Chem8028(1314) - Spin Dynamics: Spin Interactions
|
|
- Mark Fowler
- 6 years ago
- Views:
Transcription
1 Chem8028(1314) - Spin Dynamics: Spin Interactions Malcolm Levitt see also IK m106 1
2 Nuclear spin interactions (diamagnetic materials) 2
3 Chemical Shift 3
4 Direct dipole-dipole coupling 4
5 J-coupling 5
6 Nuclear quadrupole coupling (1) spin > 1/2 only 6
7 Spin System spin-spin coupling chemical shift 7
8 Spin System Ensemble (perfectly rigid solid) all spin interactions are coherent (the same all the time, and the same for each member) 8
9 Spin System Ensemble (liquid) most spin interactions are incoherent (fluctuating, and different for each member) 9
10 Spin System Ensemble (liquid) most spin interactions are incoherent (fluctuating, and different for each member) 9
11 Spin Interactions coherent same for all spin systems in the ensemble NMR peak frequencies incoherent fluctuating in time a snapshot would show differences between different spin systems in the ensemble linewidths and relaxation 10
12 Coherent interactions Solids: chemical shifts (both isotropic and CSA) DD-couplings J-couplings Isotropic liquids: isotropic chemical shifts J-couplings 11
13 Coherent spin interactions (isotropic liquids) 12
14 Coherent spin interactions (solids) 13
15 Isotropic and anisotropic spin interactions Isotropic: independent of molecular orientation with respect to the magnetic field Anisotropic: dependent on molecular orientation with respect to the magnetic field often represented by a tensor (drawn as a 3D ellipsoid) 14
16 Tensors Spinach representation 15
17 Tensors principal axes Spinach representation 15
18 J-coupling 16
19 J-coupling Hamiltonian: homonuclear case H J k = 2π J k I I k I I k = I x I kx + I y I ky + I z I kz
20 J-coupling Hamiltonian: heteronuclear case H J k = 2π J k I z I kz
21 Direct dipole-dipole coupling 19
22 Direct dipole-dipole coupling The magnetic field generated by one spin influences its neighbour 20
23 Dipole-dipole coupling constant b k = ( µ 0 4π )!γ γ k r k 3 (in rad s -1 ) Note: The DD coupling in Hz is b k / 2π cube of the distance between the spins Examples: Two protons at 3Å separation: DD coupling = -4.5 khz Two 13 C s at 1.5Å separation: DD coupling =-2.2 khz Two 13 C s at 5Å separation: DD coupling = -61 Hz Two 13 C s at 8Å separation: DD coupling = -15 Hz 21
24 DD Hamiltonian: homonuclear b k = ( µ 0 4π )!γ γ k r k 3 H k DD = d k ( 3I z I kz I I ) k d k = b k 1 ( 2 3cos2 θ k 1) 22
25 DD Hamiltonian: heteronuclear b k = ( µ 0 4π )!γ γ k r k 3 H k DD = d k 2I z I kz d k = b k 1 ( 2 3cos2 θ k 1) 23
26 Principal axes of DD coupling The principal z-axis of the DD coupling between two spins is along the internuclear vector 1 2 x y P 12 z 24
27 Chemical Shift 25
28 Mechanism of chemical shift 26
29 CSA 27
30 CSA tensors field field Chemical shift depends on molecular orientation with respect to the field CSA tensor 28
31 Oriented 15 N-labelled spider silk field vary angle between the silk fibre and the magnetic field Zhao and Asakura (2001) 29
32 Chemical shift tensor induced field at spin (a three-component vector) δ = B induced = δ B applied δ xx δ yx δ zx δ xy δ yy δ zy δ xz δ yz δ zz applied field (a three-component vector) CS tensor The induced field is not (usually) parallel to the applied field. 30
33 Principal axes There are three special directions in which the induced field is parallel to the applied field. These are called the principal axes of the chemical shift tensor (denoted (X,Y,Z) ). The principal axes are in general different for different chemical sites. Z Y P P X Y principal axes shown as the axes of 3D ellipsoids Z X 31
