Nuclear Magnetic

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Nuclear Magnetic Resonance
A Tutorial
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Atoms with an odd of protons or odd atomic
weight have nuclear spin. Nuclear spin is a
fundamental property just like mass or charge and
the spin has a force of 2 x 10-18 N. Examples of
atoms with this property are 1H, 13C and 31P.
This spinning creates a small magnetic field
around each atom. This is called a magnetic
moment. Although for simplicity sake the
spinning nucleus is usually drawn as spinning
straight up and down, it actually precesses more
like a childs top. The easiest way to think of
this spinning nucleus is to imagine it as being a
very small bar magnet.
Representations of a spinning nucleus
N
S
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In the absence of any field, the nuclei of those
atoms with nuclear spin, spin in all directions
they have no orientation. When an external
magnetic field is applied, the spins will align
either with the magnet or against the magnet
however, more nuclei will align in the lowest
energy state, with the magnet.
S
S
S
S
N
S
N
N
N
N
S
N
S
N
N
N
N
N
N
N
S
S
S
S
S
S
S
N
S
N
No Field
Applied Magnetic Field
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Those nuclei aligned with the magnetic field are
in the low energy a-spin state and those against
are in the high energy ß-spin state. The
difference in energy between the two states can
be expressed by the equation ?E
?(h/2p)H0 where ? is the gyromagnetic ratio, h is
Plancks constant and H0 is the strength of the
magnet (applied field).
S
ß-spin state
S
S
N
N
? E
N
N
N
N
N
S
S
S
S
S
a-spin state
N
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The ?E between the two spin states is very small.
Nuclei in a 25,000 gauss magnet (earth is 0.57
gauss) will have a ?E of 10-5 kcal/mol. This
?E is the same amount of energy as provided by
radio waves in the electromagnetic spectrum.
When aligned nuclei are exposed to a radio
frequency (RF) that exactly matches the ?E, the
energy is absorbed by the nuclei causing them
flip to the ß-spin state. The nuclei are then
said to be in resonance thus the term Nuclear
Magnetic Resonance. The absorbance of that
frequency can be detected. A plot of all
absorbance's resulting from the RF radiation of
an organic compound yields an NMR spectrum.
RF wave
H0 (applied magnetic field)
H0 (applied magnetic field)
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The NMR Spectrometer
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The ?E for each spinning nucleus is not usually
the same and can be different for two reasons.
First, the ?E for each type of atom that has a
magnetic moment (1H, 13C, etc.) will be different
because the gyromagnetic ratio (?) for each of
these atoms is different. The equation
expressing the ?E was ?E ?(h/2p)H0, therefore,
?E is directly proportional to ?. For example, a
hydrogen atom (usually referred to as a proton),
will have a higher ?E than a 13C atom because the
? for the hydrogen is larger.
15 MHz
13C
13C
13C
1H
1H
1H
1H
1H
1H
1H
1H
13C
13C
13C
13C
13C
H0 14,100 gauss
H0
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In a 14,100 gauss magnet the energy of a 60 MHz
wave is required to cause a proton to be in
resonance.
60 MHz
1H
1H
1H
1H
1H
1H
1H
13C
1H
13C
13C
13C
13C
13C
13C
13C
H0 14,100 gauss
H0
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The second reason why spinning nuclei can have a
different ?E is because the ?E is also dependent
upon the local electronic environment that the
atom is in. Electron density surrounding a
nucleus provides a shield against the applied
magnetic field. The electrons circulating around
the nucleus induce a magnetic field that is
opposite to the applied field. The induced field
lowers the energy of the a-spin state and raises
the energy of the ß-spin state.
1H
1H
ß-spin state
1H
E
? E
1H
a-spin state
Induced Magnetic field
H0
Shielding
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This means that a proton surrounded by high
electron density will have a higher ?E than a
proton surrounded by low electron density. A
higher frequency will have to be used to put a
more shielded nuclei in resonance.
Low Frequency Radio Waves
H0
H0
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This complexity is what allows us to explore the
structure of an organic compound. For example,
the ?E for each non-equivalent proton in
pent-1-ene-3-ol will be different because the
shielding of each proton will be different.
Also, the ?E for each non-equivalent carbon in
the structure will be different because the
shielding of each carbon will be different.
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If we investigate the electron density of the
alkenol, it would look as follows
Lowest Electron Density
Highest Electron Density
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A simplified 1H spectrum of the alkenol would
look as shown below. All peaks, also called
signals, are referenced to trimethyl silane (TMS)
which contains the most shielded protons known.
