NMR Dynamics and Relaxation
|
|
- Zoe Harrell
- 6 years ago
- Views:
Transcription
1 NMR Dynamics and Relaxation Günter Hempel MLU Halle, Institut für Physik, FG Festkörper-NMR 1
2 Introduction: Relaxation Two basic magnetic relaxation processes: Longitudinal relaxation: T 1 Relaxation Return to equilibrium Non-equilibrium states: Non-Boltzmannian level populations Transverse relaxation: T transverse phase correlations
3 Relaxation Thermal motion spin interactions Dipol-dipol interaction Chemical shift anisotropy Quadrupolar interaction Scalar coupling Spin-rotational interaction Nuclear spin system is forced to relax 3
4 Relaxation temperature dependence Two groups of relaxation times: ln T T 1, T 1ρ, T 1D, T SE, T eff T, T SE, T IS 1/T 4
5 Dipole-dipole interaction B 0 S 1 Detecting the resonance of the S spins in the neighbourhood of I we observe a freqency shift caused by the field of the I spin. I S B local = B 0 + B = B res = 0 + Local field > 0 for position 1 but < 0 for position. If I is antiparallel to B 0 then B and change sign. 5
6 Dipole-dipole interaction N S S N S N N S N S S N N S N S S N S N N S S N 6
7 Dipole-dipole interaction + thermal motion 7
8 Anisotropy of chemical shift x xx z B (1 ) B loc xx 0 z zz x B (1 ) B loc zz 0 The magnitude of the shielding of a nucleus depends on the spatial orientation of the electron cloud surrounding the nucleus. 8
9 Chemical Shift Anisotropy (CSA) B 0 z B loc x B 0X B 0Z B loc X, (1 XX) B 0X B loc Z, (1 ZZ) B 0Z H I σ B CSA 0 9
10 CSA + thermal motion 10
11 Quadrupolar interaction Nuclei with spin > 1/: Non-spherical charge distribution. electrical quadrupole moment eq This interacts with the electric field gradient eq caused by the electron shell. I = 1/ I 1 H Qu µ 0 eqq 1 3IZ II 1 I I 4 4I I 1 Quadrupole coupling constant: C q = e qq/h 11
12 Quadrupolar interaction H NMR = H Z + H Q (+ H CS ) I=1 I=5/ Zeeman 1 st order H Q nd order H Q -h 0 m (hc q /40)(3cos -1) (9hC q / ) H Z H Q -1 5(sin + sin 4 ) 0 3(sin 4 -sin ) +1 (sin 4 -sin ) observed splittings: cos 1 angle with B 0 -(sin 4 -sin ) -3(sin 4 -sin ) -5(sin + sin 4 ) 1
13 Scalar interaction H J I I J 1 Energy exchange between different nuclei Spin-rotation interaction H SR I C F Interaction of nuclear spin with the angular momentum of the molecule. 13
14 Effectiveness of the interactions I > ½: I = ½, I = ½, Quadrupolar interaction dominates (except on highly symmetric sites). small nuclei ( 1 H, 13 C, 9 Si), not too large fields: Dipolar interaction determines relaxation. large B 0 and/or larger nuclei: chemical-shift anisotropy can be the strongest mechanism. Spin-rotation interaction: Only detectable for small molecules and high temperatures Scalar interaction can be neglected as relaxation mechanism in almost all cases 14
15 Transitions between levels H H H Zeeman 't No fluctuation ω E / Medium fluctuation ω E / Fast fluctuation ω E / 15
16 Dephasing evolution evolution 16
17 Questions How we can obtain the relaxation time if the transition probability would be known? Master equations How to obtain the transition probability? time-dependent perturbation theory What is the frequency of a random process? description by correlation functions 17
18 Random functions Example: Two functions with values ±1 which are equally distributed, i.e. f = 0 Randomly changing sign. But they differ in the rate of change. f(t) 1 fs(t) t f f (t) f(t) How to define a frequency of such a function? t 18
19 Correlation function Definition autocorrelation function: * K τ f t f t τ t Properties: τ 0 : K 0 f t (Mean square) τ : lim K τ f t (Square of the mean value) τ because: There is no correlation between f(t) and f(t+τ) hence the averaging of the product ia the product of the averages. 19
20 0
21 Numeric example: Resulting correlation function 1,0 0,5 K s () K() K f () 0,0-0,
22 Real systems Averaging over much more data points. Spectral density: () = K () τ J ω FT{ } Markov processes: 1,0 Exponential correlations τ c : correlation time () exp - τ K τ = K0 τc J() / x10-3 s 0,5 Example: τ c = 10-3 s Spectral density: K c J ω τ 0 1 ωτ c 0, log /( Hz)
23 Spectral densities Markov process: log J() c =10-3 s c =10-6 s c =10-9 s log ( /) Other examples: See Noack, F., Nuclear Magnetic Relaxation Spectroscopy, in NMR Basic Principles and Progress Vol. 3, pp. 84, Springer
