Nuclear Magnetic Resonance
-an analytical tool in Physical ChemistryTodays lecture
•Physical underpinnings to NMR
•Integration and quantitative aspects
•The Chemical Shift
•The interplay of kinetic and equilibria phenomena in NMR
measurements.
•The investigation of an equilibrium behavior in the
Physical Chemistry Lab. Before class/lab, read and
understand the lab writeup for the NMR experiment.
Background Reading
Go to the link below:
http://astro.temple.edu/%7Edebrosse/
Here, read specifically:
•the UserGuide for the Inova300
•Guide to moving NMR data to PCs
•UserGuide for NUTS, the offline NMR data processing
software
Also read:
•The PChem lab writeup “NMRPchemLab.doc”
What is NMR Spectroscopy?
• Nuclear Magnetic Resonance
• Radio Frequency Absorption Spectra of atomic nuclei in
substances subjected to magnetic fields.
• Spectral Dispersion is Sensitive to the chemical
environment via “coupling” to the electrons surrounding
the nuclei.
• Interactions can be interpreted in terms of structure,
bonding, reactivity
NMR-What is it Good For?
(absolutely everything!)
• Solving structures of compounds like synthetics, impurities, natural
Based on what
products
you know from
• Identifying metabolites
sophomore
• Stereochemical determination
• Follow reactions
organic, you
• Validating electronic theory; trends within series of compds.
would think that
• Kinetics
NMR is really
• Extended structure, e.g. protein nmr
just for
• Molecular interactions e.g. ligand binding
fingerprinting
• Acid-base questions
organic
• Purities
structures, and
• Mechanisms, e.g. isotope distributions, other effects
determining
• Questions about the solid state
their structures!
• Imaging
• Todays’s focus, NMR as an Analytical Tool for quantifying mixtures
What are the Measurables in
NMR?
• Intensity (analytical parameter, proportional
to molarity)
• Chemical Shift (the electronic
surroundings)
• Couplings (scalar J and dipolar D; bond
paths, angles connectivity and distances)
• Relaxation parameters (motions, distances)
Origin of the NMR Effect
• Nuclei with other than A(#protons+neutrons) and Z(#protons) both even
numbers, possess net spin and associated angular momenta
• Reveals itself only in magnetic field. As usual, such momenta are
quantized
• States have different energies, populated according to Boltzmann
distribution
• States are 1/2, 3/2, 5/2…for A= odd number and integer if A= even
number and Z= odd number
• Transitions of individual nuclei between spin states is possible (both
directions) leading to an equilibrium of populations
• Number of states is 2I + 1
• Many elements have NMR active nuclei.
• Those elements like 1H, 13C, 31P, 19F are the most popular and accessible
because they have spin I = 1/2, and this makes their NMR signals narrow
and relatively easy to measure and interpret.
Why NMR?
•
•
•
•
•
•
Unmatched versatility as an Analytical technique
High on chemical information content
Significant interpretability
Interpretable at several levels of sophistication
Response related to molar preponderance
These attributes are true for solids, liquids,
mixtures, and to a small extent, gas phase
• More than half the periodic table has at least one
NMR active isotope
But on the other Hand…
• NMR is one of the least sensitive analytical methods
• Characterized by long relaxation time constants, limiting
experimental efficiency in real time
• Sometimes too much information. Can be demanding on
interpretation skill
• Relatively Expensive compared with other analytical
methods
• As with other methods NMR has “blind spots” and cannot
serve as an analytical panacea
The Chemical Shift
• The Chemical shift makes NMR useful in Chemistry (they
named it after us)
• Arises from the electrons surrounding our nuclei, responding to
a magnetic field.
• Induced circulation of electrons, Lenz’s law; this circulation
generates a small magnetic field opposed to H0
• The small negative field diminishes the H0 experienced by a
nucleus. This differentiates sites, based on chemical nature
• Effect grows directly proportional to H0
A Picture of this…
How many signals do we Expect
in an NMR Spectrum?
