NMR Spectroscopy

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NMR Spectroscopy

• Part I. Origin of NMR

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Nuclei in Magnetic Field

• Nucleus rotate about an axis -- spin

Nucleus bears a charge, its spin gives rise to a
magnetic field . The resulting magnetic moment is
oriented along the axis of spin and is
proportional to angular momentum m g p

• magnetic moment
• p angular momentum
• g magnetogyric ratio

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Nuclei in Magnetic Field

• Spin Quantum Number I
• a characteristic property of a nucleus. May be
  an integer or half integer

of protons of neutrons I even even 0 odd
odd integer 1,2,3 even even half
integral odd odd half integral
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Nuclei in Magnetic Field

• Properties of nucleus with spin quantum number I

1. An angular momentum of magnitude
I(I1)1/2h 2. A component of angular momentum
mIh on an arbitrary axis where mII, I-1, -I
(magnetic quantum number) 3. When Igt0, a magnetic
moment with a constant magnitude and an
orientation that is determined by the value of
mI. m g mI h
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Nuclei in Magnetic Field

• In a magnetic field B (in z direction) there are
  2I1 orientations of nucleus with different
  energies.

B0 magnetic field in z direction nL Larmor
Frequency
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Nuclei in Magnetic Field

• For I1/2 nucleus mI 1/2 and 1/2

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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
Distribution between two states
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Nuclei in Magnetic Field
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Nuclei in Magnetic Field
Magnetizaton
The difference in populations of the two states
can be considered as a surplus in the lower
energy state according to the Boltzmann
distribution A net magnetization of the sample is
stationary and aligned along the z axis (applied
field direction)
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Nuclei in Magnetic Field
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Effect of a radio frequency
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Effect of a radio frequency
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Effect of a radio frequency
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NMR Signals
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Relaxation- Return to Equilibrium
t
t
z axis
x,y plane
0
0
Longitudinal
Transverse
1
1
t
t
2
2
E-t/T2
1-e-t/T1
8
8
Transverse always faster!
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NMR Spectroscopy

• Part II. Signals of NMR

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Free Induction Decay (FID)

• FID represents the time-domain response of the
  spin system following application of an
  radio-frequency pulse.
• With one magnetization at w0, receiver coil would
  see exponentially decaying signal. This decay is
  due to relaxation.

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Fourier Transform
The Fourier transform relates the time-domain
f(t) data with the frequency-domain f(w) data.
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Fourier Transform
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Fourier Transform
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NMR line shape
Lorentzian line A amplitude W half-line width
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Resolution

• Definition
• For signals in frequency domain it is the
  deviation of the peak line-shape from standard
  Lorentzian peak. For time domain signal, it is
  the deviation of FID from exponential decay.
  Resolution of NMR peaks is represented by the
  half-height width in Hz.

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Resolution
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Resolution-digital resolution
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Resolution

• Measurement
• half-height width
• 1015 solution of 0-dichlorobenzene (ODCB)
  in acetone
• Line-shape
• Chloroform in acetone

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Resolution

• Factors affect resolution
• Relaxation process of the observed nucleus
• Stability of B0 (shimming and deuterium
  locking)
• Probe (sample coil should be very close to the
  sample)
• Sample properties and its conditions

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Sensitivity

• Definition
• signal to noise-ratio
• A height of the chosen peak
• Npp peak to peak noise

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Sensitivity

• Measurement
• 1H 0.1 ethyl benzene in deuterochloroform
• 13C ASTM, mixture of 60 by volume
  deuterobenzene and dioxan or 10 ethyl benzene
  in chloroform
• 31P 1 trimehylphosphite in deuterobenzene
• 15N 90 dimethylformamide in deutero-dimethyl-
  sulphoxide
• 19F 0.1 trifluoroethanol in deuteroacetone
• 2H, 17O tap water

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Sensitivity

• Factors affect sensitivity
• Probe tuning, matching, size
• Dynamic range and ADC resolution
• Solubility of the sample in the chosen solvent

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Spectral Parameters

• Chemical Shift
• Caused by the magnetic shielding of the nuclei
  by their surroundings. d-values give the position
  of the signal relative to a reference compound
  signal.
• Spin-spin Coupling
• The interaction between neighboring nuclear
  dipoles leads to a fine structure. The strength
  of this interaction is defined as spin-spin
  coupling constant J.
• Intensity of the signal

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Chemical Shift

• Origin of chemical shift
• s shielding constant
• Chemically non-equivalent nuclei are shielded to
  different extents and give separate resonance
  signals in the spectrum

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Chemical Shift
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Chemical Shift