24 Two-level system (One spin 1/) W AB W AB Level A: N A spins Level B: N B spins Magnetisation ΔN = N B N A Master equation: Solution: dn A dt dn B dt NW NW NW B BA A AB NW A AB B BA AB BA N N N N e 0 W W t ΔN 1 WAB T 1 W BA ΔN t 4
25 Four-level system (Two spins 1/) 1 3 W 13 W 1 Magnetisation N 3 N 1, because level does not contribute W1 dn 1 dt dn dt dn dt 3 Master equation: W N W N W N W N W N W N W N W N W N W N W N N N N N e Solution: 0 W W t 1 W W T
26 Time-dependent perturbation theory 1st order: Transition probability per time unit: 1 t W lim φ H ' t ' φ exp iω t' dt' ; ω t AB A B AB AB t 0 E A E B Transformation into a form where we can realize the correlation of H at different times: 1 t WAB FT KAB τ ; KAB τ H ' AB th ' AB * t τ 1 Particularly: Dipolar interaction within spin pairs (see above: W1 W13 ): T 1 1 J ω J ω T ; J ω FT K τ AB AB 6
27 Dipolar Hamiltonian Two spins: H DD µ 4 r Ir Sr 0 IS 3 3 µ 4 r 0 3 A B C D E F r Dipolar alphabet A I S m 1 3cos z z 0 1 B 1 3cos IS IS 4 m 0 3 sin cos i C e ISz IzS m 1 3 sin cos i D e ISz IzS m 1 3 sin i E e I S m 4 3 sin i F e I S m 4 7
28 1 3 4 and two matrix elements: Basis set (order: I - S) Now we need H 1 and H 13. µ 0 3 µ 0 H' 1 C sincos e r 4 4 r µ 0 3 µ 0 i H' 13 E sin e r 4 4 r i Correlation functions: Time dependence is included in r,, and. We use the approach * t t F t F t F t exp t t µ µ H' t ; H' t 4 r 40 4 r 10 C Spectral density: 3 µ C J r 1 C 0 C 1 C 6 µ C J r C exp exp it dt C 8
29 Result: BPP equations ln T 1 µ 0 C 4 C II ( 1) 6 T1 54 r 10C 140C T µ 0 5C C II ( 1) 3 6 C T 54 r 1 0 C 14 0 C T µ 0 C II ( 1) 6 T 54 r C Bloembergen N, Purcell EM, Pound RV, Phys. Rev. 73 (1948) 679 Conditions: Isolated Pairs of equal spins; Sinle, isotropic motion (i.e. the correlation decays completely) τ C << T Asymptotic behaviour: High temperature ( 0 C << 1): 0 C = 0,615 1 C = 1/ T ln C µ 0 ( II1) T T r Low temperature ( 0 C >> 1): 1 µ II ( 1) 6 T 4 5 r C 1 0 C T : Third condition violated. 9
30 Summary and outlook Thermal motion Particular thermal motion spin interactions Creating transition probability reducing dephasing dephasing Correlation function What is the meaning of the correlation function? Possible temp. depend.: Arrhenius? WLF? Other? Shape of the correlation function? Order parameter? transition probability Relaxation time Nuclear spin system is forced to relax Properties of particular rel.times? Spin temperature Formalisms in intermediate range 30
Spin 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 informationRelaxation. Ravinder Reddy
Relaxation Ravinder Reddy Relaxation What is nuclear spin relaxation? What causes it? Effect on spectral line width Field dependence Mechanisms Thermal equilibrium ~10-6 spins leads to NMR signal! T1 Spin-lattice
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 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 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 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 informationSpin 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 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 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 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 information1 Magnetism, Curie s Law and the Bloch Equations
1 Magnetism, Curie s Law and the Bloch Equations In NMR, the observable which is measured is magnetization and its evolution over time. In order to understand what this means, let us first begin with some
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 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 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 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 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 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 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 informationChapter 8 Magnetic Resonance
Chapter 8 Magnetic Resonance 9.1 Electron paramagnetic resonance 9.2 Ferromagnetic resonance 9.3 Nuclear magnetic resonance 9.4 Other resonance methods TCD March 2007 1 A resonance experiment involves
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 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 informationSlow symmetric exchange