• The Chemical shift implies that we see
(potentially) a different signal for every different
chemical environment.
• Chemical environment here is the electronic
structure (electrons, hybridization, charge,
polarizability etc.) These are all things able to be
predicted to some extent by theory.
• What do we mean by “different”? (hint;
symmetry is key!)
Consider the Molecule of Interest
for this Investigation…
OH
CH3
O
O
N
H
H
H
H
H
H
H
Because of the
asymmetric carbon
center at H, the
other ring H are
potentially all at
different shifts (each
is either on same, or
opposite face from
H)
A Vector Picture
Chemical shift is the ultimate
precessional frequency of the vector
component of M in the plane
perpendicular to H0
H0(Z)
This is in units of
(radians)/sec
At some time, has
distinct angle and
as a vector in x,y
can be resolved
into x, y
components.
H0(Z)
t
t
X
Y
Precesses at a
frequency 
X
After a
pulse…
Y
The receiver works
by counting how
many times this
electric vector
whizzes past in a
unit of time
Free Precession, Rotating Frames
and the Chemical Shift
•Our vector picture can help
Now, more than one chemical shift
wil move with just a difference
from H0
Rotates at H0 MHz
Stands Still!
What if we could contrive to measure
once every H0 seconds? Strobe effect
Is The Rotating Frame
Don’t have to distinguish
25000002 from 25000005
Hz, but 2 cf. 5
Imagine a “blinking eyeball”, (strobe effect) blinks at Larmor frequency……
“Practical” Theory
• The real triumph of the shift theory is in its
relationship to electronegativity and hybridization
and easy prediction of trends based on qualitative
notions from structural theory.
• Withdrawing electron density diminishes the
screening ability of the electron cloud and the
absorbance of the nucleus goes to lower field.
• Feeding in electron density sends nucleus to
higher field.
• “Moving” electrons have some real consequences
on nearby chemical shifts.
Anisotropic Shielding Near  Electrons
Cir culat ing Electr on Cloud responding to0 H
I ncr eases t he t otal
H f ield felt at H by ca.
1.5 ppm
De s hi e ldi n g Re gi on
S h ie l din g Re gion
I nduced Curr ent
I nduced Magnet ic Field
Pronounced effect for aromatic,
in line with e circulation
Applied H 0Field
Other Anisotropic Shielding
Cones
Nitriles, acetylenes
Above, below plane
shielded
+
isonitriles
+
+
In plane
deshielded
+
+
+
+
Carbonyl, alkene
C
+
+
• Effects are ca. 2 ppm at most.
Small pos
+
O
Polarized effect
• Most Significant when a nucleus is
fixed in geometry with respect to the
neighboring field.
Best description is in
L.M. Jackman, S. Sternhell, Applications of Nuclear
Magnetic Resonance Spectroscopy in Organic
Chemistry, Pergamon Press, (1969) ch.2
+
+
This chemical shift anisotropy is the
basis for the separation, and the
direction of the separation of signals
in the Lab exercise on acetylproline
Predict that the H signals for the  protons will move
to higher shift values when the C=O is pointed at them,
compared with the other form
H
amide bond
N
O
O
CHR
"cis"
H
OH
N
RCH
O
O
"trans"
OH
Important
point: one
would have to
identify which
signals these are
in the spectrum
What are “Spin Systems”?
A network of protons of which the members are
mutually J-coupled to some (not necessarily all) of the
nearby protons, via contiguous bonds.
H
CH2 OH
H
O
H
O
H
OH
H
H
OH
H
H
H
H
O
H
H
S
OCH3
H
OH
OH
OH
O
OH
H
Breaks up the
pathway
H
H
How Do these Various Features
show up in an NMR Spectrum?