34 Principal values When the applied field is along a principal axis, the induced field is proportional to the applied field, multiplied by a number, called the principal value of the chemical shift tensor X P Z Y B induced B induced B induced ( along X ) = δ XX ( along Y ) = δ YY ( along Z) = δ ZZ B applied B applied B applied ( along X ) ( along Y ) ( along Z) chemical shift principal values of spin 32
35 Isotropic chemical shift The mean of the three principal chemical shift values is called the isotropic chemical shift. This is the chemical shift reported in solution NMR. P Z δ iso = 1 ( δ 3 XX + δ YY + δ ) ZZ X Y isotropic chemical shift of spin 33
36 Assignment of the principal axes By convention, the principal axes are assigned so that: The Z-axis is the one for which the principal value is furthest from the isotropic shift; P Z The Y-axis is the one for which the principal value is the closest to the isotropic shift; The X-axis is the other one X Y 34
37 Chemical shift anisotropy The difference between the isotropic shift and the principal value which is furthest from it is called the chemical shift anisotropy (CSA) Z δ aniso = δ ZZ δ iso P X Y 35
38 Biaxiality The difference between the x and y principal values is usually quantified by the biaxiality* η: Z η = δ YY δ XX δ aniso X P Y If η is zero, the x and y principal values are the same, and the CSA tensor is said to be uniaxial *Sometimes called (misleadingly) the asymmetry 36
39 Static spectrum (powder pattern) field δ aniso δ δ XX δ YY δ iso δ ZZ 37
40 Powder patterns δ aniso < 0 δ aniso > 0 uniaxial CSA tensor η = 0 0 < η <1 biaxial CSA tensor δ η =1 38
41 Shielding convention Bad news: In many papers and books, CSA is specified using a shielding parameter σ, with opposite sign to the (deshielding) chemical shift δ σ aniso = δ aniso Even worse news: some authors write σ when they mean δ! 39
42 Nuclear quadrupole coupling (1) spin > 1/2 only 40
43 Quadrupolar spin Hamiltonian Full form of spin interaction: 1st order term (usually sufficient for 2 H): For other nuclei, the 2nd order term is usually needed as well. 41
44 I=3/2: Nuclear quadrupole coupling (2) 1st-order: shifts spin energy levels according to M 2 2nd-order: shifts energy levels in a more complicated way -3/2 > -1/2 > +1/2 > +3/2 > 1st-order Q 2nd-order Q 42
45 Relative Magnitudes of Interactions (before motional averaging) spins > 1/2 only 43
46 Interactions after motional averaging spins > 1/2 only 44
47 Motionally-averaged spin interactions: isotropic liquids 45
48 Motionally-averaged spin interactions: spins-1/2 in solids 46
49 Motionally-averaged spin interactions: spins > 1/2 in solids 47
50 Summary Only spins >1/2 experience electric spin interactions (electric quadrupole interaction) The chemical shift is a three-body interaction between the applied field, the electrons, and the nuclei The CSA is described by three principal values and three principal axes The DD coupling is directly proportional to the inverse cube of the distance between the nuclei The DD principal axis system is aligned along the internuclear vector In high magnetic field, all interactions may be replaced by their secular (1st-order) parts, except the large quadrupole coupling, where the 2nd or higher terms must be included as well. 48
Spin Interactions. Giuseppe Pileio 24/10/2006
Spin Interactions Giuseppe Pileio 24/10/2006 Magnetic moment µ = " I ˆ µ = " h I(I +1) " = g# h Spin interactions overview Zeeman Interaction Zeeman interaction Interaction with the static magnetic field
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 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 (CHEM8028) Solid-state NMR: Anisotropic interactions and how we use them. Dr Philip Williamson January 2015
