An Introduction to NMR Spectroscopy
Shelby Feinberg and Steven Zumdahl
Nuclear magnetic resonance spectroscopy (NMR) has risen to the same level of
importance as electronic and vibrational spectroscopy as a tool for studying molecular properties,
particularly structural properties. Although the following discussion of nmr specifically deals
with hydrogen atom nuclei in organic molecules, the principles described here apply to other
types of molecules as well. Many other types of nuclei (13C,
19
F,
31
P, etc.) have nuclear spins
and thus can be studied using NMR techniques.
Certain nuclei, such as the hydrogen nucleus (but not carbon-12 or oxygen-16), have a
nuclear spin. The spinning nucleus generates a small magnetic field, called "". When placed in
a strong external magnetic field, called Ho, the nucleus can exist in two distinct spin states: a low
energy state A, in which  is aligned with the external magnetic field, Ho, and a high energy state
B, in which  is opposed to the external magnetic field, Ho (figure 1). Alignment of  with Ho is
the more stable and lower energy state.
Ho
Ho

Figure 1

Spin + 1/2
Parallel
A
Low Energy
Spin  1/2
Anti-parallel
B
High Energy
In NMR, transitions from the more stable alignment, A, (with the field) to the less stable
alignment, B, (against the field) occur when the nucleus absorbs electromagnetic energy that is
exactly equal to the energy separation between the states (E). This amount of energy is usually
found in the radiofrequency range. The condition for absorption of energy is called the condition
of resonance. It can be calculated as the following:
ΔE 
γh
H  hυ
2π
h = Planck’s constant
H = the strength of the applied magnetic field, Ho, at the nucleus
 = the gyromagnetic ratio (a constant that is characteristic of a particular nucleus)
 = the frequency of the electromagnetic energy absorbed that causes the change in
spin states
There are three features of NMR spectra that we will focus on: the number and size of
signals, the chemical shift, and spin-spin coupling.
Number and Size of Signals
Let’s consider how the NMR spectrometer can distinguish between hydrogen nuclei and
produce multiple signals. Magnetically equivalent hydrogen nuclei produce one signal. These
hydrogen nuclei experience the same local environment. For example, in a molecule such as
diethyl ether (Figure 2), there are two sets of magnetically equivalent hydrogens. The hydrogens
labeled a are six magnetically equivalent methyl hydrogens, while the hydrogens labeled b are
four magnetically equivalent methylene hydrogens. Notice that the methyl (a) hydrogens are all
located adjacent to a carbon containing two hydrogen atoms. Additionally, the methylene (b)
hydrogens are all located adjacent to an oxygen atom and a carbon atom containing three
hydrogen atoms.
Figure 2
CH3
a
CH2
b
O
CH2
CH3
b
a
Because of rapid rotations about sigma bonds and molecular symmetry, the six methyl hydrogens
(a) and the four methylene hydrogens (b) comprise two individual magnetically equivalent
groups of hydrogens. The methyl hydrogens (a) experience a different total magnetic field than
the methylene hydrogens (b), because of different local magnetic fields.
As a result, the
resonance energy, E, corresponding to the frequency of absorption, , will be different for these
two groups of hydrogen nuclei. Thus, the NMR spectrometer can distinguish between groups of
hydrogen nuclei which experience different local magnetic fields. Different frequencies are
required for the two different groups of hydrogens, thereby producing two distinct signals.
The areas of the signals are directly proportional to the number of hydrogens. So, in the
case of diethyl ether, the two peaks have an area ratio of 3:2 (or 6:4), because there are six
methyl hydrogens (a) and four methylene hydrogens (b). We will look at an actual spectrum
presently.
