Nuclear Magnetic Resonance (NMR)
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
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.) Metabolomics
5.) Drug Design
 Structure Activity Relationships by NMR
6.) 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
NMR History
1937
1946
1953
1966
1975
1984
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
Nicholson NMR metabolomics
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 residual dipolar couplings (RDC) from partial alignment in
liquid crystalline media
TROSY (molecular weight > 100 kDa)
2000s Dynamic nuclear polarisation (DNP) to enhance NMR sensitivity
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.
Bloch Equations
Net Magnetization (M) placed in a magnetic Field (B) will precess:
and relax (R)
and relax individual components:
Course Goals
• We will NOT Cover a Detailed Analysis of NMR Theory
• We will NOT Derive the Bloch Equations
• We will NOT Discuss, in detail, a Quantum Mechanical Description of
NMR
• We will NOT use Product Operator Formulism to Describe NMR
Experiments
• If Interested, Dr. Harbison will Cover These Topics in a Separate
Special Topics Course
• We Will Discuss Practical Aspects of Using an NMR
• We Will Take a Conceptual Approach to Understanding NMR
• A Focus of the Course will be the Application of NMR to Solving the
Structure of Organic Molecules
• We Will Discuss the Basic Operations of an NMR Spectrometer.
• We Will Discuss the Proper Approaches to the Set-up, Process and
Analysis of NMR Experiments
• We Will Use NMR to Solve the Structure of Unknowns
• The Goal is to Not Treat an NMR Spectrometer as a Black
Box, but to be a Competent Experimentalist
Course Goals
To Be Able to Go From This:
To This:
N-(2-Fluoroethyl)-1-((6-methoxy-5-methylpyrimidin-4-yl)methyl)-1H-pyrrolo[3,2b]pyridine-3-carboxamide (9) MS (ES+) m/z: 344. 1H NMR (300 MHz, DMSO-d6): δ 2.24 (s,
3H), 3.67 (d, J = 5.46 Hz, 1H), 3.76 (d, J = 5.46 Hz, 1H), 3.93 (s, 3H), 4.50 (t, J = 4.99 Hz, 1H),
4.66 (t, J = 4.99 Hz, 1H), 5.69 (s, 2H), 7.26 (dd, J = 8.29, 4.71 Hz, 1H), 7.94 (d, J = 8.52 Hz,
1H), 8.28 (s, 1H), 8.41 (s, 1H), 8.49 (d, J = 4.57 Hz, 1H), 8.95 (s, J = 5.89, 5.89 Hz, 1H).
HRMS (M + H) calcd for C17H18FN5O2, 344.1517; found, 344.15242.
And Understand How to Read and Interpret the NMR Spectral Data
Course Goals
To Be Able to Go From This:
To This:
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
Magnets Attract and Align
A Basic Concept in ElectroMagnetic Theory
A Direct Application to NMR
A moving 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
A Basic Concept in ElectroMagnetic Theory
For a single loop of wire, the magnetic field, B
through the center of the loop is:
B
mo I
2R
mo – permeability of free space (4p x 10-7 T · m / A)
R – radius of the wire loop
I – current
A Basic Concept in ElectroMagnetic Theory
Faraday’s Law of Induction
• If the magnetic flux (FB) through an area bounded by
a closed conducting loop changes with time, a current
and an emf are produced in the loop. This process is
called induction.
• The induced emf is:
dF B
 
dt
Simple AC generator
A Basic Concept in ElectroMagnetic Theory
Lenz’s Law
• An induced current has a direction such that the magnetic field of
the current opposes the change in the magnetic flux that produces
the current.
• The induced emf has the same direction as the induced current
Direction of current
follows motion of magnet
Theory of NMR
Quantum Description
Nuclear Spin (think electron spin)
•
Nucleus rotates about its axis (spin)
•
Nuclei with spin have angular momentum (p) or spin
1) total magnitude
 I ( I  1)
l
1) quantized, spin quantum number I
2) 2I + 1 states:
I=1/2:
I, I-1, I-2, …, -I
-1/2, 1/2
3) identical energies in absence of external magnetic field
NMR Periodic Table
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) > ½:
14N, 2H, 10B
Even atomic mass & odd number
I = +1, 0 & -1
Magnetic Moment (m)
•
spinning charged nucleus creates a magnetic field
Magnetic moment
Similar to magnetic field
created by electric current
flowing in a coil
“Right Hand Rule”
• determines the direction of the magnetic field around a currentcarrying wire and vice-versa
Gyromagnetic ratio (g)
•
related to the relative sensitive of the NMR signal
•
magnetic moment (m) is created along axis of the nuclear spin
m g p
g 
2p m m

