Nuclear Magnetic Resonance

1
Nuclear Magnetic Resonance
A.) Introduction Nuclear Magnetic Resonance
(NMR) measures the absorption of electromagnetic
radiation in the radio-frequency region (4-900
MHz) - nuclei (instead of outer electrons) are
involved in absorption process - sample needs
to be placed in magnetic field to cause different
energy states NMR was first experimentally
observed by Bloch and Purcell in 1946 (received
Nobel Prize in 1952) and quickly became
commercially available and widely used. Probe
the Composition, Structure, Dynamics and Function
of the Complete Range of Chemical Entities from
small organic molecules to large molecular weight
polymers and proteins. NMR is routinely and
widely used as the preferred technique to rapidly
elucidate the chemical structure of most organic
compounds. One of the MOST Routinely
used Analytical Techniques
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NMR History
1937 Rabi predicts and observes nuclear
magnetic resonance1946 Bloch, Purcell first
nuclear magnetic resonance of bulk sample 1953
Overhauser NOE (nuclear Overhauser effect) 1966
Ernst, Anderson Fourier transform NMR 1975
Jeener, Ernst 2D NMR 1985 Wüthrich first
solution structure of a small protein
(BPTI) from NOE derived distance restraints 1987
3D NMR 13C, 15N isotope labeling of
recombinant proteins (resolution) 1990 pulsed
field gradients (artifact suppression) 1996/7
new long range structural parameters -
residual dipolar couplings from partial alignment
in liquid crystalline media - projection angle
restraints from cross-correlated
relaxation TROSY (molecular weight gt 100
kDa) Nobel prizes 1944 Physics Rabi
(Columbia) 1952 Physics Bloch (Stanford), Purcell
(Harvard) 1991 Chemistry Ernst (ETH) 2002
Chemistry Wüthrich (ETH) 2003 Medicine Lauterbur
(University of Illinois in Urbana ),
Mansfield (University of Nottingham)
3
NMR History
First NMR Spectra on Water
1H NMR spectra of water
Bloch, F. Hansen, W. W. Packard, M. The
nuclear induction experiment. Physical Review
(1946), 70 474-85.
4
NMR History
First Observation of the Chemical Shift
1H NMR spectra ethanol
Modern ethanol spectra
Arnold, J.T., S.S. Dharmatti, and M.E. Packard,
J. Chem. Phys., 1951. 19 p. 507.
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Typical Applications of NMR 1.) Structural
(chemical) elucidation Natural product
chemistry Synthetic organic chemistry -
analytical tool of choice of synthetic
chemists - used in conjunction with MS and
IR 2.) Study of dynamic processes reaction
kinetics study of equilibrium (chemical or
structural) 3.) Structural (three-dimensional)
studies Proteins, Protein-ligand
complexes DNA, RNA, Protein/DNA complexes
Polysaccharides 4.) Drug Design Structure
Activity Relationships by NMR 5) Medicine -MRI
Taxol (natural product)
NMR Structure of MMP-13 complexed to a ligand
MRI images of the Human Brain
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Each NMR Observable Nuclei Yields a Peak in the
Spectra fingerprint of the structure
2-phenyl-1,3-dioxep-5-ene
1H NMR spectra
13C NMR spectra
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A Basic Concept in ElectroMagnetic Theory
A Direct Application to NMR
A perpendicular external magnetic field will
induce an electric current in a closed loop
An electric current in a closed loop will create
a perpendicular magnetic field
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• B.) Theory of NMR
• 1. Quantum Description
• Nuclear Spin (think electron spin)
• Nucleus rotates about its axis (spin)
• Nuclei with spin have angular momentum (p)
• 1) quantized, spin quantum number I
• 2) 2I 1 states I, I-1, I-2, , -I
• 3) identical energies in absence of external
  magnetic field
• c) NMR active Nuclear Spin (I) ½
• 1H, 13C, 15N, 19F, 31P ? biological and
  chemical relevance
• ? Odd atomic mass
• I ½ -½
• NMR inactive Nuclear Spin (I) 0
• 12C, 16O ? Even atomic mass number
• Quadrupole Nuclei Nuclear Spin (I) gt ½

l
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Information in a NMR Spectra
1) Energy E hu h is Planck constant u is NMR
resonance frequency
Observable Name
Quantitative Information Peak position
Chemical shifts (d) d(ppm) uobs
uref/uref (Hz) chemical
(electronic)


environment of nucleus Peak Splitting
Coupling Constant (J) Hz
peak separation
neighboring nuclei