Slow symmetric exchange ϕ A k k B t A B There are three things you should notice compared with the Figure on the previous slide: 1) The lines are broader, 2) the intensities are reduced and 3) the peaks
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 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 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 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 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 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 informationNMR spectroscopy. Matti Hotokka Physical Chemistry Åbo Akademi University
NMR spectroscopy Matti Hotokka Physical Chemistry Åbo Akademi University Angular momentum Quantum numbers L and m (general case) The vector precesses Nuclear spin The quantum numbers are I and m Quantum
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 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 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 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 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 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 informationMOLECULAR SPECTROSCOPY AND PHOTOCHEMISTRY
20 CHAPTER MOLECULAR SPECTROSCOPY AND PHOTOCHEMISTRY 20.1 Introduction to Molecular Spectroscopy 20.2 Experimental Methods in Molecular Spectroscopy 20.3 Rotational and Vibrational Spectroscopy 20.4 Nuclear
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 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 informationIV. Electronic Spectroscopy, Angular Momentum, and Magnetic Resonance
IV. Electronic Spectroscopy, Angular Momentum, and Magnetic Resonance The foundation of electronic spectroscopy is the exact solution of the time-independent Schrodinger equation for the hydrogen atom.
More informationMuon Spin Relaxation Functions
Muon Spin Relaxation Functions Bob Cywinski Department of Physics and Astronomy University of eeds eeds S 9JT Muon Training Course, February 005 Introduction Positive muon spin relaxation (µsr) is a point-like
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 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 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 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 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 informationBiophysical Chemistry: NMR Spectroscopy
Spin Dynamics & Vrije Universiteit Brussel 25th November 2011 Outline 1 Pulse/Fourier Transform NMR Thermal Equilibrium Effect of RF Pulses The Fourier Transform 2 Symmetric Exchange Between Two Sites
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 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 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 informationProblem Set #6 BioE 326B/Rad 226B
. Chemical shift anisotropy Problem Set #6 BioE 26B/Rad 226B 2. Scalar relaxation of the 2 nd kind. 0 imaging 4. NMRD curves Chemical Shift Anisotropy The Hamiltonian a single-spin system in a magnetic
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 informationIntroduction to solution NMR. Alexandre Bonvin. The NMR research group. Bijvoet Center for Biomolecular Research
Introduction to solution NMR 1 Alexandre Bonvin Bijvoet Center for Biomolecular Research with thanks to Dr. Klaartje Houben Bente%Vestergaard% The NMR research group Prof. Marc Baldus Prof. Rolf Boelens
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 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 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 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 informationLecture #6 Chemical Exchange
Lecture #6 Chemical Exchange Topics Introduction Effects on longitudinal magnetization Effects on transverse magnetization Examples Handouts and Reading assignments Kowalewski, Chapter 13 Levitt, sections
More informationNuclear Magnetic Resonance Spectroscopy
Nuclear Magnetic Resonance Spectroscopy Ecole Polytechnique Département de Chimie CHI 551 Dr. Grégory Nocton Bureau 01 30 11 A Tel: 44 02 Ecole polytechnique / CNRS Laboratoire de Chimie Moléculaire E-mail:
More informationPhysikalische Chemie IV (Magnetische Resonanz) HS Solution Set 2. Hand out: Hand in:
Solution Set Hand out:.. Hand in:.. Repetition. The magnetization moves adiabatically during the application of an r.f. pulse if it is always aligned along the effective field axis. This behaviour is observed
