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
NMR History
1937
1946
1953
1966
1975
1985
Rabi predicts and observes nuclear magnetic resonance
Bloch, Purcell first nuclear magnetic resonance of bulk sample
Overhauser NOE (nuclear Overhauser effect)
Ernst, Anderson Fourier transform NMR
Jeener, Ernst 2D NMR
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 > 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)
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.
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.
O
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
MRI images of the Human Brain
O
O
NH
O
O
OH
O
OH
HO
O
O
O
O
O
Taxol (natural product)
NMR Structure of MMP-13
complexed to a ligand
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
Information in a NMR Spectra
Observable
Name
Quantitative
Information
d(ppm) = uobs –uref/uref (Hz)
chemical (electronic)
environment of nucleus
peak separation
(intensity ratios)
neighboring nuclei
(torsion angles)
Peak position
Chemical shifts (d)
Peak Splitting
Coupling Constant (J) Hz
Peak Intensity
Integral
unitless (ratio)
relative height of integral curve
nuclear count (ratio)
T1 dependent
Peak Shape
Line width
Du = 1/pT2
peak half-height
molecular motion
chemical exchange
uncertainty principal
uncertainty in energy
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
Theory of NMR
Quantum Description
Nuclear Spin (think electron spin)
l
a)
Nucleus rotates about its axis (spin)
a)
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
 Odd atomic mass
I = +½ & -½
NMR “inactive” Nuclear Spin (I) = 0:
12C, 16O
 Even atomic mass & number
Quadrupole Nuclei Nuclear Spin (I) > ½:
14N, 2H, 10B
 Even atomic mass & odd number
I = +1, 0 & -1
Magnetic Moment (m)
a)
spinning charged nucleus creates a magnetic field
Magnetic moment
Similar to magnetic field
created by electric current
flowing in a coil
b)
magnetic moment (m) is created along axis of the nuclear spin
m = gp
where:
p – angular momentum
g – gyromagnetic ratio (different value for each type of nucleus)
c)
magnetic moment is quantized (m)
m = I, I-1, I-2, …, -I
for common nuclei of interest:
m = +½ & -½
Magnetic alignment
= g h / 4p
Bo
In the absence of external field,
each nuclei is energetically degenerate
Add a strong external field (Bo).
and the nuclear magnetic moment:
aligns with (low energy)
against (high-energy)
Energy Levels in a Magnetic Field
a)
Zeeman Effect -Magnetic moments are oriented in one of two directions in
magnetic field
b)
Difference in energy between the two states is given by:
DE = g h Bo / 2p
where:
Bo – external magnetic field  units:Tesla (Kg s-2 A-1)
h – Planck’s constant 
6.6260 x 10-34 Js
g – gyromagnetic ratio 
unique value per nucleus
1H:
26.7519 x 107 rad T-1 s2p (observed NMR frequency)
c)
Frequency of absorption:
n = g Bo /
d)
From Boltzmann equation:
Nj/No = exp(-ghBo/2pkT)
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
NMR Theory: Classical Description
Spinning particle precesses around an applied magnetic field
a)
Angular velocity of this motion is given by:
wo = gBo
where the frequency of precession or Larmor frequency is:
n = gBo/2p
Same as quantum mechanical description
Net Magnetization in a Magnetic Field
z
z
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
Mo
x
y
x
y
Bo
Bo
Quantum Description:
- Nuclei either populate low
energy (a, aligned with field)
or high energy (b, aligned
against field)
- Net population in a energy
level.
- Absorption of radiofrequency promotes nuclear
spins from a  b.
b
DE = h n
Bo > 0
a
Bo
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
y
x
y
Bo
Bo
Now What?
Perturbed the spin population or perform spin gymnastics
Basic principal of NMR experiments
The Basic 1D NMR Experiment
Experimental details will effect the NMR spectra and
the corresponding interpretation
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
Mo
B1
w1
z
x
B1 off…
x
Mxy
(or off-resonance)
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
Classical Description
•
Observe NMR Signal

Need to perturb system from equilibrium.