NMR (CEM808) Solid-state NMR: Anisotropic interactions and how we use them Dr Philip Williamson January 015 NMR: From Molecular to Cellular Level Cell Solid State NMR Mitochondrion Membrane Liquid NMR
More informationProblem Set 2 Due Tuesday, September 27, ; p : 0. (b) Construct a representation using five d orbitals that sit on the origin as a basis: 1
Problem Set 2 Due Tuesday, September 27, 211 Problems from Carter: Chapter 2: 2a-d,g,h,j 2.6, 2.9; Chapter 3: 1a-d,f,g 3.3, 3.6, 3.7 Additional problems: (1) Consider the D 4 point group and use a coordinate
More information6 NMR Interactions: Zeeman and CSA
6 NMR Interactions: Zeeman and CSA 6.1 Zeeman Interaction Up to this point, we have mentioned a number of NMR interactions - Zeeman, quadrupolar, dipolar - but we have not looked at the nature of these
More informationProblem Set 2 Due Thursday, October 1, & & & & # % (b) Construct a representation using five d orbitals that sit on the origin as a basis:
Problem Set 2 Due Thursday, October 1, 29 Problems from Cotton: Chapter 4: 4.6, 4.7; Chapter 6: 6.2, 6.4, 6.5 Additional problems: (1) Consider the D 3h point group and use a coordinate system wherein
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 informationSpin Dynamics Basics of Nuclear Magnetic Resonance. Malcolm H. Levitt
Spin Dynamics Basics of Nuclear Magnetic Resonance Second edition Malcolm H. Levitt The University of Southampton, UK John Wiley &. Sons, Ltd Preface xxi Preface to the First Edition xxiii Introduction
More informationA DARK GREY P O N T, with a Switch Tail, and a small Star on the Forehead. Any
Y Y Y X X «/ YY Y Y ««Y x ) & \ & & } # Y \#$& / Y Y X» \\ / X X X x & Y Y X «q «z \x» = q Y # % \ & [ & Z \ & { + % ) / / «q zy» / & / / / & x x X / % % ) Y x X Y $ Z % Y Y x x } / % «] «] # z» & Y X»
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 informationRotational Raman Spectroscopy
Rotational Raman Spectroscopy If EM radiation falls upon an atom or molecule, it may be absorbed if the energy of the radiation corresponds to the separation of two energy levels of the atoms or molecules.
More informationSymmetry-Based Double Quantum Recoupling in Solid State NMR. Marina Carravetta
Symmetry-Based Double Quantum Recoupling in Solid State NMR Marina Carravetta N. S + NH Physical Chemistry Division Arrhenius Laboratory Stockholm University 2002 PAGINA VUOTA Abstract This thesis deals
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 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 informationPrediction of NMR parameters in the solid-state
1J PO Prediction of NMR parameters in the solid-state Jonathan Yates Materials Modelling Laboratory, Oxford Materials 2J PSi 1 Nuclear Magnetic Resonance Applied Field Zero Field B Population differences!
More informationNuclear Quadrupole Resonance Spectroscopy. Some examples of nuclear quadrupole moments
Nuclear Quadrupole Resonance Spectroscopy Review nuclear quadrupole moments, Q A negative value for Q denotes a distribution of charge that is "football-shaped", i.e. a sphere elongated at the poles; a
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 informationTensor Visualization. CSC 7443: Scientific Information Visualization
Tensor Visualization Tensor data A tensor is a multivariate quantity Scalar is a tensor of rank zero s = s(x,y,z) Vector is a tensor of rank one v = (v x,v y,v z ) For a symmetric tensor of rank 2, its
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 informationDipolar Couplings in Partially Aligned Macromolecules - New Directions in. Structure Determination using Solution State NMR.
