1) NMR spectroscopy allows determination of molecular structure by measuring frequencies at which atomic nuclei absorb radio waves in a strong magnetic field. These frequencies depend on the nucleus and its chemical environment. 2) In an NMR experiment, a sample is placed in a strong magnetic field which causes atomic nuclei to align with the field. Radio waves are then applied and nuclei absorb at characteristic frequencies. 3) The frequencies observed in the NMR spectrum provide information about a molecule's structure by indicating chemically distinct nuclear environments.

1. Nuclear Magnetic Resonance Spectroscopy
In 1945, Felix Bloch and Edward Purcell described the
phenomenon of NMR.
The Nobel Prize in Physics 1952
NMR spectra are observed upon absorption of a photon of energy and the transition of
nuclear spins from ground to excited states.
The observations that nuclear transitions differed in frequency from one nucleus to another
and also showed subtle differences according the nature of the chemical group made a large
impact of NMR.

2. Nuclear Magnetic Resonance Spectroscopy
For the proton this property meant that proteins exhibited many signals with, for example, the
methyl protons resonating at different frequencies to amide protons which in turn are different
to the protons attached to the α or β carbons.
In 1957, the first NMR spectrum of a protein (ribonuclease)
was recorded, but progress as a structural technique
remained slow until Richard Ernst described the use of
transient techniques.
Nobel Prize in Chemistry in 1991
Transient signals produced after a pulse of radio frequency
(.1 to 1000 MHz) radiation are converted into a normal
spectrum by the mathematical process of Fourier
transformation.

3. Nucleons
The shell model for the nucleus tells us that nucleons, just like electrons, fill orbital. When the
number of protons or neutrons equals 2, 8, 20, 28, 50, 82, and 126, orbital are filled.
What is nucleons or nuclides?
Spin is a fundamental property of nature like electrical charge or mass. Spin comes in
multiples of 1/2 and can be + or -. Individual unpaired electrons, protons and neutrons each
possesses a spin of 1/2.

4. Spin 1/2 nuclei represent the simplest situation and arise when the number of neutrons plus
the number of protons is an odd number.
When the number of neutrons and the number of protons are
both odd, this leads to the nucleus having an integer spin (i.e.
S=1, 2, 3, etc). For example, in the deuterium atom (2H), with
one unpaired electron, one unpaired proton and one unpaired
neutron, the total electronic spin = 1/2 and the total nuclear
spin =1.
Two or more particles with spins having opposite signs can
pair up to eliminate the observable manifestations of spin.
This occurs when the number of neutrons and the number of
protons are even. For example, helium (2
4He) whose spin
number equals zero.

5. The associated quantum number is known as the magnetic quantum number (m) and can take
values from +I to −I, in integer steps. Hence for any given nucleus, there are a total of 2I + 1
angular momentum states.
In NMR, it is unpaired nuclear spins that are of importance. Molecules having spin zero, show
no magnetic field and from a NMR standpoint are uninteresting.
The basis for NMR is the observation that many atomic nuclei spin about an axis and generate
their own magnetic field or magnetic moment.

6. Spin states
When a sample is kept in a tube, the magnetic moments of its
hydrogen atoms are randomly oriented.
It is referred to as the +½ spin state if the hydrogen's
magnetic moment is aligned with the direction of B0,
while in the -½ spin state if it is aligned opposed to
the direction of B0.
When the same sample is placed within the field of a very
strong magnet (applied field, B0), each hydrogen will
assume one of two possible spin states.

7. Think of the spin of this proton as a magnetic moment vector, causing the proton to behave
like a tiny magnet with a north and south pole.
When the proton is placed in an external magnetic field, the spin vector of the particle aligns
itself with the external field, just like a magnet would. There is a low energy configuration or
state where the poles are aligned N-S-N-S and a high energy state N-N-S-S.
To understand how particles with spin behave in a magnetic field, consider a proton. This
proton has the property called spin.