Net magnetization (Mo) now precesses about Bo and B1




B1 field (radio frequency pulse) with gBo/2p frequency
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
Absorption of RF Energy or NMR RF Pulse
z
Classic View:
90o pulse
- 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
--
z
Mo
B1
w1
x
B1 off…
x
Mxy
(or off-resonance)
y
w1 = gB1
precession stops when B1
turned off
y
w1
b
Quantum Description:
- enough RF energy has been
absorbed, such that the
population in a/b are now
equal
- No net magnetization along
the z-axis
DE = h n
a
Bo > 0
Please Note: A whole variety of pulse widths are possible, not quantized dealing
with bulk magnetization
An NMR Experiment
What Happens Next?
The B1 field is turned off and Mxy continues to precess about Bo at frequency wo.
z
x
Mxy
wo
y
Receiver coil (x)
 NMR signal
FID – Free Induction Decay
Mxy is precessing about z-axis in the x-y plane
y
Time (s)
y
y
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.
A magnetic field perpendicular to a circular
loop will induce a current in the loop.
NMR Probe (antenna)
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).
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
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
Peak shape also affected by magnetic field homogeneity or shimming
NMR Relaxation
a)
No spontaneous reemission of photons to relax down to ground state
Probability too low  cube of the frequency
b)
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
Mz = M0(1-exp(-t/T1))
Recycle Delay: General practice is to wait 5xT1 for the system to have fully relaxed.
NMR Relaxation
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
Mx = My = M0 exp(-t/T2)
(derived from Heisenberg uncertainty principal)
Please Note: Line shape is also affected by the magnetic fields homogeneity
NMR Sensitivity
The applied magnetic field causes an energy
difference between aligned(a) and unaligned(b) nuclei
b
Low energy gap
DE = h n
Bo > 0
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
Na / Nb = 1.000064
Very Small !
~64 excess spins per
million in lower state
NMR Sensitivity
NMR signal depends on: signal (s) ~ g4Bo2NB1g(u)/T
1) Number of Nuclei (N) (limited to field homogeneity and filling factor)
2) Gyromagnetic ratio (in practice g3)
3) Inversely to temperature (T)
4) External magnetic field (Bo2/3, in practice, homogeneity)
5) B12 exciting field strength
DE = g h Bo / 2p
Na / Nb = e DE / kT
Increase energy gap -> Increase population difference -> Increase NMR signal
DE
≡
Bo ≡
g - Intrinsic property of nucleus can not be changed.
g
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/gC)3
1H
for 13C is 64x (gH/gN)3 for 15N is 1000x
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
NMR Sensitivity
Increase in Magnet Strength
is a Major Means to Increase
Sensitivity
NMR Sensitivity
But at a significant cost!
~$800,000
~$2,00,000
~$4,500,000
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
Chemical Shift
a)
Small local magnetic fields (Bloc) are generated by electrons as
they circulate nuclei.
• Current in a circular coil generates a magnetic field
b)
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 )
Chemical Shift
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
Chemical Shift
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
The NMR scale (d, ppm)
Bo >> Bloc
-- MHz compared to Hz
Comparing small changes in the context of a large number is cumbersome
d=
w - wref
wref
ppm (parts per million)
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)
CH 3
Tetramethyl silane (TMS) is a common reference chemical
H3C
Si
CH 3
CH 3
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.
