Nuclear Magnetic Resonance (NMR)

1
Nuclear Magnetic Resonance (NMR)
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. One of
the MOST Routinely used Analytical Techniques
2
Common NMR Utility

• Structural (chemical) elucidation
• Natural product chemistry.
• Synthetic organic chemistry. Analytical tool of
  choice of
• synthetic chemists.
• Study of dynamic processes
• Reaction kinetics.
• Study of equilibrium (chemical or structural).
• Structural (three-dimensional) studies
• Proteins.
• DNA. Protein/DNA complexes

3
NMR fingerprint of the compounds chemical
structure
2-phenyl-1,3-dioxep-5-ene
1H NMR spectra
13C NMR spectra
4
Protein Structures from NMR
2D NOESY Spectra at 900 MHz
Lysozyme Ribbon Diagram
5
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)
6
Some Suggested NMR References
Basic One- and Two-Dimensional NMR Spectroscopy
Horst Friebolin Modern NMR Techniques for
Chemistry Research Andrew E. Derome NMR and
Chemistry- an introduction to the fourier
transform-multinuclear era 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 NMR of Proteins
and Nucleic Acids Kurt Wuthrich Tables of
Spectral Data for Structure Determination of
Organic Compounds Pretsch, Clerc, Seibl and
Simon Spectrometric Identification of Organic
Compounds Silverstein, Bassler and Morrill
7
Some NMR Web Sites
The Basics of NMR Hypertext based NMR course
http//www.cis.rit.edu/htbooks/nmr/nmr-main.htm E
ducational 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/
8
Basic NMR Spectrometer
9
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
10
Source of the NMR Signal
From Quantum Theroy Nuclear Spin (Think Electron
Spin) NMR active Nuclear Spin (I) ½ 1H,
13C, 15N, 19F, 31P ? biological and chemical
relevance ? Odd atomic mass 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
11
Zeeman Effect and Nuclear Spin Quantum Number
Zeeman effect splitting of energy levels in
magnetic field
E gBo

• magnetogyric ratio (radians/Tesla) - unique
  value per nucleus
• 
  1H
  26.7519 x 107 rad T-1 s-1
• Bo applied magnetic field -
  unitsTesla (Kg s-2 A-1)

NMR frequency n g Bo / 2p
I hyperfine interaction associate with
magnetization due to nuclear spin quantum
transitions
2I 1 possible energy levels For I 1/2 m -1/2
1/2
m magnetic quantum number
12
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)
13
Another Viewpoint Magnetic Moment (Nuclear Spin)
It is a vector quantity that gives the direction
and magnitude (or strength) of the nuclear
magnet
magnetic moment (m) g I h / 2p
quantized by Plancks constant (h)
By convention spin 1/2 gt a - low energy
state spin -1/2 gt b
Analogous to current moving in a loop which
induces a magnetic field (right-hand rule)
14
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
15
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
16
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 !!
17
NMR Sensitivity
Increase in Magnet Strength is a Major Means to
Increase Sensitivity But at a significant cost!
2,00,000
4,500,000
800,000
18
NMR Frequency Range (expensive radios)
g-rays x-rays UV VIS IR m-wave
radio
10-10 10-8 10-6 10-4 10-2
100 102
wavelength (cm)
DE h n n g Bo / 2p DE g
h Bo / 2p
For 1H in normal magnets (2.35 - 18.6 T), this
frequency is in the 100-800 MHz range.
19
Classical View of NMR (compared to Quantum view)
w 2pn ? wo g Bo (radians)
Precession or Larmor frequency
angular momentum (l)
l
wo
m
Bo
Simply, the nuclei spins about its axis creating
a magnetic moment m
Apply a large external field (Bo) and m will
precess about Bo at its Larmor (w) frequency.
Maxwell Magnetic field Moving charge