The Chemical Shift
When an organic molecule is placed in an external magnetic field, H o, each hydrogen
nucleus experiences a total field that is the sum of Ho and two other local magnetic fields: one
produced by bonding and non-bonding electrons, He, and the other produced by neighboring
protons which possess a nuclear spin, Hh. Thus, the applied magnetic field (Ho) is constant,
while the magnetic fields produced as He and Hh are not constant. The magnetic field produced
by the neighboring electrons (He) determines the position (relative frequency) of an nmr peak
(called the chemical shift). The magnetic fields produced by neighboring nuclei (Hh) are smaller
than He and cause splitting of an NMR peak (called spin-spin coupling). This will be discussed
later.
For the moment, let’s assume that Hh is zero. There is no spin-spin coupling. Under
these conditions, the total magnetic field, H, experienced by a particular nucleus is given by Ho +
He. That is, we are assuming that the resonance energy is only dependent on the sum of the
external magnetic field and the magnetic field produced by neighboring electrons. A
mathematical representation of the value of this resonance energy is the following:
ΔE 
γh
(Ho  He)  hυ
2π
If we vary the frequency () of the electromagnetic energy until h = E, absorption will cause a
transition in spin states, and a signal will be recorded by the NMR spectrometer.
The position of an NMR signal is recorded relative to the position of the signal of an
internal standard. This standard is commonly tetramethyl silane (TMS), (CH3)4Si. If TMS
absorbs at frequency s, and the hydrogen nucleus of interest absorbs at , the spectrometer will
record a signal at
( υ  υs )
 10 6  δ , where o is the spectrometer frequency (commonly 60
υo
megacycles per second).  is called the position of absorption, or the chemical shift, expressed
as parts per million (ppm) on a scale of 0-10 ppm. TMS absorbs at 0.0 ppm, while most nuclei
absorb downfield towards 10 ppm. The value of  is independent of Ho, but it DOES depend on
He. Figure 3 gives a few examples of how neighboring atoms affect the chemical shifts of
hydrogen atoms.
Figure 3
H
O
H
H
C
C   C  C   C   C
C
O
O
RCOH
RCH
H
H
X
N
H
H
C
(satd.)
C
C (or O)
10
9
8
Downfield
Deshielding
7
6
Ho
5
4
3
Upfield
Shielding
2
TMS
1
0 (ppm)
Hydrogen nuclei which absorb at large  are said to be deshielded from the external
magnetic field. These signals appear downfield (towards 10 ppm) from TMS because the
frequency at which they absorb differs greatly from the frequency of the TMS hydrogens. As a
result, the value of   s is large. Deshielding is caused by adjacent atoms which are strongly
electronegative (e.g. oxygen, nitrogen, halogen) or groups of atoms which possess -electron
clouds (e.g. C=O, C=C, aromatics).
Let’s now look at the nmr spectrum of benzyl acetate (Figure 4).
Figure 4
O
CH2 O
b
C
CH3
a
c
c
a
b
TM S
600
300
0
Note that there are three absorptions corresponding to the three sets of magnetically equivalent
hydrogens. Compare the chemical shifts with those given in Figure 3. The relative area of the
peaks corresponds to the number of hydrogens in each set (3:2:5).
Spin-Spin Coupling
We have discussed how the position of an NMR absorption is affected by the magnetic
field produced by neighboring electrons (He). Now, let’s examine how the magnetic field
produced by neighboring protons (Hh) affects the splitting of the NMR absorption. The peaks
can appear as singlets, doublets, triplets, etc… Let’s first consider the absorption of a hydrogen
atom (Hx) with only one neighboring hydrogen atom (Hy) (Figure 5).
Figure 5
*Hx =
*Hx
Hy
C
C
Ho
nmr spectrum for *Hx =
Hy =
= A = Ho + He + Hh (low energy)
Hy =
= B = Ho + He + Hh (high energy)
intensity ratio = 1:1
If we assume that Hx is aligned with Ho, then the neighboring hydrogen nucleus will have
approximately equal probability of existing in either the low energy state, A, or the high energy
state, B. Refer to Figure 1 for a clear picture of these energy states. For those molecules in
which the neighboring hydrogen nucleus exists in the low energy state, its magnetic field (H h)
will add to the magnetic field (Ho + He) and for those molecules in which the neighboring
hydrogen nucleus exists in the high energy state, its magnetic field (Hh) will subtract from the
magnetic field (Ho + He). As a result, two different peaks are observed. A higher frequency is
required for the low energy state, while a lower frequency is required for the high energy state.