NMR Spectra Terminology
TMS
CHCl3
7.27
increasing d
low field
down field
high frequency (u)
de-shielding
Paramagnetic
600 MHz
1H
0
decreasing d
high field
up field
low frequency
high shielding
diamagnetic
150 MHz
13C
ppm
92 MHz
2H
Increasing field (Bo)
Increasing frequency (u)
Increasing g
Increasing energy (E, consistent with UV/IR)
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)
Chemical Shift Trends
Acids
Aldehydes
Alcohols, protons a
to ketones
Aromatics
Amides
Olefins
Aliphatic
ppm
15
C=O in
ketones
10
7
5
Aromatics,
conjugated alkenes
Olefins
2
0
TMS
Aliphatic CH3,
CH2, CH
ppm
210
150
C=O of Acids,
aldehydes, esters
100
80
50
0
TMS
Carbons adjacent to
alcohols, ketones
CHARACTERISTIC PROTON CHEMICAL SHIFTS
Common Chemical Shift Ranges
Carbon chemical shifts have
similar trends, but over a
larger sweep-width range
(0-200 ppm)
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
C=C-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
C=C-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-C=O
2-2.7
Aldehydic
R-(H-)C=O
9-10
Hydroxylic
R-C-OH
1-5.5
Phenolic
Ar-OH
4-12
Enolic
C=C-OH
15-17
Carboxylic
RCOOH
10.5-12
Amino
RNH2
1-5
Coupling Constants
through-bond interaction that results in the splitting of a single peak into multiple
peaks of various intensities
1)
The spacing in hertz (hz) between the peaks is a constant
i. coupling constant (J)
bonding electrons convey spin states of bonded nuclei
1)
spin states of nuclei are “coupled”
2)
alignment of spin states of bonded nuclei affects energy of the
ground (a) and excited states (b) of observed nuclei
3)
Coupling pattern and intensity follows Pascal’s triangle
Coupling Constants
Energy level of a nuclei are affected by covalently-bonded neighbors spin-states
1
H
13
1
1
H
H
three-bond
C
one-bond
Spin-States of covalently-bonded nuclei want to be aligned.
+J/4
I
-J/4
bb
S
ab
J (Hz)
ba
S
+J/4
I
aa
I
S
The magnitude of the separation is called coupling constant (J) and has units
of Hz.
Coupling Constants
1
11
121
1331
14641
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
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.
singlet doublet triplet quartet
1:1
1:2:1 1:3:3:1
pentet
1:4:6:4:1
Coupling Rules:
1. equivalent nuclei do not interact
2.
3.
4.
5.
6.
coupling constants decreases with separation ( typically # 3 bonds)
multiplicity given by number of attached equivalent protons (n+1)
multiple spin systems  multiplicity  (na+1)(nb+1)
Relative peak heights/area follows Pascal’s triangle
Coupling constant are independent of applied field strength
IMPORTANT: Coupling constant pattern allow for the identification of bonded nuclei.
Karplus Equation – Coupling Constants
J = const. + 10Cosf
Relates coupling constant to
Torsional angle.
Used to solve Structures!
Example: The proton NMR spectrum is for a compound of empirical formula C4H8O.
Identify the compound
Absence of peak at ~9.7 ppm
eliminates aldehyde group
And suggests ketone
Triplet at ~1.2 ppm suggests a
methyl group coupled to a
methylene group
Strong singlet at ~2.25 ppm
methyl next to carbonyl
Quartet at ~2.5 ppm suggests
a methylene next to a carbonyl
coupled to a methyl
Nuclear Overhauser Effect (NOE)
a)
b)
c)
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
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.
hi = (I-Io)/Io
where Io is thermal equilibrium intensity
Saturation – elimination of a population difference between transitions
(irradiating one transition with a weak RF field)
irradiate
bb
ab
N
N-d
X
A
ba
X
aa
N+d
N
A
Populations and energy levels of a homonuclear
AX system (large chemical shift difference)
Observed signals only occur
from single-quantum transitions
Nuclear Overhauser Effect (NOE)
Saturated
(equal population)
ab
N-½d
saturate
bb N-½d
I
S
ba
I
aa
N+½d
N+½d
S
Saturated
(equal population)
Observed signals only occur
from single-quantum transitions
Populations and energy levels immediately
following saturation of the S transitions
bb
ab
W1A
N-½d
W1X
N-½d
W2
W0
aa
W1X
N+½d
ba
W1A
Relaxation back to equilibrium can occur through:
Zero-quantum transitions (W0)
Single quantum transitions (W1)
Double quantum transitions (W2)
N+½d
The observed NOE will depend on the “rate” of these relaxation pathways
NMR Instrumentation (block diagram)
Superconducting Magnet
a)
solenoid wound from superconducting niobium/tin or niobium/titanium wire
b)
kept at liquid helium temperature (4K), outer liquid N2 dewar
near zero resistance  minimal current lose  magnet stays at field for
years without external power source
Cross-section of magnet
magnet
spinner
sample lift
NMR Tube
RF coils
cryoshims
shimcoils
Superconducting
solenoid
Use up to 190
miles of wire!
