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NMR, nuclear magnetic resonance, is important because it provides a powerful way to
deduce the structures of organic molecules. In addition, the same principle is used in
MRI medical imaging. Unfortunately, the physics behind NMR is extremely
complicated. What follows is an attempt to provide all the information you need to
understand the basic principles underlying the NMR technique.
Charge-magnetic field interactions:
1) Moving charge creates a magnetic field.
2) Charges will interact with an external magnetic field (created by a big magnet in
the laboratory), causing them to move in response to the field. This, in turn,
induces an additional magnetic field because of 1) above.
3) This is how electromagnets and other cool things work, but also describes how
charged subatomic particles, namely electrons and protons in molecules, interact
with a magnetic field and with each other.
Quantum mechanical description of nuclear spin. These are the essential facts you need
before we describe NMR.
1)
Atomic nuclei with an odd atomic mass or an odd atomic number have a
quantum mechanical property called “spin” that is designated by a spin
quantum number such as 1/2 or 1. For NMR experiments, we are only
concerned with nuclei having a spin quantum number of 1/2. In particular we
are interested in 1H (most common isotope of hydrogen by far) and 13C (rare
but useful isotope of carbon, the most common isotope being 12C). Recall
from general chemistry that the number 1,12, 13 etc. is the atomic mass, that
is, the total number of protons and neutrons in the given isotope.
A) Nuclear spin can be thought of as the positive charge of protons
“circulating”. In other words you should think about nuclear spin as
circulating charge. I know this sounds weird, but just accept it and realize
this is best way to think about spin. There are two consequences here:
i. Nuclear spin can interact with an external magnetic field.
ii. Nuclear spin creates its own magnetic field that can interact with
other nuclei having spin.
2)
Nuclei with spin can have only a fixed number of allowed states (i.e. the
number of states are quantized, hence the term quantum mechanics).
A) Nuclei with spin quantum number of 1/2 have two allowed spin states,
+1/2 and –1/2. “Allowed” is a fancy way of saying this is what can
happen. In other words, any given nucleus will either be in a spin state of
+1/2 or –1/2.
B) In the absence an external magnetic field, nuclei in either a +1/2 or –1/2
spin state are of the same energy.
C) The key idea for the NMR experiment is that in an external magnetic field,
the two spin states have different energies. The +1/2 spin state is lower in
energy, and the –1/2 spin state is higher in energy. The difference in
energy is proportional to the strength of the external magnetic field. In
other words, the bigger the magnet in the laboratory, the larger the
difference in energy between +1/2 and –1/2 nuclear spin states.
Now, review the above so you can recite all of the points. These form the basis of the
NMR experiment. Sorry about the complicated story here, but this is important for
another reason. It answers the question “How does MRI work?”, a question many of you
will be asked when you become physicians.
The NMR experiment
1) The simplest NMR experiment is carried out such that a sample is placed in a
strong, constant magnetic field. Electromagnetic radiation of the proper
wavelength is added and the sample absorbs the energy as nuclear spins are
excited from the lower energy spin state (+1/2) to the higher energy spin state
(-1/2).
a. The NMR spectrometer measures when the wavelength of the energy
that is absorbed.
b. The electromagnetic radiation used is in the radio frequency range in
energy.
2) The NMR spectrometer consists of a strong magnet in which the sample is
placed (inside a tube). A radiofrequency generator excites the sample, and
sensitive electronics detect when the energy is absorbed.
3) Modern NMR spectrometers operate using the principle of Fourier transform,
but this is beyond the scope of this class. I just wanted you to know this was
out there, but we will not be discussing it further because it requires an
explanation of much more complex quantum mechanics.
Information obtained from and NMR spectrum
1)
If all nuclei in a molecule absorbed the same frequency of electromagnetic
radiation, the NMR experiment would not be useful.
2)
In fact, different nuclei absorb radio frequency electromagnetic radiation
at slightly different characteristic frequencies, and because of this you can
determine which types of atoms are present in a molecule. More
importantly, adjacent atoms with spin influence the frequency as well, so
you can tell which atoms are adjacent to each other in a molecule. In other
words, you can determine the structure of an organic molecule with NMR!
More physics.
1)
Both electrons and other nuclei with spin in a molecule have their own
magnetic fields.
2)
The magnetic field “felt” by any given nucleus in a molecule is actually
the sum of (i) the external magnetic field plus (ii) the magnetic field of the electrons
around the nucleus plus (iii) the magnetic fields caused by the different spin states of
adjacent nuclei.
A)
Electron density around a nucleus circulates in a
characteristic fashion when placed in the magnetic field.
This circulation creates its own magnetic field that
B)
opposes the external magnetic field. Thus, nuclei
surrounded by more electron density are more shielded
from the external magnetic field and these nuclei “feel” a
smaller total magnetic field. Nuclei surrounded by less
election density are less shielded. Read these sentences
again as they are key to understanding NMR, and this
concept is really subtle.
The magnetic field produced by a nucleus in a –1/2 spin
state is different than a nucleus in a +1/2 spin state. At
room temperature, any given nucleus in a magnetic field
has only a slight excess of probability of being in the
lower energy state. Thus, across a population of
molecules in a sample, it is roughly 50-50 whether a
given nucleus is in the +1/2 or –1/2 spin state.
Chemical equivalence
Here is the hardest part of all and the last piece of the puzzle. Certain atoms in a
molecule are equivalent. Trust me this is important and it is key to the NMR story.