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Nuclear Magnetic Resonance Spectroscopy
Introduction
ORGANIC I LABORATORY
W. J. Kelly
WHAT IS NMR SPECTROSCOPY?
•Nuclear magnetic resonance, or NMR as it is abbreviated by scientists, is a
phenomenon which occurs when the nuclei of certain atoms are immersed in a
static magnetic field and exposed to an oscillating electromagnetic field.
Some nuclei experience this phenomenon, and others do not, dependent upon
whether they possess a property called spin.
•Nuclear magnetic resonance spectroscopy is the use of the NMR
phenomenon to study physical, chemical, and biological properties of matter.
As a consequence, NMR spectroscopy finds applications in several areas of
science. NMR spectroscopy is routinely used by chemists to study chemical
structure using simple one-dimensional techniques. Two-dimensional
techniques are used to determine the structure of more complicated
molecules.
•The versatility of NMR makes it pervasive in the sciences.
WHAT IS SPECTROSCOPY?
•Spectroscopy is the study of the interaction of electromagnetic radiation
with matter.
•The Light of Knowledge is an often used phrase. Most of what we know
about the structure of atoms and molecules comes from studying their
interaction with light (electromagnetic radiation). Different regions of the
electromagnetic spectrum provide different kinds of information as a result
of such interactions.
WHAT IS ELECTROMAGNETIC RADIATION?
•Realizing that light may be considered to have both wave-like and particlelike characteristics, it is useful to consider that a given frequency or
wavelength of light is associated with a "light quanta" of energy we now call a
photon. As noted in the following equations, frequency and energy change
proportionally, but wavelength has an inverse relationship to these quantities.
•The frequency of electromagnetic radiation may be reported in cycles per
second or radians per second. Frequency in cycles per second (Hz) have units
of inverse seconds (s-1) and is given the symbol 
SPIN PROPERTIES OF ATOMIC NUCLEI
What is spin?
The Simple explanation
•Spin is a fundamental property of nature like electrical charge or mass.
•Spin is a measure of angular momentum (rotation about an axis) hence the term
•Spin comes in multiples of 1/2 (0, 1/2, 1, 3/2, 2, 5/2…) and can be + or -.
•Protons, electrons, and neutrons possess spin.
•Individual unpaired electrons, protons, and neutrons each possesses a spin of 1/2
•Atomic nuclei composed of neutrons and protons may also possess spin.
•The spin of an atomic nucleus is determined by the number of protons and
neutrons in the nucleus.
•Atoms with and odd number of protons will have spin
•Atoms with an odd number of neutrons will have spin
•Atoms with an odd number of both protons and neutrons will have spin
•Atoms with an even number of both protons and neutrons will not have spin
•The value of nuclear spin is represented by the symbol I, the nuclear spin
quantum number. (I = 0, 1/2, 1, 3/2, 2, 5/2….)
•A nucleus with spin of I can exist in (2I+1) spin states.
SPIN PROPERTIES OF ATOMIC NUCLEI
What is spin?
The fundamental explanation.
The shell model for the nucleus tells us that nucleons (protons and neutrons),
just like electrons, fill orbitals. When the number of protons or neutrons equals 2,
8, 20, 28, 50, 82, and 126, orbitals are filled. Because nucleons have spin, just like
electrons do, their spin can pair up when the orbitals are being filled and cancel
out. Odd numbers mean unfilled orbitals, that do not cancel out.
Nuclei
1H
2H
31P
23Na
14N
13C
19F
COMMON NUCLEI WITH SPIN
Unpaired Protons
Unpaired Neutrons
1
0
1
1
1
0
1
2
1
1
0
1
1
0
Almost every element has an isotope with spin
Net Spin
1/2
1
1/2
3/2
1
1/2
1/2
MAGNETIC PROPERTIES OF ATOMIC NUCLEI
What is the physical result of spin?
A spinning charge generates a magnetic field. An atomic
nucleus has an inherent charge due to the protons within it.
Thus an atomic nucleus with spin (I>0) will have a magnetic
field associated with it.
The nucleus generates a magnetic dipole along the spin axis,
and the intrinsic magnitude of this dipole is a fundamental
nuclear property called the nuclear magnetic moment, 
The nuclear angular momentum quantum number I
determines the nuclear magnetic moment according to the
following equation:
 = N mN [I(I + 1)]1/2
Where both N and mN are constants for a given nucleus N
A spinning nuclei behaves as if it were a tiny bar
magnet
Qu i ck Ti m e ™ an d a
GI F d ec om pr es so r
ar e n ee de d t o s ee t h is pi ct u re .