Probe
Liquid N2
Liquid He
Superconducting Magnet
a)
Problems:
Field drifts (B0 changes)
Remember:
Field Drift over 11 Hrs (~ 0.15Hz/hr
Field is not constant over sample (spatial variation)
n = gBo/2p
Lock System
a)
c)
Corrects for magnetic field drift
NMR probes contains an additional transmitter coil tuned to deuterium frequency
changes in the intensity of the reference absorption signal controls a feedback
circuit; a frequency generator provides a fixed reference frequency for the lock
signal
Lock Feedback Circuit
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
Lock Changes From
Off-resonance to Onresonance
Shim System
a)
c)
Corrects for magnetic inhomogeneity
Spatial arrangement of 20 coils
actual shim coils
Sketch of shim coils
change current in each coil to “patch” differences in field and fix distortions in peak shape
Tune and Match System
a)
c)
Tune- corrects the differences between observed and desired frequency
Match – correct impedance difference between resonant circuit and transmission
line (should be 50W )
Adjust two capacitors until the tuning and desired frequency match and you obtain a null
Affects:
signal-to-noise
accuracy of 90o pulse
sample heating
chemical shift accuracy
Receiver Gain
a)
b)
c)
Amplifies the radio frequency FID signal from the probe
Set to maximize signal-to-noise
Signal is dependent on sample concentration
The Analog to Digital Converter (ADC) has a maximum range of integers
Clipped Fid
Clipped FID
Dynamic Range Problem
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)
NMR Pulse
a) In FT-NMR, how are all the individual nuclei excited simultaneously?
b) RF pulses are typically short-duration (msecs)
- produces bandwidth (1/4t) centered around single frequency
- shorter pulse width  broader frequency bandwidth
Heisenberg Uncertainty Principal: Du.Dt ~ 1/2p
A radiofrequency pulse is a
combination of a wave (cosine) of
frequency w o and a step function
*
=
tp
Pulse length (time, tp)
FT
The Fourier transform indicates the
pulse covers a range of frequencies
NMR Pulse
NMR pulse length or Tip angle (tp)
z
Mo
z
x
qt
tp
x
B1
Mxy
y
y
qt = g * tp * B1
The length of time the B1 field is on => torque on bulk magnetization (B1)
A measured quantity – instrument and sample dependent.
NMR Pulse
Some useful common pulses
z
z
90o pulse
Mo
Maximizes signal in x,y-plane
where NMR signal detected
x
p/2
90o
y
x
Mxy
y
z
180o pulse
Inverts the spin-population.
No NMR signal detected
Mo
z
x
y
Can generate just about any pulse width desired.
p
180o
x
y
-Mo
NMR Data Detection and Processing
Fourier Transform NMR
Increase signal-to-noise (S/N) by collecting multiple copies of FID and
averaging signal.
S / N  number of scans
But, total experiment time is proportional to the number of scans
time ~ (number of scans) x (recycle delay)
Proper Spectral Width
Needs to be large enough to capture all the NMR resonances
Correct Spectra
Spectra with carrier offset resulting
in peak folding or aliasing
Sweep Width
(range of radio-frequencies monitored for nuclei absorptions)
Digital Resolution – number of data points
The FID is digitized
Equal delay between points
(dwell time)
DT = 1 / (2 * SW)
Want to maximize digital resolution,
more data points increases acquisition time (AQ) and experimental time (ET):
AQ = DT x NP
ET = AQ x NS
larger spectral width (SW) requires more data points for the same resolution
Digital Resolution – number of data points
Want to maximize digital resolution:
Proper Acquisition Time
Needs to be long enough to allow FID to Completely Decay
Sinc Wiggles
Truncated FID
Zero Filling
Improve digital resolution by adding zero data points at end of FID
8K data
8K FID
No zero-filling
8K zero-fill
16K FID
8K zero-filling
Window Functions
Emphasize the signal or decrease the noise by applying a mathematical function
to the FID.
Good stuff
Mostly noise
Sensitivity
Resolution
F(t) = 1 * e - ( LB * t ) – line broadening
Effectively adds LB in Hz to peak
Line-widths
Can either increase S/N
or
Resolution
Not
Both!