A TMS proton has the greatest ?E, requires the
most energy (the most field strength) for
resonance and so that end of the spectra is said
to be upfield. All other peaks are downfield
from the TMS reference with the least shielded
proton being the most down field. Any OH and NH
peaks are usually weak due to deuterium exchange.
10 9 8 7 6
5 4 3 2 1
0 d
Shift downfield from TMS (Hz) Spectrometer
frequency (MHz)
Chemical shift (ppm, d)
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Typical Resonance Frequency Values
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A truer NMR spectrum of our example compound
would actually look as represented below. The
splitting of the signals, into various numbers of
peaks is due to the perturbation of the induced
magnetic field of one proton by its neighboring
protons. This is known as multiplicity. The area
under the peaks is dependent upon the number of
equivalent protons. It is common for OH and NH
peaks to not show splitting patterns.
3 protons
1 proton
10 9 8 7 6
5 4 3 2 1
0 d
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Signal splitting or spin-spin splitting is a
result of magnetic coupling. If two neighboring
protons have magnetic fields that are aligned,
there is an increase in the induced field. If two
neighboring protons have magnetic fields that are
opposed, there is a decrease in the induced
field. All possible combinations of fields
either aligned and opposed are present in the
time scale of NMR so there will be a peak for
each combination.
Possible Coupling Combinations
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The n 1 rule defines the number of
combinations and it simply states that you will
have one more peak than the number of protons on
adjacent carbons. The areas of each of the peaks
is defined by Pascals triangle.
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We can re-evaluate the NMR of our example
compound and verify that this defined splitting
pattern is present. Additional information about
the compound can be gained from calculating the
coupling constant. The coupling constant, also
called the J value, is the distance in Hz between
the first and the last peak of a signal. It can
tell us the type of bonding to the neighboring
carbon when the calculated J values are compared
to a standard table. If two sets of peaks have
the same J value, it can usually be assumed that
those protons are on neighboring carbons.
7 Hz
10 Hz
7 Hz
10 Hz
10 9 8 7 6
5 4 3 2 1
0 d
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Values for Coupling Constants
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There are additional factors that may make a
splitting pattern more complex. The first factor
is that although it is the nearest neighboring
protons that most affect the splitting pattern,
protons up to about 3 carbons away can have some
effect. Also, if the protons on the same carbon
are not actually equivalent and are in different
environments, the splitting can become very
complicated.
Styrene
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The job of an NMR spectroscopist is to assign
spectra. A spectroscopist should be able to
absolutely determine the structure of simple
compounds from a proton NMR if at least the
molecular formula is known. A 13C NMR can also
help verify the proposed structure of simple
compounds and help with the assignment of more
complex compounds. Because the gyromagnetic
ratio for carbons is lower than that for protons,
the ?E is smaller and the chemical shift numbers
are larger (more downfield).
120 110 100 90 80 70
60 50 40 30 20
d
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There are some problems associated with 13C NMR.
First, the isotopic abundance of 13C is quite low
and so it requires many NMR scans to obtain a
good spectrum. If just one scan were taken, the
13C signals would be hidden within the background
noise. Usually several hundred scans are taken
for a good 13C NMR. Second, the peak area does
not necessarily represent the number of
equivalent carbons. The peak area can be
affected by how many hydrogens are directly
attached to that carbon. Third, though there is
no carbon-carbon signal splitting, there is
complex carbon-hydrogen splitting. To minimize
this, the protons are kept irradiated
continuously so all the proton magnetic fields
are aligned the same way and dont split the
carbon signal. This simplifies the spectrum but
some information is lost. A technique called
off-resonance decoupling does allow some coupling
and therefore some splitting to occur and can
help with assignments. The coupling technique
allows a carbon signal to be split only by the
hydrogens that are directly bonded to that carbon.
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13C NMR
120 110 100 90 80 70
60 50 40 30 20
d
Off-resonance decoupled 13C NMR
120 110 100 90 80 70
60 50 40 30 20
d
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Two 13C NMR Spectra
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Combined 13C and 1H Spectra
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Summary of Hydrogen and Carbon Chemical Shifts
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http//arrhenius.rider.edu/nmr/NMR_tutor/pages/ana
l/anal_b1.html
http//physchem.ox.ac.uk/hill/tutorials/year3/nm/
nm3_tq1.pdf
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http//www.bch.bris.ac.uk/staff/pfdg/teaching/nmr.
htm
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http//microscopy.fsu.edu/electromag/java/nmr/lore
ntzian/
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Homework problem 1 2-methyl-1,3-propanediol
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Homework problem 2 Ethyl acetoacetate
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Homework problem 3 Propylbenzene
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Homework problem 4 4-penten-1-ol
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References http//www.cis.rit.edu/htbooks/nmr/ins
ide.htm
Wade Text