8. When a top slows down a little and the spin axis is no longer completely vertical, it begins to
exhibit precessional motion, as the spin axis rotates slowly around the vertical. In the same
way, hydrogen atoms spinning in an applied magnetic field also exhibit precessional motion
about a vertical axis. It is this axis (which is either parallel or antiparallel to B0) that defines
the proton’s magnetic moment.
Nuclear precession

9. The condition for resonance
The frequency of precession (also called the Larmour frequency, ωL) is simply the number
of times per second that the proton precesses in a complete circle. A proton’s precessional
frequency increases with the strength of B0.
If a proton that is precessing in an applied magnetic field is exposed to electromagnetic
radiation of a frequency ν that matches its precessional frequency ωL, we have a condition
called resonance.

10. In the resonance condition, a proton in the lower-energy +½ spin state (aligned with B0) will
transition (flip) to the higher energy –½ spin state (opposed to B0). In doing so, it will absorb
radiation at this resonance frequency ν = ωL.
This frequency corresponds to the energy difference between the proton’s two spin states.
The difference in energy between the two spin states increases with increasing strength of B0.

11. Boltzmann Statistics
At room temperature, the +½ spin state is slightly lower in energy whereas, –½ state is higher
in energy. Thus, in a large population of organic molecules slightly more than half of the
hydrogen atoms will occupy +½ state (Np) while slightly less than half will occupy the –½
state (Nap).
Boltzmann statistics tells us that
Nap/Np = e-ΔE/kT =exp [(γ* h/2π *B0)/ kT].
ΔE is the energy difference between the spin states; k is
Boltzmann's constant (1.3805x10-23 J/Kelvin) and T is the
temperature in Kelvin.
As the temperature decreases, so does the ratio Nap/Np. As the
temperature increases, the ratio approaches one.

12. The energy of these levels is given by the classical formula for a magnetic dipole in a
homogenous magnetic field of the strength B0:
E = - µz * B0 = - m*γ*h/(2π)*B0
where m=magnetic quantum number, γ = gyromagnetic ratio, h=Plank’s constant.
The Larmor frequency depends on the gyromagnetic ratio and the strength of the magnetic
field i.e. ωL = γ * B0. Thus, it is different for different isotopes.

13. In the NMR experiment, the frequency of the photon is in the radio frequency (RF) range.
ΔE= 8.0 x 10-5 kJ/mol for magnetic field strength of 4.7T.
For hydrogen nuclei, ν= ωL is between 60 and 800 MHz.
For field strength of 4.7T, radiofrequency (rf) of ν= 200 MHz is required to bring 1H nuclei
into resonance.
At a magnetic field of 18.7T, the Larmor frequency of protons is 800 MHz.
For a field strength of 4.7T, radiofrequency (rf) of ν = 50 MHz is required to bring 13C nuclei
into resonance.

14. Resonance frequencies are not uniform for all protons in a molecule. In an external magnetic
field of a given strength, protons in different locations in a molecule have different resonance
frequencies, because they are in non-identical electronic environments.
On the other hand, the three Ha protons are all in the same electronic environment and are
chemically equivalent to one another. They have identical resonance frequencies. The same is
true for the three Hb protons.
The Nature of NMR absorptions
For example, in methyl acetate, there are two ‘sets’ of protons. The three protons labeled Ha
have a different resonance frequency than the three Hb protons, because the two sets of
protons are in non-identical environments (they are chemically nonequivalent).

15. The ability to recognize chemical equivalency and nonequivalency among atoms in a
molecule is central to understanding NMR.
In each of the molecules below, all protons are chemically equivalent and therefore will have
the same resonance frequency in an NMR experiment.

16. Schematic operation of a basic NMR spectrometer

17. Nuclei with the following properties exhibit NMR phenomenon
• All nuclei with odd number of protons
• All nuclei with odd number of neutrons
The NMR behavior of some common nuclei
Magnetic nuclei Non-magnetic nuclei
1H 12C
13C 16O
2H 32S
14N
19F
31P
NMR-active nuclei
Narrow NMR absorption range
• 0 to 10 δ for 1H NMR
• 0 to 220 δ for 13C NMR

18. The basics of an NMR experiment
Given that chemically nonequivalent protons have different resonance frequencies in the same
applied magnetic field, we can see how NMR spectroscopy can provide us with useful
information about the structure of an organic molecule.
All of the protons begin to precess: the Ha protons at precessional frequency ωa, the Hb
protons at ωb. At first, the magnetic moments of slightly more than half of the protons are
aligned with B0 and half are aligned against B0.
Let us assume that a sample compound (e.g. methyl acetate) is placed inside a very strong
applied magnetic field (B0).