• d scale or abscissa scale

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Chemical Shift

• Shielding s
• CH3Br lt CH2Br2 lt CH3Br lt TMS

90 MHz spectrum
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Abscissa Scale
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Chemical Shift

• d is dimensionless expressed as the relative
  shift in parts per million ( ppm ).
• d is independent of the magnetic field
• d of proton 0 13 ppm
• d of carbon-13 0 220 ppm
• d of F-19 0 800 ppm
• d of P-31 0 300 ppm

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Chemical Shift

• Charge density
• Neighboring group
• Anisotropy
• Ring current
• Electric field effect
• Intermolecular interaction (H-bonding solvent)

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Chemical Shift anisotropy of neighboring group
c susceptibility r distance to the dipoles
center
Differential shielding of HA and HB in the
dipolar field of a magnetically anisotropic
neighboring group
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Chemical Shift anisotropy of neighboring group
d2.88
d9-10
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• Electronegative groups are "deshielding" and tend
  to move NMR signals from neighboring protons
  further "downfield" (to higher ppm values).
• Protons on oxygen or nitrogen have highly
  variable chemical shifts which are sensitive to
  concentration, solvent, temperature, etc.
• The -system of alkenes, aromatic compounds and
  carbonyls strongly deshield attached protons and
  move them "downfield" to higher ppm values.

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• Electronegative groups are "deshielding" and tend
  to move NMR signals from attached carbons further
  "downfield" (to higher ppm values).
• The -system of alkenes, aromatic compounds and
  carbonyls strongly deshield C nuclei and move
  them "downfield" to higher ppm values.
• Carbonyl carbons are strongly deshielded and
  occur at very high ppm values. Within this group,
  carboxylic acids and esters tend to have the
  smaller values, while ketones and aldehydes
  have values 200.

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Ring Current

• The ring current is induced form the delocalized
  p electron in a magnetic field and generates an
  additional magnetic field. In the center of the
  arene ring this induced field in in the opposite
  direction t the external magnetic field.

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Ring Current -- example
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Spin-spin coupling
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Spin-spin coupling
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AX system
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AX2 system
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Spin-spin coupling
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AX3 system
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Multiplicity Rule
Multiplicity M (number of lines in a multiplet) M
2n I 1 n equivalent neighbor nuclei I spin
number
For I ½ M n 1
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Example AX4 system
I1 n3
AX4
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Order of Spectrum
Zero order spectrum only singlet First order
spectrum Dn gtgt J Higher order spectrum Dn J
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AMX system
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Spin-spin coupling

• Hybridization of the atoms
• Bond angles and torsional angles
• Bond lengths
• Neighboring p-bond
• Effects of neighboring electron lone-pairs
• Substituent effect

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JH-H and Chemical Structure

• Geminal couplings 2J (usually lt0)
• H-C-H bond angle
• hybridization of the carbon atom
• substituents

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Geminal couplings 2J bond angle
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Geminal couplings 2J
Effect of Neighboring p-electrons
Substituent Effects
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Vicinal couplings 3JH-H

• Torsional or dihedral angles
• Substituents
• HC-CH distance
• H-C-C bond angle

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Vicinal couplings 3JH-H dihedral angles

• Karplus curves

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Chemical Shift of amino acid
http//bouman.chem.georgetown.edu/nmr/interaction/
chemshf.htm
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Chemical Shift Prediction
Automated Protein Chemical Shift
Prediction http//www.bmrb.wisc.edu8999/shifty.ht
ml
BMRB NMR-STAR Atom Table Generator for Amino Acid
Chemical Shift Assignments http//www.bmrb.wisc.ed
u/elec_dep/gen_aa.html
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http//bouman.chem.georgetown.edu/nmr/interaction/
chemshf.htm
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Example 1
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NMR Spectroscopy

• Relaxation Time
• Phenomenon Application

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Relaxation- Return to Equilibrium
t
t
z axis
x,y plane
Longitudinal
Transverse
0
0
1
1
t
t
2
2
E-t/T2
1-e-t/T1
8
8
Transverse always faster!
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Relaxation
magnetization vector's trajectory The initial
vector, Mo, evolves under the effects of T1 T2
relaxation and from the influence of an applied
rf-field. Here, the magnetization vector M(t)
precesses about an effective field axis at a
frequency determined by its offset. It's ends up
at a "steady state" position as depicted in the
lower plot of x- and y- magnetizations.
http//gamma.magnet.fsu.edu/info/tour/bloch/index.
html
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Relaxation
The T2 relaxation causes the horizontal (xy)
magnetisation to decay. T1 relaxation
re-establishes the z-magnetisation. Note that T1
relaxation is often slower than T2 relaxation.
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Relaxation time Bloch Equation