MAGNETIC PROPERTIES OF ATOMIC NUCLEI
For our purposes, consider the behavior of a 1H atom. The magnetic
moment  is a vector quantity, that is it has both magnitude and
direction.
In the absence of an external magnetic field, the magnetic moments
of a collection of a large number of hydrogen atoms orient themselves
in a random fashion. That is, no particular orientation is preferred.
RANDOM ORIENTATION
Qu i ck Ti me™ a nd a
GIF d ec omp res so r
are n ee de d to se e thi s p ic ture.

THE EXTERNAL MAGNETIC FIELD
If two magnets are brought near each other they will exert a
force on each other and will try to align themselves. For simple bar
magnets, the favored alignment is parallel (north pole of one
magnet faces the south pole of the second).
N
Applied
External
Magnetic
Field
of Field
Strength B o
S
Similarly, when a
magnetic nucleus (I>0) is
placed between the
poles of an external
magnet, it too will try to
align itself with respect
to this externally
applied magnetic field
(Bo).
THE EXTERNAL MAGNETIC FIELD
In the macroscopic world, two magnets can be aligned in an infinite number of
orientations . At the atomic level, these alignments are quantized. There are
only a finite number of alignments a nucleus can take against an external
magnetic field. This number depends on the value of its spin number I. Each
possible alignment is assigned a value called Iz which ranges from -I to +I in
steps of 1. These orientations are referred to as spin states. The diagram
illustrates the possible spin states for a spin 1/2 nucleus.
In quantum mechanical terms, the nuclear
magnetic moment of a nucleus can align
with an externally applied magnetic field
of strength Bo in only 2I + 1 ways, either
parallel or opposing Bo. The energetically
preferred orientation has the magnetic
moment aligned parallel with the applied
field (spin +1/2) and is often given the
notation a, whereas the higher energy
anti-parallel orientation (spin -1/2) is
referred to as b.
QUANTIZED SPIN STATES AND NET MAGNETIZATION
When a “magnetic” nuclei of
I=1/2 such as a hydrogen
atoms are placed in an
external magnetic field only
two spin states are possible.
The two states labeled 
(+1/2) and  (-1/2) have
different energies. Since
nature always prefers the
lower energy situation,
more hydrogens will
“choose” the  state over
the  state, although the
population difference will
be small.
N
Applied
>
External
Magnetic
Field
Net
Magnetic
Moment
of Field
Strength B o
S

E
N
E
R
G
Y
No External Field
Random Orientation
All Spins Equal Energy
Turn on B o

GYROSCOPIC PRECESSION
Magnets, when brought together, will align exactly parallel to each other and will
maintain this alignment in a static fashion. Magnetic nuclei, due to restrictions
described by quantum mechanics, do not align exactly parallel to or against the
external magnetic field but rather, they align at an angle. This has an important
consequence that can be illustrated by considering a gyroscope.
A spinning gyroscope, when placed in a specific
orientation, will tend to hold that orientation despite
the effects of external forces like gravity. In a
vertical gravity field (gravity pulling straight down) a
gyroscope placed vertically will maintain this
orientation motionlessly. If a force is applied to the
gyroscope perpendicular to the gravity field, it will
rotate about an axis parallel to the gravity field
demonstrating something call precession. The
frequency of this precession depends on two factors,
the force exerted by the gravity field, and the force
exerted by the gyroscope
NUCLEAR PRECESSION
Just as a gyroscope will precess in a gravitational field, the magnetic moment μ
associated with a spinning spherical charge will precess in an external magnetic
field. In the following illustration, the spinning nucleus has been placed at the
origin of a cartesian coordinate system, and the external field is oriented along
the z-axis.
The angular frequency at which this
precession occurs is given by
 = Bo/2
and is called the Larmor frequency. The
value, , is the magnetogyric ratio and is
characteristic for each type of nucleus. It
relates to the strength of the nucleus'
magnetic field. H is the strength of the
externally applied magnetic field. For
example, a 1H atom in a magnetic field
H=1.41 Tesla has a Larmor frequency of 60
megahertz (MHz).