Dipolar Couplings in Partially Aligned Macromolecules - New Directions in Structure Determination using Solution State NMR. Recently developed methods for the partial alignment of macromolecules in dilute
More informationTutorial Session - Exercises. Problem 1: Dipolar Interaction in Water Moleclues
Tutorial Session - Exercises Problem 1: Dipolar Interaction in Water Moleclues The goal of this exercise is to calculate the dipolar 1 H spectrum of the protons in an isolated water molecule which does
More informationLecture 7. Properties of Materials
MIT 3.00 Fall 2002 c W.C Carter 55 Lecture 7 Properties of Materials Last Time Types of Systems and Types of Processes Division of Total Energy into Kinetic, Potential, and Internal Types of Work: Polarization
More informationWaves in Linear Optical Media
1/53 Waves in Linear Optical Media Sergey A. Ponomarenko Dalhousie University c 2009 S. A. Ponomarenko Outline Plane waves in free space. Polarization. Plane waves in linear lossy media. Dispersion relations
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 informationLOWELL WEEKLY JOURNAL
Y -» $ 5 Y 7 Y Y -Y- Q x Q» 75»»/ q } # ]»\ - - $ { Q» / X x»»- 3 q $ 9 ) Y q - 5 5 3 3 3 7 Q q - - Q _»»/Q Y - 9 - - - )- [ X 7» -» - )»? / /? Q Y»» # X Q» - -?» Q ) Q \ Q - - - 3? 7» -? #»»» 7 - / Q
More informationPrincipios Básicos de RMN en sólidos destinado a usuarios. Gustavo Monti. Fa.M.A.F. Universidad Nacional de Córdoba Argentina
Principios Básicos de RMN en sólidos destinado a usuarios Gustavo Monti Fa.M.A.F. Universidad Nacional de Córdoba Argentina CONTENIDOS MODULO 2: Alta resolución en sólidos para espines 1/2 Introducción
More informationMagnetized Materials: Contributions Inside Lorentz Ellipsoids
Magnetized Materials: Contributions Inside Lorentz Ellipsoids S.Aravamudhan Department of Chemistry North Eastern Hill University PO NEHU Campus Mawkynroh Umshing Shillong (Meghalaya) 793022 E-mail: saravamudhan@nehu.ac.in
More informationHyperfine interaction
Hyperfine interaction The notion hyperfine interaction (hfi) comes from atomic physics, where it is used for the interaction of the electronic magnetic moment with the nuclear magnetic moment. In magnetic
More informationModern Solid State NMR strategies for the structural characterization of amorphous solids Leo van Wüllen
Modern Solid State NMR strategies for the structural characterization of amorphous solids Leo van Wüllen Institute of Physical Chemistry University of Münster The van Wüllen group at Münster Inorganic
More informationNatural abundance solid-state 95 Mo MAS NMR of MoS 2 reveals precise 95 Mo anisotropic parameters from its central and satellite transitions
Electronic Supplementary Information for: Natural abundance solid-state 95 Mo MAS NMR of MoS 2 reveals precise 95 Mo anisotropic parameters from its central and satellite transitions Hans J. Jakobsen,*
More informationMaxwell s Equations:
Course Instructor Dr. Raymond C. Rumpf Office: A-337 Phone: (915) 747-6958 E-Mail: rcrumpf@utep.edu Maxwell s Equations: Physical Interpretation EE-3321 Electromagnetic Field Theory Outline Maxwell s Equations
More information6. 3D Kinematics DE2-EA 2.1: M4DE. Dr Connor Myant
DE2-EA 2.1: M4DE Dr Connor Myant 6. 3D Kinematics Comments and corrections to connor.myant@imperial.ac.uk Lecture resources may be found on Blackboard and at http://connormyant.com Contents Three-Dimensional
More informationGIPAW: A solid-state theory for NMR
GIPAW: A solid-state theory for NMR Jonathan Yates jonathan.yates@materials.ox.ac.uk Materials Modelling Laboratory, Oxford Materials NMR parameters we will focus on non-metallic, diamagnetic materials
More informationCHAPTER 2 BOOLEAN ALGEBRA
CHAPTER 2 BOOLEAN ALGEBRA This chapter in the book includes: Objectives Study Guide 2.1 Introduction 2.2 Basic Operations 2.3 Boolean Expressions and Truth Tables 2.4 Basic Theorems 2.5 Commutative, Associative,
More informationInvestigation of Local Structures in Cation- Ordered Microwave Dielectric a Solid-State Nmr and First Principle Calculation Study
College of William and Mary W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 2017 Investigation of Local Structures in Cation- Ordered Microwave Dielectric
More informationApplications of Eigenvalues & Eigenvectors
Applications of Eigenvalues & Eigenvectors Louie L. Yaw Walla Walla University Engineering Department For Linear Algebra Class November 17, 214 Outline 1 The eigenvalue/eigenvector problem 2 Principal
More informationNMR-CASTEP. Jonathan Yates. Cavendish Laboratory, Cambridge University. J-coupling cons. NMR-CASTEP York 2007 Jonathan Yates.