(intensity ratios)
(torsion angles) Peak Intensity
Integral
unitless (ratio)
nuclear count (ratio)

relative height of integral
curve T1 dependent Peak Shape
Line width Du
1/pT2 molecular motion
peak half-height chemical
exchange uncertainty principal unc
ertainty in energy
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• ii. Magnetic Moment (m)
• spinning charged nucleus creates a magnetic field
• magnetic moment (m) is created along axis of the
  nuclear spin
• m gp
• where
• p angular momentum

Magnetic moment
Similar to magnetic field created by electric
current flowing in a coil
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Magnetic alignment
g h / 4p
Add a strong external field (Bo). and the nuclear
magnetic moment aligns with (low energy)
against (high-energy)
In the absence of external field, each nuclei is
energetically degenerate
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• iii. Energy Levels in a Magnetic Field
• Zeeman Effect -Magnetic moments are oriented in
  one of two directions in magnetic field
• Difference in energy between the two states is
  given by
• DE g h Bo / 2p
• where
• Bo external magnetic field ? unitsTesla (Kg
  s-2 A-1)

13

• Energy Levels in a Magnetic Field
• Transition from the low energy to high energy
  spin state occurs through an absorption of a
  photon of radio-frequency (RF) energy

RF
Frequency of absorption n g Bo / 2p
14

• 2. Classical Description
• Spinning particle precesses around an applied
  magnetic field
• Angular velocity of this motion is given by
• wo gBo

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ii. Net Magnetization

• Classic View
• - Nuclei either align with or
• against external magnetic
• field along the z-axis.
• - Since more nuclei align with
• field, net magnetization (Mo)
• exists parallel to external
• magnetic field
• Quantum Description
• Nuclei either populate low
• energy (a, aligned with field)
• or high energy (b, aligned
• against field)
• - Net population in a energy

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An NMR Experiment
We have a net magnetization precessing about Bo
at a frequency of wo with a net population
difference between aligned and unaligned spins.
z
z
Mo
x
x
y
y
Bo
Bo
Now What?
Perturbed the spin population or perform spin
gymnastics Basic principal of NMR experiments
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An NMR Experiment
resonant condition frequency (w1) of B1 matches
Larmor frequency (wo) energy is absorbed and
population of a and b states are perturbed.
z
z
Mo
B1 off (or off-resonance)
x
x
B1
Mxy
w1
y
y
w1
And/Or Mo now precesses about B1 (similar to
Bo) for as long as the B1 field is applied.
Again, keep in mind that individual spins flipped
up or down (a single quanta), but Mo can have a
continuous variation.
Right-hand rule
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• Classical Description
• Observe NMR Signal
• Need to perturb system from equilibrium.
• B1 field (radio frequency pulse) with gBo/2p
  frequency
• Net magnetization (Mo) now precesses about Bo and
  B1
• MX and MY are non-zero
• Mx and MY rotate at Larmor frequency
• System absorbs energy with transitions between
  aligned and unaligned states
• Precession about B1stops when B1 is turned off

Mz
RF pulse
B1 field perpendicular to B0
Mxy
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iii. Absorption of RF Energy or NMR RF Pulse

• Classic View
• - Apply a radio-frequency (RF)
• pulse a long the y-axis
• - RF pulse viewed as a second
• field (B1), that the net
• magnetization (Mo) will
• precess about with an
• angular velocity of w1
• -- precession stops when B1
• turned off
• Quantum Description
• - enough RF energy has been
• absorbed, such that the
• population in a/b are now
• equal