This two line pattern is called a doublet, and we say that the neighboring hydrogen nucleus (H y)
splits the absorption of Hx into a doublet. The intensity of the two lines will be equal, because
the probability of the neighboring hydrogen nucleus (Hy) existing in either spin state A or B is
approximately equal.
When there are two magnetically equivalent adjacent hydrogen nuclei, three possibilities
exist for their combined magnetic fields (Figure 6).
Figure 6
*Hx =
*Hx
C
Hy
C
Hy
Hy =
(low energy)
Hy =
(middle energy)
Hy =
(middle energy)
Hy =
(high energy)
Ho
nmr spectrum for *Hx =
intensity ratio = 1:2:1
Note that both can have spin state A, one can have spin state A and the other have spin state B,
or both can have spin state B. These three possibilities have a probability ratio of 1:2:1, which
correspond to three different absorption frequencies. The appearance of the resulting NMR
signal is a three line pattern, called a triplet, with intensities 1:2:1.
When there are three magnetically equivalent neighboring hydrogen nuclei (Figure 7), the
absorption splits into a quartet with intensity pattern 1:3:3:1 for similar reasons to those
aforementioned.
Figure 7
*Hx =
Hy =
*Hx
C
Ho
nmr spectrum for *Hx =
Hy
C
Hy
Hy
(very low energy)
Hy =
(med. low energy)
Hy =
(med. high energy)
Hy =
(very high energy)
intensity ratio = 1:3:3:1
In general, N magnetically equivalent neighboring hydrogen nuclei will split the
absorption into N + 1 lines. The intensity ratios are equal to the coefficients of the expansion (a
+ b)N, or Pascal’s triangle.
The spacing between the lines of a doublet, triplet, or quartet is dependent on the
coupling constant. It is given the symbol J, and it is measured in units of cycles per second.
Coupling constants range in magnitude from 0 to 20 cps. Observable coupling will generally
occur between hydrogen nuclei which are separated by no more than three sigma bonds. For
example, in the molecule 2-butanone (Figure 8), hydrogens from groups a and b split one
another because they are only separated by three bonds. However, hydrogens from group c are
not split by any other hydrogens because they are separated from other hydrogens by more than
three sigma bonds.
Figure 8
O
CH3CH2CCH3
a
b
c
TM S
600
300
Examples of typical coupling constants are given in Figure 9.
0
Figure 9
H
H
C
12-15 cps
C
C
13-18 cps
H
H
C
O
H
0 cps
H
H
H
C
C
H
H
C
6-8 cps
C
0-3 cps
H
H
C
C
1-3 cps
O
H
H
H
H
C
C
7-12 cps
6-9 cps
Note that coupling is never observed between magnetically equivalent hydrogen atoms.
Let’s now consider the coupling of hydroxylic protons (OH). Hydroxylic protons do
not split other protons, nor are they split by other protons. These protons undergo exchange
between two molecules of alcohol. This exchange is so fast that these protons sample molecules
with all possible spin states, giving rise to a singlet in the NMR spectrum at a position which is
the average for all the spin states of the other hydrogens.
For example, ethanol gives an NMR spectrum consisting of a triplet, quartet, and a
singlet, as seen in the idealized spectrum in Figure 10. Even though the hydroxylic proton is
separated from a methylene hydrogen by three bonds, the signal given by the hydroxylic proton
is not split by the methylene protons, nor are the methylene hydrogens split by the hydroxylic
proton because of proton exchange.
Figure 10
CH3CH2OH