h I I
where:
p – angular momentum
g – gyromagnetic ratio (different value for each type of nucleus)
•
magnetic moment is quantized (m)
m = I, I-1, I-2, …, -I
for common nuclei of interest:
m = +½ & -½
Gyromagnetic ratio (g)
•
magnetic moment is quantized (m)
m = I, I-1, I-2, …, -I
for common nuclei of interest:
m = +½ & -½
Isotope
Net Spin
g / MHz T-1
Abundance / %
1H
1/2
42.58
99.98
2H
1
6.54
0.015
3H
1/2
45.41
0.0
31P
1/2
17.25
100.0
23Na
3/2
11.27
100.0
14N
1
3.08
99.63
15N
1/2
4.31
0.37
13C
1/2
10.71
1.108
19F
1/2
40.08
100.0
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)
Spins Orientation in a Magnetic Field (Energy Levels)
•
Magnetic moment are no longer equivalent
•
Magnetic moments are oriented in 2I + 1 directions in magnetic field

Vector length is:

Angle (j) given by:

Energy given by:
 I ( I  1)
cosj 
E
m
I ( I  1)
mm
Bo
I
where,
Bo – magnetic Field
m – magnetic moment
h – Planck’s constant
For I = 1/2
Spins Orientation in a Magnetic Field (Energy Levels)
•
The energy levels are more complicated for I >1/2
Spins Orientation in a Magnetic Field (Energy Levels)
•
Magnetic moments are oriented in one of two directions in magnetic field (for I =1/2)
•
Difference in energy between the two states is given by:
DE = g h Bo / 2p
where:
Bo – external magnetic field
h – Planck’s constant
g – gyromagnetic ratio
Spins Orientation in a Magnetic Field (Energy Levels)
•
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 Signal (sensitivity)
•
The applied magnetic field causes an energy difference between the
aligned (a) and unaligned (b) nuclei
•
NMR signal results from the transition of spins from the a to b state
•
Strength of the signal depends on the population difference between the a
and b spin states
b
DE = h n
Bo > 0
Bo = 0
•
Low energy gap
a
The population (N) difference can be determined from the Boltzmann
distribution and the energy separation between the a and b spin states:
Na / Nb = e DE / kT
NMR Signal (sensitivity)
Since:
DE = hn
and
n = g Bo / 2p
then:
Na / Nb = e DE / kT
Na/Nb = e(ghBo/2pkT)
The DE for 1H at 400 MHz (Bo = 9.39 T) is 6 x 10-5 Kcal / mol
Na / Nb  1.000060
Very Small !
~60 excess spins per
million in lower state
NMR Sensitivity
NMR signal (s) depends on: 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 (RF pulse)
DE  g h Bo / 2p
Na / Nb = e DE / kT
Increase energy gap -> Increase population difference -> Increase NMR signal
DE
≡
Bo ≡
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
is ~ 64x as sensitive as
13C
15N
is 1000x
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
NMR Sensitivity
An Increase in concentration is a very
common approach to increase sensitivity
30 mg
1.2 mg
http://web.uvic.ca/~pmarrs/chem363/nmr%20files/363%20nmr%20signal%20to%20noise.pdf
NMR Sensitivity
But, this can lead to concentration dependent changes in the NMR spectra
(chemical shift & line-shape) resulting from compound property changes
Dimerization as
concentration increases
from 0.4 to 50 mM
Beilstein J. Org. Chem. 2010, 6, No. 3.
H-bond and multimer
formation as concentration
increases from 1 to 30 mM
Beilstein J. Org. Chem. 2010, 6, 960–965.
NMR Sensitivity
An Increase in the number of scans (NS) or signal-averaging is the most
common approach to increase sensitivity (signal-to-noise (S/N)
S/N ≈ NS1/2
NMR Sensitivity
But, it takes significantly longer to acquire the spectrum as the number
of scans increase:
Experimental Time = Number of Scans x Acquisition Time
8 scans ~12 secs
10,000 scans ~4.2 hours
NMR Sensitivity
Lowering the temperature is usually not an effective means of increasing
sensitivity because of chemical shift changes and peak broadening
Significant chemical shift changes
Significant peak broadening
Dalton Trans.,2014, 43, 3601-3611
Theory of NMR
Classical Description
•
Spinning particle precesses around an applied magnetic field
A Spinning Gyroscope
in a Gravity Field
cosj 
m
I ( I  1)
Classical Description
•
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
Classical Description
•
Net Magnetization