SPIN STATE ENERGY AND Bo
The orientations a magnetic nucleus can take against an external magnetic are
not of equal energy. Spin states which are oriented parallel to the external
field are lower in energy than in the absence of an external field. In contrast,
spin states whose orientations more nearly oppose the external field are higher
in energy than in the absence of an external field
The difference in energy
between the two spin
states is dependent on
the external magnetic
field strength, and is
always very small. The
following diagram
illustrates that the two E
spin states have the same
energy when the external
field is zero, but diverge
as the field increases.
 -1/2
E = hBo/2
 +1/2
Bo
SPIN STATE TRANSITIONS
Where an energy separation exists there is a possibility to induce a transition
between the various spin states. By irradiating the nucleus with electromagnetic
radiation of the correct energy (as determined by its frequency), a nucleus with
a low energy orientation can be induced to "jump" to a higher energy orientation.
The absorption of energy during this transition forms the basis of the NMR
method.
If rf energy having a
frequency matching the
Larmor frequency is
introduced at a right angle
to the external field (e.g.
along the x-axis), the
precessing nucleus will
absorb energy and the
magnetic moment will flip to
its I = _1/2 state. This
excitation is shown in the
following diagram
SPIN STATE POPULATION INVERSION
Magnetic Nuclei such as hydrogen atoms when placed in a static external
magnetic field will always have a slight excess of population of atoms in the
lower energy  state. By irradiating the nucleus with electromagnetic radiation
of the correct energy (as determined by its frequency), a nucleus with a low
energy  orientation can be induced to "jump" to a higher energy  orientation.
The absorption of energy during this transition forms the basis of the NMR
method.

Bo

Apply RF
Energy
 = Bo/2


IRRADIATION FREQUENCY VS FIELD STRENGTH
Strong magnetic fields are necessary for nmr spectroscopy. The international
unit for magnetic flux is the tesla (T). The earth's magnetic field is
approximately 10-4 T at ground level. For nmr purposes, this small energy
difference (ΔE) is usually given as a frequency in units of MHz (106 Hz), ranging
from 20 to 900 Mz, depending on the magnetic field strength. Irradiation of a
sample with radio frequency (rf) energy corresponding exactly to the spin state
separation of a specific set of nuclei will cause excitation of those nuclei in the
+1/2 state to the higher -1/2 spin state.
ENERGY OF A PHOTON
E = h
SPIN STATE ENRGY DIFFERENCE
E = hBo/2
WHEN E = E, SPIN FLIP OCCURS 
h hBo/2
THE NECESSARY FREQUENCY IS:
 Bo/2
PROTON SPIN ENERGY DIFFERENCES
 -1/2
60 MHz 10 0 MHz
20 0 MHz
30 0 MHz
40 0 MHz
 +1/2
1.41T 2.34T
4.73T
7.07T
Bo
9.56T
NMR EXPERIMENT
When magnetically active nuclei
are placed into an external
magnetic field, the magnetic
fields align themselves with the
external field into two
orientations. During the
experiment, electromagnetic
radiation of a specific frequency
is applied. By sweeping the
magnetic field, an energy
difference between spin states
will occur that has the same
energy as that f the applied radio
frequency and plot of frequency
versus energy absorption can be
generated. This is the NMR
spectrum
THE CHEMICAL SHIFT
Since protons all have the same magnetic moment, we might expect all
hydrogen atoms to give resonance signals at the same field / frequency values.
Fortunately for chemistry applications, this is not true. Below are a number
of representative proton signals displayed over the same magnetic field range.
It is not possible, of course, to examine isolated protons in the spectrometer;
but from independent measurement and calculation it has been determined that
a naked proton would resonate at a lower field strength than the nuclei of
covalently bonded hydrogens.
The range of field / frequency values for all hydrogen atoms in a “Chemical”
environment is called the CHEMICAL SHIFT. The range of resonance
frequencies, or bandwith, for most hydrogens in organic molecules in an external
magnetic field (Bo=1.41T) is 600-1000 Hz, a very small range.
DIAMAGNETIC SHIELDING
Why should the proton nuclei in
different compounds behave
differently in the nmr experiment?
The answer to this question lies
with the electron(s) surrounding the
proton in covalent compounds and
ions. Since electrons are charged
particles, they move in response to
the external magnetic field (Bo) so as
to generate a secondary field that
opposes the much stronger applied
field. This secondary field shields
the nucleus from the applied field, so
Bo must be increased in order to
achieve resonance (absorption of rf
energy). Thus Bo must be increased
to compensate for the induced
shielding field.