Important This is the same frequency obtained
from the energy transition between quantum states
20
Bulk magnetization (Mo)
Now consider a real sample containing numerous
nuclear spins
Mo (Na - Nb)
m mxi myj mzk
z
z
Mo
x
x
y
y
Bo
Bo
Since m is precessing in the xy-plane, Mo ? mzk
m-zk
m is quantized (a or b), Mo has a continuous
number of states, bulk property.
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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
To perturbed the spin population need the system
to absorb energy.
z
Mo
x
B1
Bo
y
i
Transmitter coil (y)
Two ways to look at the situation (1) quantum
absorb energy equal to difference in spin
states (2) classical - perturb Mo from an
excited field B1
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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
24
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
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.
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NMR Signal Detection - FID
Mxy is precessing about z-axis in the x-y plane
Time (s)
y
y
y
The FID reflects the change in the magnitude of
Mxy as the signal is changing relative to the
receiver along the y-axis
Again, it is precessing at its Larmor Frequency
(wo).
26
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
27
Laboratory Frame vs. Rotating Frame
To simplify analysis we convert to the rotating
frame.
z
z
x
x
Mxy
Mxy
wo
Bo
y
y
Laboratory Frame
Rotating Frame
Simply, our axis now rotates at the Larmor
Freguency (wo). In the absent of any other
factors, Mxy will stay on the x-axis
All further analysis will use the rotating frame.
28
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
29
Chemical Shift
Again, consider Maxwells theorem that an
electric current in a loop generates a magnetic
field. Effectively, the electron distribution
in the chemical will cause distinct local
magnetic fields that will either add to or
subtract from Bo
HO-CH2-CH3
Beff Bo( 1 - s )
de-shielding
high shielding
Shielding local field opposes Bo
Aromaticity, electronegativity and similar
factors will contribute to chemical shift
differences
30
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
31
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

Alcohols, protons a to ketones
Aromatics Amides
Acids Aldehydes
Aliphatic
Olefins
ppm
0 TMS
2
10
7
5
15
33

• Chemical Shift Trends
• For carbon, 220 ppm

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
34
Predicting Chemical Shift Assignments

• Numerous Experimental NMR Data has been compiled
  and general trends identified
• Examples in Handout
• See also
• 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)

35
Predicting Chemical Shift Assignments
Predict the chemical shifts of Benzene
Shift NO2 effect NH2 effect Total Change sign
since table lists as downfield shift
da 7.27 0.95 -0.75 7.47 ppm dd 7.27 0.33 -0.
75 6.85 ppm dc 7.27 0.17 -0.24 7.20
ppm db 7.27 0.95 -0.63 7.59 ppm From table
3-6-1 in handout Substituent Shift relative to
benzene (ppm) ortho meta para NO2 -0.95 -0.17
-0.33 NH2 0.75 0.24 0.63
36
Predicting Chemical Shift Assignments
Predict the chemical shifts of
Cb C C C C C
C a 2 a b g d

• Chemical shift is determined by sum of carbon
  types.
• From Table 3.2 in handout
• Bs ? DmAsm gSN3 DsN4 - empirical formula
• S number of directly bonded carbons
• Dm number of directly bonded carbons having M
  attached carbons
• Np number of carbons P bonds away
• d2 B2 1xA23 1xA21 1xg2 1xD2
• d2 15.34 1X16.70 1x0 1x-2.69 1x0.25
  29.60 ppm

37
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.
38
Coupling Constants
IMPORTANT Coupling constant pattern allow for
the identification of bonded nuclei.
Multiplets consist of 2nI 1 lines I is the
nuclear spin quantum number (usually 1/2) and n
is the number of neighboring spins. The ratios
between the signal intensities within multiplets
are governed by the numbers of Pascals triangle.
Configuration Peak Ratios
A 1
AX 11
AX2 121
AX3 1331
AX4 14641

39
Coupling Constants
40
NMR Relaxation
After the B1 field (pulse) is removed the system
needs to relax back to equilibrium
Mz M0(1-exp(-t/T1))
T1 is the spin-lattice (or longitudinal)
relaxation time constant.
Think of T1 as bulk energy/magnetization exchange
with the solvent.
Please Note General practice is to wait 5xT1 for
the system to have fully relaxed.
41
NMR Relaxation
Related to line-shape
Mx My M0 exp(-t/T2)
(derived from Hisenberg uncertainty principal)
T2 is the spin-spin (or transverse) relaxation
time constant. In general T1 T2
Think of T2 as the randomization of spins in
the x,y-plane
Please Note Line shape is also affected by the
magnetic fields homogeneity
42
NMR Time Scale
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
NMR time-scale refers to the chemical shift
timescale.
43
Exchange Rates from NMR Data
dobs f1d1 f2d2 f1 f2 1
k p Dno2 /2(he - ho)
k p Dno / 21/2
k p (Dno2 -  Dne2)1/2/21/2
k p (he-ho)

• h peak-width at half-height
• peak frequency
• e with exchange
• o no exchange
• f mole fraction
• d chemical shift

