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.

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.

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.

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 (24He) whose spin

number equals zero.

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.

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.

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.

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

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.

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.

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.

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.

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.

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).

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.

Schematic operation of a basic NMR spectrometer

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

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).

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.

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.

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.

What is the meaning of the `ppm (δ)` label on the horizontal axis? Shouldn't the

frequency units be in Hz?

MHzin frequency er spectromet

TMS) to(relative Hzin position Peak ppm)(in δ

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.

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?

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?

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.