When an atom is placed in a magnetic
field, its electrons circulate about the
direction of the applied magnetic field.
This circulation causes a small magnetic
field at the nucleus which opposes the
externally applied field. The magnetic
field at the nucleus (the effective field)
is therefore generally less than the
applied field by a fraction  .
B = Bo (1-)
SHIELDING AND DESHIELDING
In a molecule, the nucleus is always
surrounded by an electron cloud. Since
the electron's magnetic field opposes
the external magnetic field, the
nucleus is "shielded" from the full
force of the external magnetic field.
Heff (Beff)is normally less than Ho (Bo).
Within a molecule there are factors
which can increase or decrease the
electron density surrounding a nucleus.
Factors which reduce the electron
density are said to deshield the nucleus
since Heff at the nucleus increases.
Similarly, factors which increase the
electron density are said to "shield"
the nucleus since Heff will decrease
CHEMICAL SHIFT - ELECTRONEGATIVITY
A nucleus is shielded or deshielded
whenever it is influenced by the magnetic
fields of nearby electrons. The closest
electrons to a nucleus are those that bond
the nucleus to its neighbouring atoms. Any
factor that effects the distribution of
these bonding electrons will also effect
the degree of shielding the nucleus
experiences.
Electronegative atoms have an affinity for electrons. The more electronegative
the atom is, the stronger this affinity. Consider the following two cases; an 1H
atom bonded to a carbon; an 1H atom bonded to an oxygen. Carbon is less
electronegative than oxygen. In an oxygen-hydrogen bond, the bonding electrons
will be drawn towards the oxygen. The electron density around the hydrogen
atom will be reduced in comparison to the same hydrogen bonded to a carbon
atom. In the case of an O-H bond, hydrogen has a lower electron density
surrounding it and is, therefore, less shielded. Electronegative atoms or
electron withdrawing functional groups are considered to be deshielding.
Electropositive atoms or electron donating functional groups are considered to
be shielding.
BANDWIDTH - PPM SCALE
The resonance frequency / magnetic field range for hydrogens in organic
compounds show below is very small.
Increasing Mag. Field at Fixed Frequency
Increasing Frequency at Fixed Mag. Field
Increased Shielding by Electrons
On a spectrometer where
the proton transition
frequencies are nominally
.60 MHz, the chemical
shift frequency changes
may be only hundreds of
hertz; about a million
times smaller than the
resonance frequency.
H
O
C
H 2C
H 2C
Cl
Cl
C C
H
H
CCl 3
H
H
H
H
H
H
H 3C
S O
H 3C
CH3 NO2
H
H
Cl
C
Cl
H 2C
H 2C
O
O
CH2
CH2
H 3C
O
C
H2
C
C
H2
CH2
CH2
CH3
H 3C Si CH3
CH3
CH3
1H NMR Resonance Signals for some Different Copounds
600 Hz Difference
10 parts per million (PPM)
Because of this relationship, chemical shifts are typically reported as a fraction
of the nominal resonance frequency. Due to their small size, parts-per-million
(ppm) are used. On a 60 MHz spectrometer, a 60 Hz chemical shift is reported
as a (60 / 60,000,000) = 1 ppm shift
CHEMICAL SHIFT -  SCALE
The chemical shift
of a nucleus is the
difference
between the
resonance
frequency of the
nucleus and a
standard, relative
. the standard.
to
This quantity is
reported in ppm
and given the
symbol delta, .
TMS Reference
Standard
 = 0.00 ppm
Increased Shielding by Electrons
 = 10.0 pp m
O
H
C
CCl 3
 = 7.2 ppm
H
H
CH3
H 3C Si CH3
 = 5.2 ppm
CH3 NO2
CH3
H
 = 2.1 ppm
H
H
H
H 3C
60 0 Hz from TMS
 = 10.0 pp m
O
C
CH3
43 2 Hz from TMS
31 3 Hz from TMS
12 6 Hz from TMS
1H NMR Resonance Signals for some Different Copounds
 = shift in Hz from TMS/spectrometer frequency
In NMR spectroscopy, this standard is often tetramethylsilane,
Si(CH3)4, abbreviated TMS. The chemical shift is a very precise metric
of the chemical environment around a nucleus