OH
O
H
H
H
CH3
N
Every different hydrogen in the
molecule has (or is entitled to have)
its own chemical shift value
O
H
H
The amount of this value is reflective
of the chemical influence of nearby
heteroatoms, electron deficency etc.
The signals have extra splitting
superimposed on them. This is
coupling, caused by the neighboring
Hs. Helps identify which H is which.
H H
Solvent
(CD3OD)
The red trace is called the integration
(area under the curve). The amount
of rise is proportional to the number
of H that cause that particular signal.
Chemical shift scale is x-axis. Units
are Hz(shift)/Hz(spectrometer) and
therefore ppm and dimensionless
Integration of Signal areas in
NMR
Integration as the area under a curve
Units are arbitrary, as the user defines the area scale.
The real units would be mV x Hz but these numerically are
unwieldy.
Areas are taken relative to each other. Generally a recognized
signal known to arise from one 1H is defined as 1.00. Can also
add a weighed amount of an internal reference compound; assign
an area to one of its signals, and compare the other signals to the
reference.
Integrating Spectra
Inegral trails
Area is given by the rise
between the two level lines.
Here we have used the
software to reset the integral
baseline between the two
signals
Signals
Then, we use the software
scale setting tool to define the
peak at 8 ppm to be 3 units
(H). The value for the other
signal is then normalized and
scaled so we know it is about
1% bigger.
Repeated
measurements
can give us the
precision (rsd)
More on Integration
Areas are proportional to molar ratios. Within a compound, if one
signal is 3x another the signals represent atom counts of 1:3, e.g a
CH, CH3. For mixtures, if we compare ratios of areas, these are
the molar ratios
Can convert to wgt% by multiplying by MW
Must compare signals from same number of Hs or normalize to
correct.
Example Say we have a mixture and want to quantify two
components by NMR. If we compare a CH3 group from compound
A with a CH2 group from compound B, the comparison is not
appropriate. (unless we know that those two signals are CH3 and
CH2, and divide the areas by 3, and 2 respectively before making
the comparison.)
NMR of Mixtures
•Potentially all the hydrogen atoms are equal to each other as
“chromophores”
•Compare with the situation of an HPLC analysis detected by
means of a UV monitored flow-cell (monitoring a given
wavelength). To interpret the areas of the HPLC peaks, one has
to either know the response factors for all the compounds at that
wavelength, (measure in a separate experiment) or assume that
the responses are all identical on a molar basis (dubious at
times).
•NMR is good for mixture analysis also because you see
everything that has hydrogen atoms. If you can locate signals
that are not overlapped among the ingredients in the mixture,
you can integrate, and obtain ratios of the molar amounts
present.
Practical Consequences of
Relaxation times for Quantitative
Interpretation
Time constant
that limits the
repeat rate for
NMR scans.
Real concern in
comparing
disparate
molecular sizes.
Solvents vs.
moderate size
organics,
common example
A Recent Example from the
Chem 314 Lab
Plots are for
varying the
delay time
between
successive
pulses.
35
30
Ibuprofen NMR Intensity
Data is the
integrated
intensity of
NMR signals
from Ibuprofen
vs an internal std
of methylene
chloride.
25 second delay
10secf ixup
5sec delay
25
20
15
10
5
0
100
200
300
400
500
600
700
mg Added Ibuprofen
800
900
Mixtures at equilibrium
A B
Keq 
C
C  ;
AB
where thebrackectedlettersrepresentthe molar
concentrations of thereactingspecies.
The NMR spectrum would likely show peaks from compound A,
compound B and compound C. Some of these peaks could be
overlapped.
The proportions of these peaks for A, B, C would be related to how
much the scientist put in the sample, and on the value of Keq
The Mixture of Interest Here
OH
Every hydrogen in the
compound gives a potentially
different signal for the cis,
and trans forms.
For these, we can see and
integrate the areas for the two
forms as major, minor
components.