• Bloch Equation

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Relaxation time Bloch equation
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Spin-lattice Relaxation time (Longitudinal) T1
Relaxation mechanisms 1. Dipole-Dipole
interaction "through space" 2. Electric
Quadrupolar Relaxation 3. Paramagnetic
Relaxation 4. Scalar Relaxation 5. Chemical
Shift Anisotropy Relaxation 6. Spin Rotation
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Relaxation

• Spin-lattice relaxation converts the excess
  energy into translational, rotational, and
  vibrational energy of the surrounding atoms and
  molecules (the lattice).
• Spin-spin relaxation transfers the excess energy
  to other magnetic nuclei in the sample.

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Longitudinal Relaxation time T1

• Inversion-Recovery Experiment

180y (or x)
90y
tD
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T1 relaxation
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Spin-spin relaxation (Transverse) T2

• T2 represents the lifetime of the signal in the
  transverse plane (XY plane)
• T2 is the relaxation time that is responsible for
  the line width.
• line width at half-height1/T2

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Spin-spin relaxation (Transverse) T2

• Two factors contribute to the decay of transverse
  magnetization.
• molecular interactions
• ( lead to a pure pure T2 molecular effect)
• variations in Bo
• ( lead to an inhomogeneous T2 effect)

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Spin-spin relaxation (Transverse) T2
180y (or x)
90y
tD
tD

• signal width at half-height (line-width ) (pi
  T2)-1

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Spin-spin relaxation (Transverse) T2
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Spin-Echo Experiment
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Spin-Echo experiment
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MXY MXYo e-t/T2
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Carr-Purcell-Meiboom-Gill sequence
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T1 and T2

• In non-viscous liquids, usually T2 T1.
• But some process like scalar coupling with
  quadrupolar nuclei, chemical exchange,
  interaction with a paramagnetic center, can
  accelerate the T2 relaxation such that T2 becomes
  shorter than T1.

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Relaxation and correlation time
For peptides in aqueous solutions the
dipole-dipole spin-lattice and spin-spin
relaxation process are mainly mediated by other
nearby protons
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Why The Interest In Dynamics?

• Function requires motion/kinetic energy
• Entropic contributions to binding events
• Protein Folding/Unfolding
• Uncertainty in NMR and crystal structures
• Effect on NMR experiments- spin relaxation is
  dependent on rate of motions ? know dynamics to
  predict outcomes and design new experiments
• Quantum mechanics/prediction (masochism)

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Application
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Characterizing Protein Dynamics
Parameters/Timescales
Relaxation
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NMR Parameters That Report On Dynamics of
Molecules

• Number of signals per atom multiple signals for
  slow exchange between conformational states
• Linewidths narrow faster motion, wide
  slower dependent on MW and conformational states
• Exchange of NH with solvent requires local
  and/or global unfolding events ? slow timescales
• Heteronuclear relaxation measurements
• R1 (1/T1) spin-lattice- reports on fast motions
• R2 (1/T2) spin-spin- reports on fast slow
• Heteronuclear NOE- reports on fast some slow

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Linewidth is Dependent on MW

• Linewidth determined by size of particle
• Fragments have narrower linewidths

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Nuclear Overhauser Effect
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Nuclear Overhauser Effect (NOE)

• A change in the integrated NMR absorption
  intensity of a nuclear spin when the NMR
  absorption of another spin is saturated.

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Nuclear Overhauser Effect
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Macromolecules or in viscous solution W0
dominant, negative NOE at i due to s Small
molecules in non-viscous solution W2 dominant,
positive NOE at i due to s
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Nuclear Overhauser EffectBrownian motion and NOE
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When 1/tc gtgtw0 (or tc2 w02 ltlt1 ) extreme
narrowing limit
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When 1/tc gtgt w0 (or tc2 w02 ltlt1 ) extreme
narrowing limit
For homo-nuclear hmax 0.5 For
hetro-nuclear hmax 0.5 (gs/gi)
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• When 1/tc w0 (or tc w0 1 ) M.W. 103
• W2 and W0 effect are balanced. ? max 0
• improvement
• Change solvent ofr temperature
• Using rotating frame NOE

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When 1/tc lt w0 (or tc w0 gtgt 1 ) M.W. gt 104 W0
dominant , ? max -1 application Useful
technique for assigning NMR spectra of protein
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Nuclear Overhauser Effect distance
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citraconic acid
mesaconic acid
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