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
2
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.
5
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
6
NMR fingerprint of the compounds chemical
structure
2-phenyl-1,3-dioxep-5-ene
1H NMR spectra
13C NMR spectra
7
Protein Structures from NMR
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
8
Some Suggested NMR References
Spin Dynamics Basics of Nuclear Magnetic
Resonance M. H. Levitt Tables of Spectral Data
for Structure Determination of Organic
Compounds Pretsch, Clerc, Seibl and
Simon Basic One- and Two-Dimensional NMR
Spectroscopy Horst Friebolin Modern NMR
Techniques for Chemistry Research Andrew E.
Derome NMR and Chemistry- an introduction to
modern NMR spectroscopy J. W. Akitt Nuclear
Magnetic Resonance Spectroscopy R. K
Harris Protein NMR Spectroscopy Principals and
Practice John Cavanagh, Arthur Palmer, Nicholas
J. Skelton, Wayne Fairbrother Biomolecular NMR
Spectroscopy J. N. S. Evans NMR of Proteins
and Nucleic Acids Kurt Wuthrich Spectrometric
Identification of Organic Compounds
Silverstein, Bassler and Morrill
9
Some NMR Web Sites
The Basics of NMR Hypertext based NMR course
http//www.cis.rit.edu/htbooks/nmr/nmr-main.htm I
ntegrated Spectral Data Base System for Organic
Compounds http//www.aist.go.jp/RIODB/SDBS/menu-e.
html Educational NMR Software All kinds of NMR
software http//www.york.ac.uk/depts/chem/services
/nmr/edusoft.html NMR Knowledge Base A lot of
useful NMR links http//www.spectroscopynow.com/
NMR Information Server News, Links, Conferences,
Jobs http//www.spincore.com/nmrinfo/ Technical
Tidbits Useful source for the art of
shimming http//www.acornnmr.com/nmr_topics.htm B
MRB (BioMagResBank) Database of NMR resonance
assignments http//www.bmrb.wisc.edu/
10
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
11
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
12
Basic NMR Spectrometer
13
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
14
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
• 14N, 2H, 10B
  ? Even atomic mass odd number
• I 1, 0 -1

l
15

• 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
16
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
17

• 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)

18

• 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
19

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

20
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

21
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
22
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
23

• 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
24
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
25
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
26
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.
27
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).
28
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
29
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
30
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 (T1)
• 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.
31
2) spin-spin or transverse relaxation (T2) 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
32
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
33
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 !!
34

• 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
35
NMR Sensitivity
Increase in Magnet Strength is a Major Means to
Increase Sensitivity
36
NMR Sensitivity
But at a significant cost!
2,00,000
4,500,000
800,000
37
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
38
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
39

• 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
40
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
41
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.
42
NMR Spectra Terminology
TMS
CHCl3
7.27 0
ppm increasing d decreasing
d low field high field
down field up field high
frequency (u) low frequency de-shielding
high shielding Paramagnetic
diamagnetic
600 MHz
150 MHz
92 MHz
1H
13C
2H
Increasing field (Bo) Increasing frequency
(u) Increasing g Increasing energy (E, consistent
with UV/IR)
43
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)
44
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
45
CHARACTERISTIC PROTON CHEMICAL SHIFTS CHARACTERISTIC PROTON CHEMICAL SHIFTS CHARACTERISTIC PROTON CHEMICAL SHIFTS
Type of Proton Structure Chemical Shift, ppm
Cyclopropane C3H6 0.2
Primary R-CH3 0.9
Secondary R2-CH2 1.3
Tertiary R3-C-H 1.5
Vinylic CC-H 4.6-5.9
Acetylenic triple bond,CC-H 2-3
Aromatic Ar-H 6-8.5
Benzylic Ar-C-H 2.2-3
Allylic CC-CH3 1.7
Fluorides H-C-F 4-4.5
Chlorides H-C-Cl 3-4
Bromides H-C-Br 2.5-4
Iodides H-C-I 2-4
Alcohols H-C-OH 3.4-4
Ethers H-C-OR 3.3-4
Esters RCOO-C-H 3.7-4.1
Esters H-C-COOR 2-2.2
Acids H-C-COOH 2-2.6
Carbonyl Compounds H-C-CO 2-2.7
Aldehydic R-(H-)CO 9-10
Hydroxylic R-C-OH 1-5.5
Phenolic Ar-OH 4-12
Enolic CC-OH 15-17
Carboxylic RCOOH 10.5-12
Amino RNH2 1-5
Common Chemical Shift Ranges
Carbon chemical shifts have similar trends, but
over a larger sweep-width range (0-200 ppm)
46
Predicting Chemical Shift Assignments