H
H
O
H
H
H
(Solvent)
Acetyl
CH3
CH3
O
N
H
H
H H
Note here that
the H, H
happen to
overlap. We
cannot
conveniently
integrate these
separately, or
evaluate the
major/minor
ratio
A Closer look at
the fine
structure…
An Expansion of
the NMR spectrum
for the H region.
Each of the
compounds two
forms shows its
own  hydrogen at
a separate
chemical shift.
The individual
peaks within
these clusters
are the fine
structure due to
couplings to
nearby H’s
Assessing Equilibria
The integrated areas, normalized for the number of
contributing signals, can be taken as proportional to the
molarity.
All the components are in the same volume of solution.
To use the example for this lab exercise:
cis
trans

trans
Keq 
cis
There are only two
“compounds” in the mixture.
Conc of each is proportional to
int. area for each, normalized.
Energies and dipole moments of NAcProline Conformers
From ab initio (density functional at B3LYP/6-31G level of theory) calculations
6.36 debyes
-553.8249 h
6.02 debyes
-553.8072 h
5.74 debyes
-553.5800 h
3.03 debyes
-553.8136 h
Systems Approaching Chemical Equilibrium
A Collorary:
Get time
distribution
curves at
different
Temperatures,
e.g.
Care must be
taken that the
time for the
measurement is
not significant
w.r.t. the
chemical time
scale.
A system of
chemically
related species
may or may not
be equilibrated.
If you take a
repeat spectrum
are the ratios
unchanged?
Chemical Reactions and Kinetics
and NMR Spectroscopy
• NMR is a powerful technique for exploring reactions
• Equilibrium and Kinetics are both accessible
• In solution, we get total chemical picture (of NMR active
atoms)
• Can evaluate chemical exchange that is not accessible
through other methods
• Like any mechanistic study, requires controls, temperature
regulation, careful integration, thoughtful interpretation
Systems in Chemical Equilibrium
NMR and Kinetics a great fit but…
k1
A
B
k-1
 (Hz) in
kinetics is a
reciprocal
chemical
lifetime
 (Hz) in
NMR is a
chemical shift A
difference
related to the 2
chemical
environments

B
Spectra are affected when the 1/(chemical lifetime) becomes similar to the  that separates
the chemical shifts of the atoms in exchange. Important corollary: Since the chemical shifts
of these two are what is observed,  for the same process will vary with magnet strength.
The same sample, same process, same NMR tube, same temperature can give two differentappearing spectra, at two different fields.
Chemical process can be rotation, proton exchange, isomerization, rearrangement,
dissociation or almost any reaction. Lifetime (sec) can be expressed as rate.
The chemical and the NMR ’s different numbers!!!
What is the Picture?
Imagine a chemical species A, in chemical
equilibrium with B, and that they have different
NMR signals (can be proton, carbon phosphorus,
etc.)
Hz?
Is k near in value
to ?
A
B
A and B are
separated in the
Spectrum by
some number of
Hz. What gives
us the ability to
see these as
separated peaks?
Hint, Hz is a
reciprocal
lifetime
What is meant by “The NMR
Time Scale”?
•Imagine two signals that are chemically changing their identities.
•They have chemical shifts, 1, 2
•These shifts are also separated by a given number of Hz; (=1-2)
•Remember, that Hz has units of 1/sec.
•The chemical shift difference in Hz can be compared to a “chemical lifetime” or
its reciprocal the reaction rate constant k. k has units of 1/sec.
•If the reaction rate k is faster than , we can only observe a signal at the
average of the two chemical shifts. Intensity will be the sum.
•We can address this experimentally by making k smaller (lower the temperature)
or making  bigger (use a higher field NMR magnet)
•Practically, the relevant time scale for exchange here is 10s of msec.
Take home message
The NMR’s ability to see different signals for
compounds that are in chemical exchange is limited.
The limit is determined by the comparison of the rate
(1/lifetime) for the chemistry, with the separation in Hz
of the related signals.