 2D NMR Spectroscopy (4) Vector Model and Relaxations Lecturer: Weiguo Hu 7-1428 weiguoh@polysci.umass.edu October 2009 1 Approximate Description 1: Energy level model Magnetic field
More informationChem8028(1314) - Spin Dynamics: Spin Interactions
Chem8028(1314) - Spin Dynamics: Spin Interactions Malcolm Levitt see also IK m106 1 Nuclear spin interactions (diamagnetic materials) 2 Chemical Shift 3 Direct dipole-dipole coupling 4 J-coupling 5 Nuclear
More informationDouble-Resonance Experiments
Double-Resonance Eperiments The aim - to simplify complicated spectra by eliminating J-couplings. omonuclear Decoupling A double resonance eperiment is carried out using a second rf source B 2 in addition
More informationSolid-state NMR and proteins : basic concepts (a pictorial introduction) Barth van Rossum,
Solid-state NMR and proteins : basic concepts (a pictorial introduction) Barth van Rossum, 16.02.2009 Solid-state and solution NMR spectroscopy have many things in common Several concepts have been/will
More informationPolarised Nucleon Targets for Europe, 2nd meeting, Bochum 2005
Polarised Nucleon Targets for Europe, nd meeting, Bochum Temperature dependence of nuclear spin-lattice relaxations in liquid ethanol with dissolved TEMPO radicals H. Štěpánková, J. Englich, J. Kohout,
More informationQUANTUM MECHANICS. Franz Schwabl. Translated by Ronald Kates. ff Springer
Franz Schwabl QUANTUM MECHANICS Translated by Ronald Kates Second Revised Edition With 122Figures, 16Tables, Numerous Worked Examples, and 126 Problems ff Springer Contents 1. Historical and Experimental
More informationCHEM / BCMB 4190/6190/8189. Introductory NMR. Lecture 10
CHEM / BCMB 490/690/889 Introductory NMR Lecture 0 - - CHEM 490/690 Spin-Echo The spin-echo pulse sequence: 90 - τ - 80 - τ(echo) Spins echoes are widely used as part of larger pulse sequence to refocus
More informationTable of Contents. Chapter 1 lntroduction and Practical Considerations of Two-Dimensional. Chapter 2 Establishing Proton-Proton Connectivities
Table of Contents Chapter 1 lntroduction and Practical Considerations of Two-Dimensional NMR Spectroscopy lntroduction Fundamental Segments of Two-Dimensional NMR Experiments Preparation Evolution Mixing
More informationINTRODUCTION TO NMR and NMR QIP
Books (NMR): Spin dynamics: basics of nuclear magnetic resonance, M. H. Levitt, Wiley, 2001. The principles of nuclear magnetism, A. Abragam, Oxford, 1961. Principles of magnetic resonance, C. P. Slichter,
More informationA Hands on Introduction to NMR Lecture #1 Nuclear Spin and Magnetic Resonance
A Hands on Introduction to NMR 22.920 Lecture #1 Nuclear Spin and Magnetic Resonance Introduction - The aim of this short course is to present a physical picture of the basic principles of Nuclear Magnetic
More informationBiophysical Chemistry: NMR Spectroscopy
Relaxation & Multidimensional Spectrocopy Vrije Universiteit Brussel 9th December 2011 Outline 1 Relaxation 2 Principles 3 Outline 1 Relaxation 2 Principles 3 Establishment of Thermal Equilibrium As previously
More information9. Nuclear Magnetic Resonance
9. Nuclear Magnetic Resonance Nuclear Magnetic Resonance (NMR) is a method that can be used to find structures of proteins. NMR spectroscopy is the observation of spins of atoms and electrons in a molecule
More informationUNESCO - EOLSS SAMPLE CHAPTER
NMR SPECTROSCOPY Juan Carlos Paniagua and Miquel Pons University of Barcelona, Spain Keywords: chemical shift, correlation spectroscopy, diffusion coefficient, Fourier transform spectroscopy, imaging,
More informationFundamental MRI Principles Module 2 N. Nuclear Magnetic Resonance. X-ray. MRI Hydrogen Protons. Page 1. Electrons
Fundamental MRI Principles Module 2 N S 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons positively charged neutrons no significant charge electrons negatively charged Protons
More informationPhysical Background Of Nuclear Magnetic Resonance Spectroscopy
Physical Background Of Nuclear Magnetic Resonance Spectroscopy Michael McClellan Spring 2009 Department of Physics and Physical Oceanography University of North Carolina Wilmington What is Spectroscopy?