More informationNuclear Spin and Stability. PHY 3101 D. Acosta
Nuclear Spin and Stability PHY 3101 D. Acosta Nuclear Spin neutrons and protons have s = ½ (m s = ± ½) so they are fermions and obey the Pauli- Exclusion Principle The nuclear magneton is eh m µ e eh 1
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 informationSecond Order Effects, Overtone NMR, and their Application to Overtone Rotary Recoupling of 14 N- 13 C Spin Pairs under Magic-Angle-Spinning
Second Order Effects, Overtone NMR, and their Application to Overtone Rotary Recoupling of 14 N- 13 C Spin Pairs under Magic-Angle-Spinning 1. The NMR Interactions NMR is defined by a series of interactions,
More informationMagnetic Resonance in magnetic materials
Ferdinando Borsa, Dipartimento di Fisica, Universita di Pavia Magnetic Resonance in magnetic materials Information on static and dynamic magnetic properties from Nuclear Magnetic Resonance and Relaxation
More information3. Perturbed Angular Correlation Spectroscopy
3. Perturbed Angular Correlation Spectroscopy Dileep Mampallil Augustine K.U.Leuven, Belgium Perturbed Angular Correlation Spectroscopy (PAC) is a gamma ray spectroscopy and can be used to investigate
More information7. Basics of Magnetization Switching
Beyond CMOS computing 7. Basics of Magnetization Switching Dmitri Nikonov Dmitri.e.nikonov@intel.com 1 Outline Energies in a nanomagnet Precession in a magnetic field Anisotropies in a nanomagnet Hysteresis
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 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 informationSpins and spin-orbit coupling in semiconductors, metals, and nanostructures
B. Halperin Spin lecture 1 Spins and spin-orbit coupling in semiconductors, metals, and nanostructures Behavior of non-equilibrium spin populations. Spin relaxation and spin transport. How does one produce
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 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 informationNMR course at the FMP: NMR of organic compounds and small biomolecules - II -
NMR course at the FMP: NMR of organic compounds and small biomolecules - II - 16.03.2009 The program 2/76 CW vs. FT NMR What is a pulse? Vectormodel Water-flip-back 3/76 CW vs. FT CW vs. FT 4/76 Two methods
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 informationProtein dynamics from NMR Relaxation data
Protein dynamics from NMR Relaxation data Clubb 3/15/17 (S f2 ) ( e ) Nitrogen-15 relaxation ZZ-exchange R 1 = 1/T 1 Longitudinal relaxation (decay back to z-axis) R 2 = 1/T 2 Spin-spin relaxation (dephasing
More informationSimulations of spectra and spin relaxation
43 Chapter 6 Simulations of spectra and spin relaxation Simulations of two-spin spectra We have simulated the noisy spectra of two-spin systems in order to characterize the sensitivity of the example resonator
More informationPrinciples of Molecular Spectroscopy: Electromagnetic Radiation and Molecular structure. Nuclear Magnetic Resonance (NMR)
Principles of Molecular Spectroscopy: Electromagnetic Radiation and Molecular structure Nuclear Magnetic Resonance (NMR) !E = h" Electromagnetic radiation is absorbed when the energy of photon corresponds
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 informationShimming of a Magnet for Calibration of NMR Probes UW PHYSICS REU 2013
Shimming of a Magnet for Calibration of NMR Probes RACHEL BIELAJEW UW PHYSICS REU 2013 Outline Background The muon anomaly The g-2 Experiment NMR Design Helmholtz coils producing a gradient Results Future
More informationChaotic Scattering of Microwaves in Billiards: Induced Time-Reversal Symmetry Breaking and Fluctuations in GOE and GUE Systems 2008
Chaotic Scattering of Microwaves in Billiards: Induced Time-Reversal Symmetry Breaking and Fluctuations in GOE and GUE Systems 2008 Quantum billiards and microwave resonators as a model of the compound
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 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 informationPhysics 221A Fall 1996 Notes 13 Spins in Magnetic Fields
Physics 221A Fall 1996 Notes 13 Spins in Magnetic Fields A nice illustration of rotation operator methods which is also important physically is the problem of spins in magnetic fields. The earliest experiments
More informatione 2m p c I, (22.1) = g N β p I(I +1), (22.2) = erg/gauss. (22.3)