Nuclei either align with or against external magnetic field along the z-axis.
Since more nuclei align with field, net magnetization (Mo, MZ) exists parallel
to external magnetic field.

Net Magnetization along +Z, since higher population aligned with Bo.

Magnetization in X,Y plane (MX,MY) averages to zero.
z
z
Mo
x
y
Bo
y
Bo
x
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.



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
Classical Description
•
Rotating Frame


To simplify the vector description, the X,Y axis rotates about the Z axis at
the Larmor frequency (X’,Y’)
B1 is stationary in the rotating frame
Mz
+
Mxy
Classical Description
•
NMR Pulse

Applying the B1 field for a specified duration (Pulse length or width)

Net Magnetization precesses about B1 a defined angle (90o, 180o, etc)
z
z
90o pulse
Mo
B1
w1
x
B1 off…
x
Mxy
(or off-resonance)
y
w1 = gB1
y
w1
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
Absorption of RF Energy or NMR RF Pulse
A whole variety of pulse
widths are possible, not
quantized dealing with
bulk magnetization
90o
60o
Signal intensity decreases
significantly when not at
optimal 90o pulse length
35o
20o
10o
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
Classical Description
•
Observe NMR Signal
Remember: a moving magnetic field perpendicular to a coil will induce a
current in the coil.

The induced current monitors the nuclear precession in the X,Y plane

X
y
Detect signal along X
RF pulse along Y
n = gBo/2p
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 - FID
The appearance of the FID depends on how the frequency
of the signal differs from the Larmor Frequency
Larmor Frequency
Time Domain
Frequency Domain
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)
NMR signal relaxes back to ground state through two distinct processes
NMR Relaxation
c)
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
c) Spin-Lattice or Longitudinal Relaxation (T1)
i. Commonly measure T1 with an inversion recovery pulse sequence
5xT1 fully relaxed
NMR Relaxation
d) 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
Mx = My = M0 exp(-t/T2)
NMR Relaxation
d) spin-spin or transverse relaxation (T2)
iii. related to NMR peak line-width
(derived from Heisenberg uncertainty principal)
Please Note: Line shape is also affected by the magnetic fields homogeneity
NMR Relaxation
d) spin-spin or transverse relaxation (T2)
iii. Usually measured with a Carr-Purcell-Meiboom-Gill (CPMG) Pulse sequence
NMR Relaxation
d) Another way to look at T1 and T2
i. T2 is the time it takes a stove to heat a house and T1 is the time it takes for the
heat to be lost to the surrounding environment
ii. If the house is insulated, T1 will be larger than T2
NMR Relaxation
d) One more way to look at T1 and T2
i. Relaxation of 13C occurs through two distinct interactions
ii. Magnetic fields produced by the 1H magnetic dipoles are felt by the 13C spin
•
These magnetic fields are modulated by random Brownian motions
(rotational, translational)
iii. Relaxation between 13C and 1H in same molecule - intramolecular relaxation (T2)
iv. Relaxation between 13C and 1H from solvent- intermolecular relaxation (T1)