Jonathan Yates Cavendish Laboratory, Cambridge University 2 2 1 3 2 N1a-N7b a hemical shift Experiment Calculation [ppm] [ppm] -43.8-47.4 "(31P) 29 "( Si1) -213.3-214.8 "(29Si2) -217.0-218.7 29-119.1-128.6
More informationStress transformation and Mohr s circle for stresses
Stress transformation and Mohr s circle for stresses 1.1 General State of stress Consider a certain body, subjected to external force. The force F is acting on the surface over an area da of the surface.
More information4: birefringence and phase matching
/3/7 4: birefringence and phase matching Polarization states in EM Linear anisotropic response χ () tensor and its symmetry properties Working with the index ellipsoid: angle tuning Phase matching in crystals
More informationcompound Cs 2 Cu 2 Mo 3 O 12
133 Cs-NMR study on aligned powder of competing spin chain compound A Yagi 1, K Matsui 1 T Goto 1, M Hase 2 and T Sasaki 3 1 2 Sophia University, Physics Division, Tokyo, 102-8554, Japan National Institute
More informationThe Physical Basis of the NMR Experiment
The Physical Basis of the NMR Experiment 1 Interaction of Materials with Magnetic Fields F F S N S N Paramagnetism Diamagnetism 2 Microscopic View: Single Spins an electron has mass and charge in addition
More informationCourse 2BA1: Hilary Term 2007 Section 8: Quaternions and Rotations
Course BA1: Hilary Term 007 Section 8: Quaternions and Rotations David R. Wilkins Copyright c David R. Wilkins 005 Contents 8 Quaternions and Rotations 1 8.1 Quaternions............................ 1 8.
More informationPrincipios Básicos de RMN en sólidos destinado a usuarios. Gustavo Monti. Fa.M.A.F. Universidad Nacional de Córdoba Argentina
Principios Básicos de RMN en sólidos destinado a usuarios Gustavo Monti Fa.M.A.F. Universidad Nacional de Córdoba Argentina Ministerio de Ciencia Tecnología e Innovación Productiva de la Nación Sistemas
More informationPRACTICAL ASPECTS OF NMR RELAXATION STUDIES OF BIOMOLECULAR DYNAMICS
PRACTICAL ASPECTS OF MR RELAXATIO STUDIES OF BIOMOLECULAR DYAMICS Further reading: Can be downloaded from my web page Korzhnev D.E., Billeter M., Arseniev A.S., and Orekhov V. Y., MR Studies of Brownian
More information2.1. NMR Spectroscopy, Anisotropic Nuclear Spin Interaction.
Chapter II. Molecular segments orientation study using 29 Si NMR methods. 2.1. NMR Spectroscopy, Anisotropic Nuclear Spin Interaction. The term Nuclear Magnetic Resonance (NMR) unifies a big variety of
More informationPeter Werhun. Master of Science. A thesis submitted in partial fulfillment of the requirements for the degree of
Nuclear Magnetic Resonance of Low-Receptivity Nuclides: The First Demonstration of 61 Ni SSNMR as Applied to Structural and Crystallographic Characterization of Diamagnetic Nickel Complexes Peter Werhun
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 informationEquilibrium of Deformable Body
Equilibrium of Deformable Body Review Static Equilibrium If a body is in static equilibrium under the action applied external forces, the Newton s Second Law provides us six scalar equations of equilibrium
More informationNeatest and Promptest Manner. E d i t u r ami rul)lihher. FOIt THE CIIILDIIES'. Trifles.