Chemistry 26 Molecular Spectra & Molecular Structure Week # 7 Nuclear Magnetic Resonance Spectroscopy Along with infrared spectroscopy, nuclear magnetic resonance (NMR) is the most important method available
More informationControl of Spin Systems
Control of Spin Systems The Nuclear Spin Sensor Many Atomic Nuclei have intrinsic angular momentum called spin. The spin gives the nucleus a magnetic moment (like a small bar magnet). Magnetic moments
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 informationParity Violation in Diatomic Molecules
Parity Violation in Diatomic Molecules Jeff Ammon, E. Altuntas, S.B. Cahn, R. Paolino*, D. DeMille Physics Department, Yale University *Physics Department, US Coast Guard Academy DeMille Group Funding:
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 informationNuclear spin maser with a novel masing mechanism and its application to the search for an atomic EDM in 129 Xe
Nuclear spin maser with a novel masing mechanism and its application to the search for an atomic EDM in 129 Xe A. Yoshimi RIKEN K. Asahi, S. Emori, M. Tsukui, RIKEN, Tokyo Institute of Technology Nuclear
More information11.1. FÖRSTER RESONANCE ENERGY TRANSFER
11-1 11.1. FÖRSTER RESONANCE ENERGY TRANSFER Förster resonance energy transfer (FRET) refers to the nonradiative transfer of an electronic excitation from a donor molecule to an acceptor molecule: D *
More informationFluorescence Spectroscopy
Fluorescence Spectroscopy Raleigh light scattering light all freqs Fluorescence emission Raleigh Scattering 10 nm Raleigh light scattering Fluorescence emission 400 nm Scattering - TWO particle 10 nm Particle
More informationLecture #9 Redfield theory of NMR relaxation
Lecture 9 Redfield theory of NMR relaxation Topics Redfield theory recap Relaxation supermatrix Dipolar coupling revisited Scalar relaxation of the st kind Handouts and Reading assignments van de Ven,
More informationIn this lecture, we will go through the hyperfine structure of atoms. The coupling of nuclear and electronic total angular momentum is explained.
Lecture : Hyperfine Structure of Spectral Lines: Page- In this lecture, we will go through the hyperfine structure of atoms. Various origins of the hyperfine structure are discussed The coupling of nuclear
More information2m 2 Ze2. , where δ. ) 2 l,n is the quantum defect (of order one but larger
PHYS 402, Atomic and Molecular Physics Spring 2017, final exam, solutions 1. Hydrogenic atom energies: Consider a hydrogenic atom or ion with nuclear charge Z and the usual quantum states φ nlm. (a) (2
More information7 Spin Lattice Relaxation
D. Freude and J. Haase, version of April 205 7 7 Spin Lattice Relaxation The recovery of the population ratio / of the Zeeman levels and from an off equilibrium state to the Boltzmann equilibrium / exp
More informationLecture 11: calculation of magnetic parameters, part II
TO DO IS TO BE SOCRATES TO BE IS TO DO SARTRE OO BE DO BE DO SINATRA Lecture 11: calculation of magnetic parameters, part II classification of magnetic perturbations, nuclear quadrupole interaction, J-coupling,
More informationNuclear spin spectroscopy for semiconductor hetero and nano structures
(Interaction and Nanostructural Effects in Low-Dimensional Systems) November 16th, Kyoto, Japan Nuclear spin spectroscopy for semiconductor hetero and nano structures Yoshiro Hirayama Tohoku University
More informationVIII. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY
1 VIII. NUCLEAR MAGNETIC RESONANCE (NMR) SPECTROSCOPY Molecules are extremely small entities; thus, their direct detection and direct investigation is still almost impossible. For the detection and detailed
More informationTopics. The concept of spin Precession of magnetic spin Relaxation Bloch Equation. Bioengineering 280A Principles of Biomedical Imaging
Bioengineering 280A Principles of Biomedical Imaging Fall Quarter 2006 MRI Lecture 1 Topics The concept of spin Precession of magnetic spin Relaxation Bloch Equation 1 Spin Intrinsic angular momentum of
More informationNMR-spectroscopy in solution - an introduction. Peter Schmieder
NMR-spectroscopy in solution - an introduction 2/92 Advanced Bioanalytics NMR-Spectroscopy Introductory session (11:00 12:30) Basic aspects of NMR-spectroscopy NMR parameter Multidimensional NMR-spectroscopy
More information