More information14. Coherence Flow Networks
14. Coherence Flow Networks A popular approach to the description of NMR pulse sequences comes from a simple vector model 1,2 in which the motion of the spins subjected to RF pulses and chemical shifts
More informationIt is possible to choose the temperature for each experiment by setting a temperature under the Temp pane (under the Standard panel).
1 2 The study queue gives a lot of flexibility for lining up experiments: they can be run at different temperatures or at different times. You must respect the instrument limits: do not submit experiments
More informationAnalytical Mechanics for Relativity and Quantum Mechanics
Analytical Mechanics for Relativity and Quantum Mechanics Oliver Davis Johns San Francisco State University OXPORD UNIVERSITY PRESS CONTENTS Dedication Preface Acknowledgments v vii ix PART I INTRODUCTION:
More informationThe Nuclear Emphasis
The Nuclear Emphasis Atoms are composed of electrons and nuclei we ll focus almost exclusively on the physical properties of the nucleus and the chemicoelectronic attributes of its environment. The nucleus
More informationNMR: Formalism & Techniques
NMR: Formalism & Techniques Vesna Mitrović, Brown University Boulder Summer School, 2008 Why NMR? - Local microscopic & bulk probe - Can be performed on relatively small samples (~1 mg +) & no contacts
More informationModern Optical Spectroscopy
Modern Optical Spectroscopy With Exercises and Examples from Biophysics and Biochemistry von William W Parson 1. Auflage Springer-Verlag Berlin Heidelberg 2006 Verlag C.H. Beck im Internet: www.beck.de
More informationChemistry 431. Lecture 23
Chemistry 431 Lecture 23 Introduction The Larmor Frequency The Bloch Equations Measuring T 1 : Inversion Recovery Measuring T 2 : the Spin Echo NC State University NMR spectroscopy The Nuclear Magnetic
More informationNMR Dynamics and Relaxation
NMR Dynamics and Relaxation Günter Hempel MLU Halle, Institut für Physik, FG Festkörper-NMR 1 Introduction: Relaxation Two basic magnetic relaxation processes: Longitudinal relaxation: T 1 Relaxation Return
More informationThe Basics of Magnetic Resonance Imaging
The Basics of Magnetic Resonance Imaging Nathalie JUST, PhD nathalie.just@epfl.ch CIBM-AIT, EPFL Course 2013-2014-Chemistry 1 Course 2013-2014-Chemistry 2 MRI: Many different contrasts Proton density T1
More informationCOPYRIGHTED MATERIAL. Production of Net Magnetization. Chapter 1
Chapter 1 Production of Net Magnetization Magnetic resonance (MR) is a measurement technique used to examine atoms and molecules. It is based on the interaction between an applied magnetic field and a
More informationMRI Physics I: Spins, Excitation, Relaxation
MRI Physics I: Spins, Excitation, Relaxation Douglas C. Noll Biomedical Engineering University of Michigan Michigan Functional MRI Laboratory Outline Introduction to Nuclear Magnetic Resonance Imaging
More informationNUCLEAR MAGNETIC RESONANCE. Introduction. Vol. 10 NUCLEAR MAGNETIC RESONANCE 637
Vol. 10 NUCLEAR MAGNETIC RESONANCE 637 NUCLEAR MAGNETIC RESONANCE Introduction An important objective in materials science is the establishment of relationships between the microscopic structure or molecular
More informationList of Comprehensive Exams Topics
List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle
More informationFundamental MRI Principles Module Two
Fundamental MRI Principles Module Two 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons neutrons electrons positively charged no significant charge negatively charged Protons
More information10.4 Continuous Wave NMR Instrumentation
10.4 Continuous Wave NMR Instrumentation coherent detection bulk magnetization the rotating frame, and effective magnetic field generating a rotating frame, and precession in the laboratory frame spin-lattice
More informationMOLECULAR SPECTROSCOPY
MOLECULAR SPECTROSCOPY First Edition Jeanne L. McHale University of Idaho PRENTICE HALL, Upper Saddle River, New Jersey 07458 CONTENTS PREFACE xiii 1 INTRODUCTION AND REVIEW 1 1.1 Historical Perspective
More informationIntroduction to MRI. Spin & Magnetic Moments. Relaxation (T1, T2) Spin Echoes. 2DFT Imaging. K-space & Spatial Resolution.