• Numerous Experimental NMR Data has been compiled
  and general trends identified
• See
• Tables of Spectral Data for Structure
  Determination of
• Organic Compounds Pretsch, Clerc, Seibl and
  Simon
• Spectrometric Identification of Organic
  Compounds
• Silverstein, Bassler and Morrill
• Spectral Databases
• Aldrich/ACD Library of FT NMR Spectra
• Sadtler/Spectroscopy (UV/Vis, IR, MS, GC and
  NMR)

Ongoing effort to predict chemical shifts from
first principals (quantum mechanical description
of factors contributing to chemical shifts)
47
Predicting Chemical Shift Assignments
Empirical Chemical Shift Trends (Databases) Have
Been Incorporated Into A Variety of Software
Applications

• Example ChemDraw
• Program that allows you to generate a 2D sketch
  of any compound
• can also predict 1H and 13C chemical shifts
• matches sub-fragments of structure to structures
  in database

48
Predicting Chemical Shift Assignments
How Does the Predicted Results Compare to
Experimental Data?
Parameter Experimental ( ppm) Predicted (ppm)
D(A) 6.22 6.44 D(B) 6.53 6.44 D(C)
5.85 5.22
Typical accuracy

• A number of factors can affect prediction
• Similarity of structures in reference database
• Solvent
• Temperature
• structure/conformation
• additive nature of parts towards the whole

49
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.
50
Coupling Constants

• 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
Pascal's triangle
a
b
51
Common NMR Splitting Patterns
Multiplets consist of 2nI 1 lines I is the
nuclear spin quantum number (usually 1/2) and n
is the number of neighboring spins.

• 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.
52
(No Transcript)
53
Karplus Equation Coupling Constants
J const. 10Cosf
Relates coupling constant to Torsional
angle. Used to solve Structures!
54
Nuclear Overhauser Effect (NOE)

1. Interaction between nuclear spins mediated
   through empty space (5Å) ? like ordinary bar
   magnets
2. Important effect is time-averaged
3. Gives rise to dipolar relaxation (T1 and T2) and
   specially to cross-relaxation

Perturb 1H spin population affects 13C spin
population NOE effect
55
Nuclear Overhauser Effect (NOE)
Nuclear Overhauser Effect (NOE, h) the change
in intensity of an NMR resonance when the
transition of another are perturbed, usually by
saturation. Saturation elimination of a
population difference between transitions
(irradiating one transition with a weak RF
field)
hi (I-Io)/Io where Io is thermal
equilibrium intensity
irradiate
N-d
bb
X
A
N
N
ab
ba
X
Nd
A
aa
Observed signals only occur from single-quantum
transitions
Populations and energy levels of a homonuclear AX
system (large chemical shift difference)
56
Nuclear Overhauser Effect (NOE)
Saturated (equal population)
saturate
N-½d
bb
I
S
N-½d
N½d
ab
ba
I
N½d
S
aa
Saturated (equal population)
Observed signals only occur from single-quantum
transitions
Populations and energy levels immediately
following saturation of the S transitions
N-½d
bb
Relaxation back to equilibrium can occur
through Zero-quantum transitions (W0) Single
quantum transitions (W1) Double quantum
transitions (W2)
W1A
W1X
W2
N-½d
N½d
ab
ba
W0
W1X
W1A
aa
N½d
The observed NOE will depend on the rate of
these relaxation pathways
57
Nuclear Overhauser Effect (NOE)

• Mechanism for Relaxation
• Dipolar coupling between nuclei
• local field at one nucleus is due to the
  presence of the other
• depends on orientation of the whole molecule
• Dipolar coupling, T1 and NOE are related through
  rotational correlation time (tc)
• rotational correlation is the time it takes a
  molecule to rotate one radian (360o/2p).
• Relaxation or energy transfers only occurs if
  some frequencies of motion match the frequency of
  the energy of transition
• the available frequencies for a molecule
  undergoing Brownian tumbling depends on tc

NOE is dependent on the distance (1/r6)
separating the two dipole coupled nuclei
Important the effect is time-averaged!
58
2D NOESY (Nuclear Overhauser Effect)
Relative magnitude of the cross-peak is related
to the distance (1/r6) between the protons ( 5?).
NOE is a relaxation factor that builds-up
during The mixing-time (tm)
59
NMR Structure Determination
NOE Data Is the Fundamental Piece of Information
to Determine Any Structure (DNA, RNA, Protein,
small molecule)
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
60
Continuous Wave (CW) vs. Pulse/Fourier Transform
NMR Sensitivity Issue
A frequency sweep (CW) to identify resonance is
very slow (1-10 min.) Step through each
individual frequency.
Pulsed/FT collect all frequencies at once in time
domain, fast (N x 1-10 sec) Increase
signal-to-noise (S/N) by collecting multiple
copies of FID and averaging signal.
S/N r number of scans