90o pulse
w1 gB1
Bo gt 0
Please Note A whole variety of pulse widths are
possible, not quantized dealing with bulk
magnetization
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An NMR Experiment
What Happens Next?
The B1 field is turned off and Mxy continues to
precess about Bo at frequency wo.
z
x
wo
Mxy
y
? NMR signal
Receiver coil (x)
FID Free Induction Decay
Mxy is precessing about z-axis in the x-y plane
Time (s)
y
y
y
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An NMR Experiment
The oscillation of Mxy generates a fluctuating
magnetic field which can be used to generate a
current in a receiver coil to detect the NMR
signal.
NMR Probe (antenna)
A magnetic field perpendicular to a circular
loop will induce a current in the loop.
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NMR Signal Detection - FID
The FID reflects the change in the magnitude of
Mxy as the signal is changing relative to the
receiver along the y-axis
Detect signal along X
RF pulse along Y
Again, the signal is precessing about Bo at its
Larmor Frequency (wo).
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NMR Signal Detection - Fourier Transform
So, the NMR signal is collected in the Time -
domain
But, we prefer the frequency domain.
Fourier Transform is a mathematical procedure
that transforms time domain data into frequency
domain
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NMR Signal Detection - Fourier Transform
After the NMR Signal is Generated and the B1
Field is Removed, the Net Magnetization Will
Relax Back to Equilibrium Aligned Along the Z-axis
T2 relaxation
Two types of relaxation processes, one in the x,y
plane and one along the z-axis
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• iv. NMR Relaxation
• No spontaneous reemission of photons to relax
  down to ground state
• Probability too low ? cube of the frequency
• Two types of NMR relaxation processes
• spin-lattice or longitudinal relaxation
• i. transfer of energy to the lattice or
  solvent material
• ii. coupling of nuclei magnetic field with
  magnetic fields created
• by the ensemble of vibrational and
  rotational motion of the
• lattice or solvent.
• iii. results in a minimal temperature increase
  in sample
• iv. Relaxation time (T1) ? exponential decay

Mz M0(1-exp(-t/T1))
Please Note General practice is to wait 5xT1 for
the system to have fully relaxed.
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2) spin-spin or transverse relaxation i.
exchange of energy between excited nucleus and
low energy state nucleus ii.
randomization of spins or magnetic moment in
x,y-plane iii. related to NMR peak
line-width iv. relaxation time (T2)
Mx My M0 exp(-t/T2)
(derived from Heisenberg uncertainty principal)
Please Note Line shape is also affected by the
magnetic fields homogeneity
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NMR Sensitivity
The applied magnetic field causes an energy
difference between aligned(a) and unaligned(b)
nuclei
b
Low energy gap
Bo gt 0
DE h n
a
Bo 0
The population (N) difference can be determined
from
Boltzmman distribution
Na / Nb e DE / kT
The DE for 1H at 400 MHz (Bo 9.5 T) is 3.8 x
10-5 Kcal / mol
Very Small ! 64 excess spins per million in
lower state
Na / Nb 1.000064
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NMR Sensitivity

• NMR signal depends on
• Number of Nuclei (N) (limited to field
  homogeneity and filling factor)
• Gyromagnetic ratio (in practice g3)
• Inversely to temperature (T)
• External magnetic field (Bo2/3, in practice,
  homogeneity)
• B12 exciting field strength

signal (s) g4Bo2NB1g(u)/T
DE g h Bo / 2p
Na / Nb e DE / kT
Increase energy gap -gt Increase population
difference -gt Increase NMR signal
DE


g
Bo
g
- Intrinsic property of nucleus can not be
changed.
(gH/gN)3 for 15N is 1000x
(gH/gC)3 for 13C is 64x
1H is 64x as sensitive as 13C and 1000x as
sensitive as 15N ! Consider that the natural
abundance of 13C is 1.1 and 15N is
0.37 relative sensitivity increases to 6,400x
and 2.7x105x !!
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• NMR Sensitivity
• Relative sensitivity of 1H, 13C, 15N and other
  nuclei NMR spectra depend on
• Gyromagnetic ratio (g)
• Natural abundance of the isotope