Introduction to MRI Spin & Magnetic Moments Relaxation (T1, T2) Spin Echoes 2DFT Imaging Selective excitation, phase & frequency encoding K-space & Spatial Resolution Contrast (T1, T2) Acknowledgement:
More informationNMR Spectroscopy of Polymers
UNESCO/IUPAC Course 2005/2006 Jiri Brus NMR Spectroscopy of Polymers Brus J 1. part At the very beginning the phenomenon of nuclear spin resonance was studied predominantly by physicists and the application
More informationNMR Spectroscopy Laboratory Experiment Introduction. 2. Theory
1. Introduction 64-311 Laboratory Experiment 11 NMR Spectroscopy Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful and theoretically complex analytical tool. This experiment will introduce to
More informationSupplementary Information: Dependence of nuclear spin singlet lifetimes on RF spin-locking power
Supplementary Information: Dependence of nuclear spin singlet lifetimes on RF spin-locking power Stephen J. DeVience a, Ronald L. Walsworth b,c, Matthew S. Rosen c,d,e a Department of Chemistry and Chemical
More information8.2 The Nuclear Overhauser Effect
8.2 The Nuclear Overhauser Effect Copyright Hans J. Reich 2016 All Rights Reserved University of Wisconsin An important consequence of DD relaxation is the Nuclear Overhauser Effect, which can be used
More informationNMR journey. Introduction to solution NMR. Alexandre Bonvin. Topics. Why use NMR...? Bijvoet Center for Biomolecular Research
2 NMR journey Introduction to solution NMR Alexandre Bonvin Bijvoet Center for Biomolecular Research with thanks to Dr. Klaartje Houben EMBO Global Exchange course, CCMB, Hyderabad, India November 29th
More informationCOSY type experiments exploring through-bond homonuclear correlations
COSY type experiments exploring through-bond homonuclear correlations Assistant Professor Kenneth Kongstad Bioanalytical Chemistry and Metabolomics Research Group Section for Natural Products and Peptides
More informationBCMB/CHEM Spin Operators and QM Applications
BCMB/CHEM 8190 Spin Operators and QM Applications Quantum Description of NMR Experiments Not all experiments can be described by the Bloch equations A quantum description is necessary for understanding
More informationLong-lived spin echoes in magnetically diluted system: an NMR study of the Ge single crystals Alexander M. Panich,
Long-lived spin echoes in magnetically diluted system: an NMR study of the Ge single crystals Alexander M. Panich, Department of Physics, Ben-Gurion University of the Negev, Beer Sheva, Israel N. A. Sergeev,
More informationPhysical fundamentals of magnetic resonance imaging
Physical fundamentals of magnetic resonance imaging Stepan Sereda University of Bonn 1 / 26 Why? Figure 1 : Full body MRI scan (Source: [4]) 2 / 26 Overview Spin angular momentum Rotating frame and interaction
More informationBiochemistry 530 NMR Theory and Practice
Biochemistry 530 NMR Theory and Practice David Baker Autumn Quarter 2014 Slides Courtesy of Gabriele Varani Recommended NMR Textbooks Derome, A. E. (1987) Modern NMR Techniques for Chemistry Research,
More informationSpin-spin coupling I Ravinder Reddy
Spin-spin coupling I Ravinder Reddy Spin-interactions External interactions Magnetic field Bo, RF field B1 Internal Interactions Molecular motions Exchange Chemical shifts J-coupling Spin Diffusion Dipolar
More informationThe Quantum Theory of Magnetism
The Quantum Theory of Magnetism Norberto Mains McGill University, Canada I: 0 World Scientific Singapore NewJersey London Hong Kong Contents 1 Paramagnetism 1.1 Introduction 1.2 Quantum mechanics of atoms
More informationNMR in Structural Biology
NMR in Structural Biology Exercise session 2 1. a. List 3 NMR observables that report on structure. b. Also indicate whether the information they give is short/medium or long-range, or perhaps all three?