44
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

45
NMR Pulse
A radiofrequency pulse is a combination of a wave
(cosine) of frequency wo and a step function


tp
Pulse length (time, tp)
The fourier transform indicates the pulse covers
a range of frequencies
FT
Hisenberg Uncertainty principal again Du.Dt
1/2p Shorter pulse length larger frequency
envelope Longer pulse length selective/smaller
frequency envelope
Sweep Width f 1/t
46
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 dependent.
47
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.
48
NMR Data Acquisition
Collect Digital Data ADC analog to digital
converter
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
49
Quadrature detection
carrier

• Frequency of B1 (carrier) is set to center of the
  spectra.
• small pulse length to excite entire spectrum
• minimizes folded noise

carrier
If carrier is at edge of spectra, then peaks are
all positive or negative relative to carrier.
But excite twice as much including noise
How to differentiate between peaks upfield and
downfield from carrier?
50
Quadrature detection
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
51
Receiver Gain
The NMR-signal received from the resonant circuit
in the probehead needs to be amplified to a
certain level before it can be handled by the
computer.
The detected NMR-signals vary over a great range
due to differences in the inherent sensitivity of
the nucleus and the concentration of the sample.
52
Data Processing Window Functions
The NMR signal Mxy is decaying by T2 as the FID
is collected.
Good stuff
Mostly noise
Resolution
Sensitivity
Emphasize the signal and decrease the noise by
applying a mathematical function to the FID
F(t) 1 e - ( LB t ) line broadening
Effectively adds LB in Hz to peak Line-widths
53
Can either increase S/N or
Resolution Not Both!
LB -1.0 Hz
LB 5.0 Hz
Increase Sensitivity
Increase Resolution
FT
FT
54
NMR Data size
A Number of Interdependent Values (calculated
automatically)
digital resolution (DR) as the number of Hz per
point in the FID for a given spectral width. DR
SW / SI SW - spectral width (Hz) SI - data
size (points) Remember SR 1 / (2 SW) Also
SW 1/2DW
Total Data Acquisition Time
AQ TD DW TD/2SWH
Should be long enough to allow complete delay of
FID
Higher Digital Resolution requires longer
acquisition times
55
Zero Filling
Improve digital resolution by adding zero data
points at end of FID
8K data
8K zero-fill
8K FID
16K FID
No zero-filling
8K zero-filling
56
MultiDimensional NMR
Up to now, we have been talking about the basic
or 1D NMR experiments
1D NMR
More complex NMR experiments will use multiple
time-dimensions to obtain data and simplify the
analysis. In a 1D NMR experiment the FID
acquisition time is the time domain (t1)
Multidimensional NMR experiments may also
observe multiple nuclei (13C,15N) in addition to
1H. But usually detect 1H.
57
MultiDimensional NMR
2D COSY (Correlated SpectroscopY) Correlate
J-coupled NMR resonances
A series of FIDs are collected where the delay
between 90o pulses (t1) is incremented. t2 is
the normal acquisition time.
58
MultiDimensional NMR
During the t1 time period, peak intensities are
modulated at a frequency corresponding to the
chemical shift of its coupled partner.
Solid line connects diagonal peaks (normal 1D
spectra). The off-diagonal or cross-peaks
indicate a correlation between the two diagonal
peaks J-coupled.
59
Karplus Equation Coupling Constants
J const. 10Cosf
Relates coupling constant to Torsional
angle. Used to solve Structures!
60
Karplus Equation Coupling Constants
For Protein Backbones
61
Nuclear Overhauser Effect (NOE)
Interaction between nuclear spins mediated
through empty space (5A) (like ordinary bar
magnets). Important Effect is
Time-Averaged! Give rise to dipolar relaxation
(T1 and T2) and specially to cross-relaxation and
the NOE effect.
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
62
DEPT Experiment Distortionless Enhancement by
Polarization Transfer
13C spectra is perturbed based On the number of
attached 1H Takes advantage of
different patterns of polarization
transfer 1H-13C NOE
63
2D NOESY (Nuclear Overhauser Effect)
Diagonal peaks are correlated by
through-space Dipole-dipole interaction. NOE is
a relaxation factor that builds-up during The
mixing-time (tm) The relative magnitude of the
cross-peak is Related to the distance (1/r6)
between the Protons ( 5A). Basis for solving
a Structure!
64
Protein NMR
Number of atoms in a protein makes NMR spectra
complex
Resonance overlap
Isotope label protein with 13C and 15N and spread
spectra out in 3D and 4D
65
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
66
Protein NMR
Assignment strategy
We know the primary sequence of the protein.
Connect the overlapping correlation between NMR
experiments
67
(No Transcript)
68
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
69
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