g
- Intrinsic property of nucleus can not be
changed.
(gH/gN)3 for 15N is 1000x
(gH/gC)3 for 13C is 64x
1H is 64x as sensitive as 13C and 1000x as
sensitive as 15N ! Consider that the natural
abundance of 13C is 1.1 and 15N is
0.37 relative sensitivity increases to 6,400x
and 2.7x105x !!
1H NMR spectra of caffeine 8 scans 12 secs
13C NMR spectra of caffeine 8 scans 12 secs
13C NMR spectra of caffeine 10,000 scans 4.2
hours
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NMR Sensitivity
Increase in Magnet Strength is a Major Means to
Increase Sensitivity
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NMR Sensitivity
But at a significant cost!
2,00,000
4,500,000
800,000
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Chemical Shift
Up to this point, we have been treating nuclei in
general terms. Simply comparing 1H, 13C, 15N etc.
If all 1H resonate at 500MHz at a field strength
of 11.7T, NMR would not be very interesting
The chemical environment for each nuclei results
in a unique local magnetic field (Bloc) for each
nuclei
Beff Bo - Bloc --- Beff Bo( 1 - s )
s is the magnetic shielding of the nucleus
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• v. Chemical Shift
• Small local magnetic fields (Bloc) are generated
  by electrons as they circulate nuclei.
• Current in a circular coil generates a magnetic
  field
• These local magnetic fields can either oppose or
  augment the external magnetic field
• Typically oppose external magnetic field
• Nuclei see an effective magnetic field (Beff)
  smaller then the external field
• s magnetic shielding or screening constant
• i. depends on electron density
• ii. depends on the structure of the compound

Beff Bo - Bloc --- Beff Bo( 1 - s )
HO-CH2-CH3
s reason why observe three distinct NMR peaks
instead of one based on strength of B0
n gBo/2p
de-shielding
high shielding
Shielding local field opposes Bo
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• Effect of Magnetic Anisotropy
• 1) external field induces a flow (current) of
  electrons in p system ring
• current effect
• 2) ring current induces a local magnetic field
  with shielding (decreased
• chemical shift) and deshielding (increased
  chemical shifts)

Decrease in chemical shifts
Increase in chemical shifts
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The NMR scale (d, ppm)
Bo gtgt Bloc -- MHz compared to Hz
Comparing small changes in the context of a large
number is cumbersome
w - wref d ppm (parts per million)
wref
Instead use a relative scale, and refer all
signals (w) in the spectrum to the signal of a
particular compound (wref).
IMPORTANT absolute frequency is field dependent
(n g Bo / 2p)
Tetramethyl silane (TMS) is a common reference
chemical
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The NMR scale (d, ppm)
Chemical shift (d) is a relative scale so it is
independent of Bo. Same chemical shift at 100 MHz
vs. 900 MHz magnet
IMPORTANT absolute frequency is field dependent
(n g Bo / 2p)
At higher magnetic fields an NMR spectra will
exhibit the same chemical shifts but with higher
resolution because of the higher frequency range.
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Chemical Shift Trends
For protons, 15 ppm For carbon, 220 ppm
Carbon chemical shifts have similar trends, but
over a larger sweep-width range (0-200 ppm)
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Chemical Shift Trends
Alcohols, protons a to ketones
Aromatics Amides
Acids Aldehydes
Aliphatic
Olefins
ppm
0 TMS
2
10
7
5
15
Aromatics, conjugated alkenes
CO in ketones
Aliphatic CH3, CH2, CH
Olefins
ppm
50
150
100
80
210
0 TMS
CO of Acids, aldehydes, esters
Carbons adjacent to alcohols, ketones
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Common Chemical Shift Ranges
Carbon chemical shifts have similar trends, but
over a larger sweep-width range (0-200 ppm)
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Coupling Constants
Energy level of a nuclei are affected by
covalently-bonded neighbors spin-states
three-bond
one-bond
Spin-States of covalently-bonded nuclei want to
be aligned.
J (Hz)
J/4
bb
S
I
ab
ba
-J/4
S
I
I S
aa
J/4
The magnitude of the separation is called
coupling constant (J) and has units of Hz.
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• vi. Spin-Spin Splitting (J-coupling)
• through-bond interaction that results in the
  splitting of a single peak into multiple peaks of
  various intensities
• The spacing in hertz (hz) between the peaks is a
  constant
• i. coupling constant (J)
• bonding electrons convey spin states of bonded
  nuclei
• spin states of nuclei are coupled
• alignment of spin states of bonded nuclei affects
  energy of the ground (a) and excited states (b)
  of observed nuclei
• Coupling pattern and intensity follows Pascals
  triangle