» ~ $ ) 7 x X ) / ( 8 2 X 39 ««x» ««! «! / x? \» «({? «» q «(? (?? x! «? 8? ( z x x q? ) «q q q ) x z x 69 7( X X ( 3»«! ( ~«x ««x ) (» «8 4 X «4 «4 «8 X «x «(» X) ()»» «X «97 X X X 4 ( 86) x) ( ) z z
More informationMECH 5312 Solid Mechanics II. Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso
MECH 5312 Solid Mechanics II Dr. Calvin M. Stewart Department of Mechanical Engineering The University of Texas at El Paso Table of Contents Preliminary Math Concept of Stress Stress Components Equilibrium
More informationBiaxial Nematics Fact, Theory and Simulation
Soft Matter Mathematical Modelling Cortona 12 th -16 th September 2005 Biaxial Nematics Fact, Theory and Simulation Geoffrey Luckhurst School of Chemistry University of Southampton Fact The elusive biaxial
More informationQuantification of Dynamics in the Solid-State
Bernd Reif Quantification of Dynamics in the Solid-State Technische Universität München Helmholtz-Zentrum München Biomolecular Solid-State NMR Winter School Stowe, VT January 0-5, 206 Motivation. Solid
More informationA Primer for Nuclear Magnetic Relaxation in Liquids
A Primer for Nuclear Magnetic Relaxation in Liquids NAGARAJAN MURALI, V.V. KRISHNAN Varian NMR Systems, 3 Hansen Way M/S D-98, Palo Alto, California 9434 Molecular Biophysics Group, Biology and Biotechnology
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 informationSupramolecular Order and Dynamics of Functional Materials Studied by Solid State NMR
Supramolecular rder and Dynamics of Functional Materials Studied by Solid State M Dissertation Zur Erlangung des Grades Doktor des aturwissenschaften am Fachbereich Chemie und Pharmazie der Johannes Gutenberg-Universität
More informationResolution Improvement in Multidimensional Nuclear Magnetic Resonance Spectroscopy of Proteins
Resolution Improvement in Multidimensional Nuclear Magnetic Resonance Spectroscopy of Proteins Luminita Duma To cite this version: Luminita Duma. Resolution Improvement in Multidimensional Nuclear Magnetic
More informationTwo Posts to Fill On School Board
Y Y 9 86 4 4 qz 86 x : ( ) z 7 854 Y x 4 z z x x 4 87 88 Y 5 x q x 8 Y 8 x x : 6 ; : 5 x ; 4 ( z ; ( ) ) x ; z 94 ; x 3 3 3 5 94 ; ; ; ; 3 x : 5 89 q ; ; x ; x ; ; x : ; ; ; ; ; ; 87 47% : () : / : 83
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 informationGG303 Lecture 6 8/27/09 1 SCALARS, VECTORS, AND TENSORS
GG303 Lecture 6 8/27/09 1 SCALARS, VECTORS, AND TENSORS I Main Topics A Why deal with tensors? B Order of scalars, vectors, and tensors C Linear transformation of scalars and vectors (and tensors) II Why
More informationHydraulic properties of porous media
PART 5 Hydraulic properties of porous media Porosity Definition: Void space: n V void /V total total porosity e V void /V solid Primary porosity - between grains Secondary porosity - fracture or solution
More informationNMR STUDY OF EXCHANGE AND HYDRATION SITE IDENTIFICATION IN MCM-41
NMR STUDY OF EXCHANGE AND HYDRATION SITE IDENTIFICATION IN MCM-41 by Jamal Hassan A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy
More informationDiffusion Tensor Imaging (DTI): An overview of key concepts
Diffusion Tensor Imaging (DTI): An overview of key concepts (Supplemental material for presentation) Prepared by: Nadia Barakat BMB 601 Chris Conklin Thursday, April 8 th 2010 Diffusion Concept [1,2]:
More informationNMR-spectroscopy of proteins in solution. Peter Schmieder
NMR-spectroscopy of proteins in solution Basic aspects of NMR-Spektroskopie Basic aspects of NMR-spectroscopy 3/84 Prerequisite for NMR-spectroscopy is a nuclear spin that can be thought of as a mixture
More informationNMR Relaxation and Molecular Dynamics
Ecole RMN Cargese Mars 2008 NMR Relaxation and Molecular Dynamics Martin Blackledge IBS Grenoble Carine van Heijenoort ICSN, CNRS Gif-sur-Yvette Solution NMR Timescales for Biomolecular Motion ps ns µs
More informationMore NMR Relaxation. Longitudinal Relaxation. Transverse Relaxation
More NMR Relaxation Longitudinal Relaxation Transverse Relaxation Copyright Peter F. Flynn 2017 Experimental Determination of T1 Gated Inversion Recovery Experiment The gated inversion recovery pulse sequence
More informationExperiment and Modelling in Structural NMR
EPJ Web of Conferences 30, 04002 (2012) DOI: 10.1051/epjconf/20123004002 Owned by the authors, published by EDP Sciences, 2012 Experiment and Modelling in Structural NMR November 28th December 2 nd 2011
More informationRotational Motion. Chapter 4. P. J. Grandinetti. Sep. 1, Chem P. J. Grandinetti (Chem. 4300) Rotational Motion Sep.