More informationSpectroscopy. Practical Handbook of. J. W. Robinson, Ph.D., D.Sc, F.R.C.S. Department of Chemistry Louisiana State University Baton Rouge, Louisiana
Practical Handbook of Spectroscopy Edited by J. W. Robinson, Ph.D., D.Sc, F.R.C.S. Department of Chemistry Louisiana State University Baton Rouge, Louisiana CRC Press Boca Raton Ann Arbor Boston TABLE
More informationGroup Theory and Its Applications in Physics
T. Inui Y Tanabe Y. Onodera Group Theory and Its Applications in Physics With 72 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Contents Sections marked with
More informationNomenclature: Electron Paramagnetic Resonance (EPR) Electron Magnetic Resonance (EMR) Electron Spin Resonance (ESR)
Introduction to EPR Spectroscopy EPR allows paramagnetic species to be identified and their electronic and geometrical structures to be characterised Interactions with other molecules, concentrations,
More informationPrinciples of Magnetic Resonance Imaging
Principles of Magnetic Resonance Imaging Hi Klaus Scheffler, PhD Radiological Physics University of 1 Biomedical Magnetic Resonance: 1 Introduction Magnetic Resonance Imaging Contents: Hi 1 Introduction
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationLECTURES ON QUANTUM MECHANICS
LECTURES ON QUANTUM MECHANICS GORDON BAYM Unitsersity of Illinois A II I' Advanced Bock Progrant A Member of the Perseus Books Group CONTENTS Preface v Chapter 1 Photon Polarization 1 Transformation of
More informationBasic MRI physics and Functional MRI
Basic MRI physics and Functional MRI Gregory R. Lee, Ph.D Assistant Professor, Department of Radiology June 24, 2013 Pediatric Neuroimaging Research Consortium Objectives Neuroimaging Overview MR Physics
More informationLecture #6 NMR in Hilbert Space
Lecture #6 NMR in Hilbert Space Topics Review of spin operators Single spin in a magnetic field: longitudinal and transverse magnetiation Ensemble of spins in a magnetic field RF excitation Handouts and
More informationChem 325 NMR Intro. The Electromagnetic Spectrum. Physical properties, chemical properties, formulas Shedding real light on molecular structure:
Physical properties, chemical properties, formulas Shedding real light on molecular structure: Wavelength Frequency ν Wavelength λ Frequency ν Velocity c = 2.998 10 8 m s -1 The Electromagnetic Spectrum
More informationIntroduction solution NMR
2 NMR journey Introduction solution NMR Alexandre Bonvin Bijvoet Center for Biomolecular Research with thanks to Dr. Klaartje Houben EMBO Global Exchange course, IHEP, Beijing April 28 - May 5, 20 3 Topics
More informationBiochemistry 530 NMR Theory and Practice
Biochemistry 530 NMR Theory and Practice Gabriele Varani Department of Biochemistry and Department of Chemistry University of Washington Lecturer: Gabriele Varani Biochemistry and Chemistry Room J479 and
More information