11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6
15 20 15 6 11 7 21 35 35 21 7 1
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Common NMR Splitting Patterns

• Coupling Rules
• equivalent nuclei do not interact
• coupling constants decreases with separation (
  typically 3 bonds)
• multiplicity given by number of attached
  equivalent protons (n1)
• multiple spin systems ? multiplicity ?
  (na1)(nb1)
• Relative peak heights/area follows Pascals
  triangle
• Coupling constant are independent of applied
  field strength

IMPORTANT Coupling constant pattern allow for
the identification of bonded nuclei.
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Karplus Equation Coupling Constants
J const. 10Cosf
Relates coupling constant to Torsional
angle. Used to solve Structures!
45

• vii. Nuclear Overhauser Effect (NOE)
• Interaction between nuclear spins mediated
  through empty space (5Å) ? like ordinary bar
  magnets
• Important effect is time-averaged
• Gives rise to dipolar relaxation (T1 and T2) and
  specially to cross-relaxation

Perturb 1H spin population affects 13C spin
population NOE effect
the 13C signals are enhanced by a factor 1 h
1 1/2 . g(1H)/g(13C) max. of 2
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Example 21 The proton NMR spectrum is for a
compound of empirical formula C4H8O. Identify the
compound
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3. NMR Instrumentation (block diagram)
48

• i. Superconducting Magnet
• solenoid wound from superconducting niobium/tin
  or niobium/titanium wire
• kept at liquid helium temperature (4K), outer
  liquid N2 dewar
• 1) near zero resistance ? minimal current lose
  ? magnet stays at
• field for years without external power
  source
• c) electric currents in the shim coils create
  small magnetic fields which compensate
  inhomogenieties

Cross-section of magnet
magnet
spinner
sample lift
NMR Tube
RF coils
cryoshims
shimcoils
Probe
Superconducting solenoid Use up to 190 miles of
wire!
Liquid N2
Liquid He
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• ii. Lock System
• NMR magnetic field slowly drifts with time.
• Need to constantly correct for the field drift
  during data collection
• c) Deuterium NMR resonance of the solvent is
  continuously irradiated and monitored to maintain
  an on-resonance condition
• 1) changes in the intensity of the reference
  absorption signal controls a
• feedback circuit
• 2) a frequency generator provides a fixed
  reference frequency for the lock
• signal
• 3) if the observed lock signal differs from the
  reference frequency, a small
• current change occurs in a room-temperature
  shim coil (Z0) to create a
• small magnetic field to augment the
  main field to place the lock-signal
• back into resonance
• d) NMR probes contains an additional transmitter
  coil tuned to deuterium frequency

Lock Feedback Circuit
Field Drift over 11 Hrs ( 0.15Hz/hr
Lock Changes From Off-resonance to On-resonance
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• iii. Sample Probe
• Holds the sample in a fixed position in the
  magnetic field
• Contains an air turbine to spin, insert and eject
  the sample
• c) Contains the coils for
• 1) transmitting the RF pulse
• 2) detecting the NMR signal
• 3) observing the lock signal
• 4) creating magnetic field gradients
• Thermocouples and heaters to
• maintain a constant temperature

51

• iv. Pulse Generator Receiver System
• Radio-frequency generators and frequency
  synthesizers produce a signal of essentially a
  single frequency.
• RF pulses are typically short-duration (msecs)
• 1) produces bandwidth (1/4t) centered around
  single frequency
• 2) shorter pulse width ? broader frequency
  bandwidth
• i. Heisenberg Uncertainty Principal Du.Dt
  1/2p