Rotational Motion Chapter 4 P. J. Grandinetti Chem. 4300 Sep. 1, 2017 P. J. Grandinetti (Chem. 4300) Rotational Motion Sep. 1, 2017 1 / 76 Angular Momentum The angular momentum of a particle with respect
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 informationUnit IV State of stress in Three Dimensions
Unit IV State of stress in Three Dimensions State of stress in Three Dimensions References Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength
More informationI690/B680 Structural Bioinformatics Spring Protein Structure Determination by NMR Spectroscopy
I690/B680 Structural Bioinformatics Spring 2006 Protein Structure Determination by NMR Spectroscopy Suggested Reading (1) Van Holde, Johnson, Ho. Principles of Physical Biochemistry, 2 nd Ed., Prentice
More informationDetermination of Locally Varying Directions through Mass Moment of Inertia Tensor
Determination of Locally Varying Directions through Mass Moment of Inertia Tensor R. M. Hassanpour and C.V. Deutsch Centre for Computational Geostatistics Department of Civil and Environmental Engineering
More informationQUALIFYING EXAMINATION, Part 1. Solutions. Problem 1: Mathematical Methods. x 2. 1 (1 + 2x 2 /3!) ] x 2 1 2x 2 /3
QUALIFYING EXAMINATION, Part 1 Solutions Problem 1: Mathematical Methods (a) Keeping only the lowest power of x needed, we find 1 x 1 sin x = 1 x 1 (x x 3 /6...) = 1 ) 1 (1 x 1 x /3 = 1 [ 1 (1 + x /3!)
More informationNMR Shifts. I Introduction and tensor/crystal symmetry.
NMR Shifts. I Introduction and tensor/crystal symmetry. These notes were developed for my group as introduction to NMR shifts and notation. 1) Basic shift definitions and notation: For nonmagnetic materials,
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 informationDipolar Recoupling in Magic-Angle-Spinning Nuclear Magnetic Resonance. Andreas Brinkmann
Dipolar Recoupling in Magic-Angle-Spinning Nuclear Magnetic Resonance Andreas Brinkmann Division of Physical Chemistry Arrhenius Laboratory Stockholm University 2001 Dipolar Recoupling in Magic-Angle-Spinning
More informationLOWELL JOURNAL. MUST APOLOGIZE. such communication with the shore as Is m i Boimhle, noewwary and proper for the comfort
- 7 7 Z 8 q ) V x - X > q - < Y Y X V - z - - - - V - V - q \ - q q < -- V - - - x - - V q > x - x q - x q - x - - - 7 -» - - - - 6 q x - > - - x - - - x- - - q q - V - x - - ( Y q Y7 - >»> - x Y - ] [
More informationCoupling of Functional Hydrogen Bonds in Pyridoxal-5 -phosphate- Enzyme Model Systems Observed by Solid State NMR
Supporting Information for Coupling of Functional ydrogen Bonds in Pyridoxal-5 -phosphate- Enzyme Model Systems bserved by Solid State NMR Shasad Sharif, David Schagen, Michael D. Toney, and ans-einrich
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 informationThe Product Operator Formalism
2 The Product Operator Formalism 1. INTRODUCTION In this section we will see that the density matrix at equilibrium can be expressed in terms of the spin angular momentum component I z of each nucleus.