61
NMR Data Detection and Processing

• i. NMR Pulse
• In FT-NMR, how are all the individual nuclei
  excited simultaneously?
• 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
62
NMR Pulse
NMR pulse length or Tip angle (tp)
z
z
qt
Mo
tp
x
x
B1
Mxy
y
y
qt g tp B1
The length of time the B1 field is on gt torque
on bulk magnetization (B1)
A measured quantity instrument and sample
dependent.
63
NMR Pulse
Some useful common pulses
z
z
90o pulse
Mo
p / 2
Maximizes signal in x,y-plane where NMR signal
detected
x
x
Mxy
90o
y
y
z
z
180o pulse
Mo
Inverts the spin-population. No NMR signal
detected
p
x
x
-Mo
180o
y
y
Can generate just about any pulse width desired.
64
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
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Correct Spectra
Spectra with carrier offset resulting in peak
folding or aliasing
Sweep Width
(range of radio-frequencies monitored for nuclei
absorptions)
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• iii. Quadrature detection
• a) Frequency of B1 (carrier) is set to the center
  of the spectra.
• Small pulse length to excite the entire spectrum
• Minimizes folded noise
• b) How to differentiate between peaks upfield
  and downfield from carrier?
• 1) observed peak frequencies are all
  relative to the carrier frequency
• c) If carrier is at edge of spectra, then peaks
  are all positive or negative relative to
• carrier
• 1) Excite twice as much noise, decrease S/N

carrier
How to differentiate between magnetization that
precesses clockwise and counter clockwise?
carrier
same frequency relative to the carrier, but
opposite sign.
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PH 0
B
F
B
Use two detectors 90o out of phase.
w (B1)
F
PH 90
PH 0
F
S
Phase of Peaks are different.
PH 90
F
S
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• iv. 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
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Can either increase S/N or
Resolution Not Both!
LB -1.0 Hz
LB 5.0 Hz
Increase Sensitivity
Increase Resolution
FT
FT
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• v. NMR data size
• Analog signal is digitized by periodically
  monitoring the induced current in the receiver
  coil
• How many data points are collected? What is the
  time delay between data points
• c) Digital Resolution (DR) number of Hz per
  point in the FID for a given spectral width.
• DR SW / TD
• where
• SW spectral width (Hz)
• TD data size (points)
• d) Dwell Time (DW) constant time interval
  between data points.
• SW 1 / (2 DW)
• e) From Nyquist Theorem, Sampling Rate (SR)
• SR 1 / (2 SW)
• f) Dependent Valuables

Total Data Acquisition Time (AQ)
AQ TD DW TD/2SWH
Should be long enough to allow complete delay of
FID
Higher Digital Resolution requires longer
acquisition times
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• vi. Zero Filling
• Improve digital resolution by adding zero data
  points at end of FID

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• vii. 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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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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NMR Dynamics and Exchange
Equal Population of Exchange Sites
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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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
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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
78
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. Example 2D NOESY NMR Spectra a) diagonal
peaks are correlated by through-space
dipole-dipole interaction (NOE) b) NOE is a
relaxation factor that builds-up during the
mixing-time (tm) c) relative magnitude of the
cross-peak is related to the distance (1/r6)
between the protons ( 5Å).
Direct (observed) 1H chemical evolves during t2
Diagonal peaks corresponds to 1D NMR spectra
2D NOESY NMR Pulse Sequence
NOE intensity evolves during tm
Indirect (second) 1H chemical evolves during t1
Cross peaks correlate diagonal peaks by
J-coupling or NOEs
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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
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Protein NMR
Detect couplings to NH
How do you assign a protein NMR spectra?
A collection of COSY-like experiments that
sequentially walk down the proteins backbone
3D-NMR experiments that Require 13C and 15N
labeled Protein sample
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Protein NMR
Assignment strategy
We know the primary sequence of the protein.
Correlation of the Cai Cai-1 and Cbi Cbi-1
sequentially aligns each pair of NHs in the
proteins sequence.
Amide Strips from the 3D CBCANH (right) and
CBCA(CO)NH (left) experiment arranged in
sequential order
Connect the overlapping correlation between NMR
experiments
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Protein NMR
Molecular-weight Problem
Higher molecular-weight gt more atoms gt more NMR
resonance overlap
More dramatic NMR spectra deteriorate with
increasing molecular-weight.
MW increases -gt correlation time increases -gt T2
decreases -gt line-width increases
NMR lines broaden to the point of not being
detected! With broad lines, correlations (J,
NOE) become less-efficient
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Protein NMR
How to Solve the Molecular-weight Problem?

• Deuterium label the protein.
• replace 1H with 2H and remove efficient
  relaxation paths
• NMR resonances sharpen
• problem no hydrogens -gt no NOEs -gt no structure
• actually get exchangeable (NH NH) noes can
• augment with specific 1H labeling
• 2) TROSY
• line-width is field dependent