A radiofrequency pulse is a combination of a wave
(cosine) of frequency wo and a step function
The Fourier transform indicates the pulse covers
a range of frequencies
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• iv. Pulse Generator Receiver System
• A magnetic field perpendicular to a circular loop
  will induce a current in the loop.
• 90o NMR pulses places the net magnetization
  perpendicular to the probes receiver coil
  resulting in an induced current in the nanovolt
  to microvolt range
• e) preamp mounted in probe amplifies the
  current to 0 to 10 V
• f) no signal is observed if net magnetization
  is aligned along the Z or Z axis

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4. NMR Data Detection and Processing

• i. Fourier Transform NMR
• Instead of sequentially scanning through each
  individual frequency, simultaneously observe
  absorption of all frequencies.
• 1) frequency sweep (CW), step through each
  individual frequency is
• very slow (1-10 min)
• 2) short RF pulses result in bandwidth that
  cover entire frequency range
• 3) Fourier Transform NMR is fast (N x 1-10 sec)
  
• 4) Increase signal-to-noise (S/N) by collecting
  multiple copies of FID
• and averaging signal.
• S/N rnumber of
  scans
• b) Observe each individual resonance as it
  precesses at its Larmor frequency (wo) in the X,Y
  plane.
• Monitor changes in the induced current in the
  receiver coil as a function of time.

X
y
Detect signal along X
RF pulse along Y
n gBo(1-s)/2p
FID Free Induction Decay
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i. Fourier Transform NMR d) Observed signal
decays as a function of T2 relaxation 1) peak
width at half-height (n½) is related to T2 e) NMR
signal is collected in Time domain, but prefer
frequency domain f) Transform from the time
domain to the frequency domain using the Fourier
function
T2 relaxation
Fourier Transform is a mathematical procedure
that transforms time domain data into frequency
domain
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ii. Sampling the Audio Signal a) Collect Digital
data by periodically sampling signal voltage 1)
ADC analog to digital converter b) To
correctly represent Cos/Sin wave, need to collect
data at least twice as fast as the signal
frequency c) If sampling is too slow, get
folded or aliased peaks
The Nyquist Theorem says that we have to sample
at least twice as fast as the fastest (higher
frequency) signal.
Sample Rate
- Correct rate, correct frequency
SR 1 / (2 SW)

• ½ correct rate, ½ correct frequency Folded peaks!
• Wrong phase!

SR sampling rate
56
Correct Spectra
Spectra with carrier offset resulting in peak
folding or aliasing
Sweep Width
(range of radio-frequencies monitored for nuclei
absorptions)
57

• iii. Window Functions
• Emphasize the signal and decrease the noise by
  applying a mathematical
• function to the FID.
• b) NMR signal is decaying by T2 as the FID is
  collected.

Good stuff
Mostly noise
Resolution
Sensitivity
F(t) 1 e - ( LB t ) line broadening
Effectively adds LB in Hz to peak Line-widths
58
Can either increase S/N or
Resolution Not Both!
LB -1.0 Hz
LB 5.0 Hz
Increase Sensitivity
Increase Resolution
FT
FT
59

• iv. Zero Filling
• Improve digital resolution by adding zero data
  points at end of FID

60

• v. NMR Peak Integration or Peak Area
• The relative peak intensity or peak area is
  proportional to the number of protons associated
  with the observed peak.
• Means to determine relative concentrations of
  multiple species present in an NMR sample.

Relative peak areas Number of protons
3
Integral trace
HO-CH2-CH3
2
1
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5. Exchange Rates and NMR Time Scale

• NMR time scale refers to the chemical shift time
  scale
• a) remember frequency units are in Hz (sec-1)
  ? time scale
• b) exchange rate (k)
• c) differences in chemical shifts between
  species in exchange indicate the
• exchange rate.
• d) For systems in fast exchange, the observed
  chemical shift is the average
• of the individual species chemical shifts.