More informationHyperfine interactions
Hyperfine interactions Karlheinz Schwarz Institute of Materials Chemistry TU Wien Some slides were provided by Stefaan Cottenier (Gent) nuclear point charges interacting with electron charge distribution
More information8 NMR Interactions: Dipolar Coupling
8 NMR Interactions: Dipolar Coupling 8.1 Hamiltonian As discussed in the first lecture, a nucleus with spin I 1/2 has a magnetic moment, µ, associated with it given by µ = γ L. (8.1) If two different nuclear
More information2 NMR Interactions. A Classification of Interactions. Interaction Magnitudes
NMR Interactions Lecture notes by Assaf al In the previous lecture we learned that the dynamics of a quantum system is governed by the Liouville equation: d ˆ, dt i What determines the time evolution of
More informationphases of liquid crystals and their transitions
phases of liquid crystals and their transitions Term paper for PHYS 569 Xiaoxiao Wang Abstract A brief introduction of liquid crystals and their phases is provided in this paper. Liquid crystal is a state
More informationModule #3. Transformation of stresses in 3-D READING LIST. DIETER: Ch. 2, pp Ch. 3 in Roesler Ch. 2 in McClintock and Argon Ch.
HOMEWORK From Dieter -3, -4, 3-7 Module #3 Transformation of stresses in 3-D READING LIST DIETER: Ch., pp. 7-36 Ch. 3 in Roesler Ch. in McClintock and Argon Ch. 7 in Edelglass The Stress Tensor z z x O
More informationThe Positive Muon as a Probe in Chemistry. Dr. Iain McKenzie ISIS Neutron and Muon Source STFC Rutherford Appleton Laboratory
The Positive Muon as a Probe in Chemistry Dr. Iain McKenzie ISIS Neutron and Muon Source STFC Rutherford Appleton Laboratory I.McKenzie@rl.ac.uk µsr and Chemistry Properties of atoms or molecules containing
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 informationProduct Operator Formalism: A Brief Introduction
Product Operator Formalism: A Brief Introduction Micholas D. Smith Physics Department, Drexel University, Philadelphia, PA 19104 May 14, 2010 Abstract Multiple spin systems allow for the presence of quantum
More informationLecture 8 Analyzing the diffusion weighted signal. Room CSB 272 this week! Please install AFNI
Lecture 8 Analyzing the diffusion weighted signal Room CSB 272 this week! Please install AFNI http://afni.nimh.nih.gov/afni/ Next lecture, DTI For this lecture, think in terms of a single voxel We re still
More informationCalculating NMR Chemical Shifts for beta-ionone O
Calculating NMR Chemical Shifts for beta-ionone O Molecular orbital calculations can be used to get good estimates for chemical shifts. In this exercise we will calculate the chemical shifts for beta-ionone.
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 information' Liberty and Umou Ono and Inseparablo "
3 5? #< q 8 2 / / ) 9 ) 2 ) > < _ / ] > ) 2 ) ) 5 > x > [ < > < ) > _ ] ]? <
More informationBasic Equations of Elasticity
A Basic Equations of Elasticity A.1 STRESS The state of stress at any point in a loaded bo is defined completely in terms of the nine components of stress: σ xx,σ yy,σ zz,σ xy,σ yx,σ yz,σ zy,σ zx,andσ
More information2.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS. differential equations with the initial values y(x 0. ; l.
Numerical Methods II UNIT.1 NUMERICAL SOLUTION OF SIMULTANEOUS FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS.1.1 Runge-Kutta Method of Fourth Order 1. Let = f x,y,z, = gx,y,z be the simultaneous first order
More informationClassical Description of NMR Parameters: The Bloch Equations
Classical Description of NMR Parameters: The Bloch Equations Pascale Legault Département de Biochimie Université de Montréal 1 Outline 1) Classical Behavior of Magnetic Nuclei: The Bloch Equation 2) Precession
More informationA Cu-Zn-Cu-Zn heterometallomacrocycle shows significant antiferromagnetic coupling between paramagnetic centres mediated by diamagnetic metal
Electronic Supplementary Information to A Cu-Zn-Cu-Zn heterometallomacrocycle shows significant antiferromagnetic coupling between paramagnetic centres mediated by diamagnetic metal Elena A. Buvaylo, a
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 informationPROTEIN 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 information