19. In doing so, the protons absorb radiation at the two resonance frequencies. The NMR
instrument records which frequencies were absorbed, as well as the intensity of each
absorbance.
• Chemically equivalent nuclei always show the same absorption
• The two methyl groups of methyl acetate are nonequivalent
Then, the sample is hit with electromagnetic radiation in the radio frequency range. The two
specific frequencies which match ωa and ωb (i.e. the resonance frequencies) cause those Ha
and Hb protons which are aligned with B0 to 'flip' so that they are now aligned against B0.

20. In most cases, a sample being analyzed by NMR is in solution. If we use a common laboratory
solvent (diethyl ether, acetone, dichloromethane, ethanol, water, etc.) to dissolve our NMR
sample, we may run into a problem. Because there are many more solvent protons in solution
than there are sample protons, so the signals from the sample protons will be overwhelmed.
Choosing the solvent for NMR
Note that deuterium is NMR-active, but its resonance frequency is very different from that of
protons and thus it is `invisible` in 1H-NMR.
To resolve this problem, a special NMR solvents is used in which all protons have been
replaced by deuterium. Some common NMR solvents are shown below.

21. The chemical shift
Let's look again at 1H-NMR plot for methyl
acetate. The vertical axis corresponds to
intensity of absorbance, the horizontal axis to
frequency.
We see three absorbance signals: two of these correspond to
Ha and Hb.
While the peak at the far right of the spectrum corresponds to
the 12 chemically equivalent protons in tetramethylsilane
(TMS), a standard reference compound added to the sample.

22. What is the meaning of the `ppm (δ)` label on the horizontal axis? Shouldn't the
frequency units be in Hz?
MHzinfrequencyerspectromet
TMS)to(relativeHzinpositionPeak
ppm)(inδ
Since different NMRs have different operating frequencies, spectra cannot be compared from
different machines if they are reported in frequency units.
For this reason, the universal ppm (parts per million) units are used in NMR. The frequency
and ppm are directly proportional.
NMR instruments of many different applied field strengths are used in different laboratories
and that the proton's resonance frequency range depends on the strength of the applied field
(ωL = γ * B0). If the external field is larger, the frequency needed to induce the +1/2 state to -
1/2 state transition is larger. It follows then that in a larger field, higher frequency radio waves
would be needed to induce the transition.

23. Why do we see peaks?
A peak will be observed for every magnetically distinct nucleus in a molecule. This happens
because nuclei that are not in identical structural situations do not experience the external
magnetic field to the same extent. The nuclei are shielded or deshielded due to small local
fields generated by circulating sigma, pi and lone pair electrons.
When the excited nuclei in the anti-parallel orientation start to relax back down to the parallel
orientation, a fluctuating magnetic field is created. This fluctuating field generates a current in
a receiver coil that is around the sample. The current is electronically converted into a peak. It
is the relaxation that actually gives the peak, not the excitation.
Why do we see peaks at different positions?

24. The two proton groups in our methyl acetate
sample are recorded as resonating at frequencies
2.05 and 3.67 ppm higher than TMS.
Assuming that spectrometer frequency is 300 MHz, what will be the frequency for 2.05
and 3.67 ppm?
2.05 ppm will correspond to 615 Hz and 3.67 ppm willl correspond to 1101 Hz.
If the TMS protons observed by our 7.1T instrument resonate at exactly 300,000,000 Hz, this
means that the protons in the methyl acetate samples are resonating at 300,000,615 and
300,001,101 Hz, respectively.
Exercise: Find out the resonating frequency of these peaks of an instrument of 2.4T magnet
which generate 100 Mz radio frequency?

25. The resonance frequency for a given proton in a molecule is called its chemical shift (δ in
ppm).
Most protons in organic compounds have chemical shift values between 0 and 12 ppm from
TMS, although values below zero and above 12 are occasionally observed.
By convention, the left-hand side of an NMR spectrum (higher chemical shift) is called
downfield and the right-hand direction is called upfield.