LB = 5.0 Hz
Increase Sensitivity
FT
LB = -1.0 Hz
Increase Resolution
FT
Baseline Correction
Need a flat baseline – prefer to fix experimentally
Apply any number of mathematical functions:
linear
Polynomial (upwards of 6-orders)
FID reconstruction
Penalized parametric smoothing
Etc.
A number of factors lead to baseline distortions:
Intense solvent or buffer peaks
Phasing problems
Errors in first data points of FID
Short recycle tines
Short acquisition times
Receiver gain
Xi & Roche BMC Bioinformatics (2008) 9:234
Phase Correction
Need a flat baseline – phase all peaks to be pure absorptive in shape
Phase is due to difference in actual
time and the zero-time point of FID
(sin + cosines)
Improper phasing can cause severe
distortions in the baseline
Xi & Roche BMC Bioinformatics (2008) 9:234
NMR Peak Integration or Peak Area
a)
The relative peak intensity or peak area is proportional to the number of protons
associated with the observed peak.
b)
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
Exchange Rates and NMR Time Scale
i.
Time Scale
Slow
Intermediate
Fast
Range (Sec-1)
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.
Chem. Shift (d)
k << dA- dB
k = dA - dB
k >> dA - dB
0 – 1000
Coupling Const. (J)
k << JA- JB
k = JA- JB
k >> JA- JB
0 –12
T2 relaxation
k << 1/ T2,A- 1/ T2,B
k = 1/ T2,A- 1/ T2,B
k >> 1/ T2,A- 1/ T2,B
1 - 20
d) For systems in fast exchange, the observed chemical shift is the average
of the individual species chemical shifts.
dobs = f1d1 + f2d2
f1 +f2 =1
where:
f1, f2 – mole fraction of each species
d1,d2 – chemical shift of each species
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
n – peak frequency
e – with exchange
o – no exchange
NMR Dynamics and Exchange
Equal Population of Exchange Sites
No exchange:
With exchange:
W1/ 2 =
1
1

pT2 ptex
k=
1
t ex
slow
k = 0.1 s-1
k = 5 s-1
Increasing Exchange Rate
W1/ 2
1
=
pT2
k = 10 s-1
k = 20 s-1
k = 40 s-1
coalescence
k = 88.8 s-1
k = 200 s-1
k = 400 s-1
k = 800 s-1
fast
k = 10,000 s-1
40 Hz
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-dimensional” 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
Creating Multiple Dimensions in NMR
a) collect a series of FIDS incremented by a second time domain (t1)
b) the normal acquisition time is t2.
c) Fourier transformation occurs for both t1 and t2, creating a twodimensional (2D) NMR spectra
Relative appearance of each
NMR spectra will be modulated
by the t1 delay
Creating Multiple Dimensions in NMR
In 2D NMR spectra, diagonal peaks are normal 1D peaks, off-diagonal or crosspeaks indicate a correlation between the two diagonal peaks
Collections of FIDs
with t1 modulations
Fourier Transform t1
obtain 2D NMR spectra
Fourier Transform t2
obtain series of NMR
spectra modulated by t1
Looking down t1
axis, each point
has characteristics
of time domain FID
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
2D 1H-1H NOESY Experiment
Diagonal peaks are correlated by through-space dipole-dipole interaction (NOE)
Relative magnitude of cross-peak is related to distance (1/R6) between protons (≥ 5Å)
Diagonal peaks corresponds
to 1D NMR spectra
Cross peaks correlate diagonal
peaks by NOEs
2D 1H-13C HSQC Experiment
Correlates all directly bonded 13C-1H pairs
generally requires 13C-labeling (1.1% natural abundance)
2D 1H-1H TOCSY Experiment
Correlates all 3-bonded 1H-1H pairs in a molecules
3D & 4D NMR Spectra
a) additional dimensions usually correspond to 13C & 15N chemical shifts.
b) primarily used for analysis of biomolecular structures
- disperses highly overlapped NMR spectra into 3D & 4D
c) view 3D, 4D experiments as collection of 2D spectra.
d) one experiment may take 2.5 to 4 days to collect.
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