Time Scale Chem. Shift (d) Coupling Const.
(J) T2 relaxation Slow k ltlt dA- dB
k ltlt JA- JB k ltlt 1/ T2,A- 1/
T2,B Intermediate k dA - dB k
JA- JB k 1/ T2,A- 1/ T2,B Fast
k gtgt dA - dB k gtgt JA- JB k gtgt
1/ T2,A- 1/ T2,B Range (Sec-1) 0 1000 0 12
1 - 20
dobs f1d1 f2d2 f1 f2 1
where f1, f2 mole fraction of each
species d1,d2 chemical shift of each species
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ii. Effects of Exchange Rates on NMR data
k p Dno2 /2(he - ho)
k p Dno / 21/2
k p (Dno2 -  Dne2)1/2/21/2
k p (he-ho)

• k exchange rate
• h peak-width at half-height
• peak frequency
• e with exchange
• o no exchange

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ii. Effects of Exchange Rates on NMR data
40 Hz
No exchange
k 0.1 s-1
slow
k 5 s-1
k 10 s-1
With exchange
k 20 s-1
k 40 s-1
Increasing Exchange Rate
coalescence
k 88.8 s-1
k 200 s-1
k 400 s-1
k 800 s-1
k 10,000 s-1
fast
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6. Multidimensional NMR

• NMR pulse sequences
• a) composed of a series of RF pulses, delays,
  gradient pulses and phases
• b) in a 1D NMR experiment, the FID acquisition
  time is the time domain (t1)
• c) more complex NMR experiments will use
  multiple time-dimensiona to
• obtain data and simplify the analysis.
• d) Multidimensional NMR experiments may also use
  multiple nuclei (2D,
• 13C,15N) in addition to 1H, but usually
  detect 1H)

1D NMR Pulse Sequence
65
ii. Creating Multiple Dimensions in NMR a)
collect a series of FIDS incremented by a second
time domain (t1) 1) evolution of a second
chemical shift or coupling constant occurs
during this time period b) the normal
acquisition time is t2. c) Fourier
transformation occurs for both t1 and t2,
creating a two- dimensional (2D) NMR
spectra
Relative appearance of each NMR spectra will be
modulated by the t1 delay
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ii. Creating Multiple Dimensions in NMR d)
During t1 time period, peak intensities are
modulated at a frequency corresponding to
the chemical shift of its coupled partner. e) In
2D NMR spectra, diagonal peaks are normal 1D
peaks, off-diagonal or cross-peaks
indicate a correlation between the two diagonal
peaks
Fourier Transform t2 obtain series of NMR spectra
modulated by t1
Collections of FIDs with t1 modulations
Looking down t1 axis, each point has
characteristics of time domain FID
Fourier Transform t1 obtain 2D NMR spectra
Peaks along diagonal are normal 1D NMR spectra
Contour map (slice at certain threshold) of 3D
representation of 2D NMR spectra. (peak intensity
is third dimension
Cross-peaks correlate two diagonal peaks by
J-coupling or NOE interactions
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iii. 2D NOESY NMR Spectra a) basis for solving a
structure b) diagonal peaks are correlated by
through-space dipole-dipole interaction (NOE) c)
NOE is a relaxation factor that builds-up during
the mixing-time (tm) d) relative
magnitude of the cross-peak is related to the
distance (1/r6) between
the protons ( 5Å).
2D NOESY NMR Pulse Sequence
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iv. 3D 4D NMR Spectra a) similar to 2D NMR with
either three or four time domains. b) additional
dimensions usually correspond to 13C 15N
chemical shifts. c) primarily used for analysis
of biomolecular structures 1) disperses highly
overlapped NMR spectra into 3 4
dimensions, simplifies analysis. d) view 3D, 4D
experiments as collection of 2D spectra. e) one
experiment may take 2.5 to 4 days to collect.
1) diminished resolution and sensitivity
Spread peaks out by 15N chemical shift of amide N
attached to NH
Further spread peaks out by 13C chemical shift of
C attached to CH