Lecture 34: NMR spectroscopy
Review
CD and optical rotation spectroscopies
Today
NMR spectroscopy
o Basic concepts
o Detection of signal
o Natural linewidth, spin-spin relaxation time
o Spin Lattice relaxation time
o Imaging
o Chemical applications
o Chemical shifts
o J-coupling
o 2D-NMR spectroscopy
o Protein structure
Basic Concepts
Nuclei of atoms not only have electrical charge but
they also have spin. For example, hydrogen nucleus
containing single proton has a nuclear spin of ½,
just like electron. Consequence of the spin is that
the nucleus has a magnetic momentum and hence it
can be thought of as tiny magnet (tiny magnetic
dipole). In magnetic field it can assume two
orientations, spin up or down, having different
energies.
In general, nuclear spin can have values different
than ½; the corresponding number of energy levels
is given by 2S+1. The magnetic dipole moment and
energy in the magnetic field is given by:
Thus the energy needed to cause the transition
between the levels is given by:
 hv  h / 2
Thus =B is the fundamental equation of magnetic
resonance.  is known as the Larmor precession
frequency.
NMR basic concepts
Table below presents gyromagnetic ratio of common
nuclei.
The energy involved in causing these nuclear transitions
is much less than kT. Thus in a given sample the upper
and lower energy levels have comparable occupancies.
To detect presence of nuclei we apply an RF field to the
sample at the Larmor frequency of nuclei.
NMR basic concepts
The presence of oscillating magnetic field in the
radiation (radio frequency) can be resolved in to two
polarized fields H1s, rotating with frequencies –0 and
0 corresponding to clockwise and anticlockwise
rotation. Only the component that is stationary in
rotating frame acts upon the magnetic moment causing it
to tip away from the direction of applied external
magnetic field as shown in the figure above. Once the
magnetization reaches x-y plane, the pulsed radio
frequency is turned off and the rotating magnetic
moment (it’s x-y components) is detected using clever
electronics. When Fourier transformed, this time
dependent signal appears as spectrum.
Where T2 is lifetime of nuclei in the excited state that
gives rise to intrinsic broadening to spectral lines.
Physically the tipping of the magnetization is equivalent
to excitation of the nuclei from lower energy state to
higher. There is, however, a fundamental difference in
the “magnetic” spectroscopy compared to the UV visible
spectroscopy. That is it is possible to achieve an
inversion in population of the lower and higher energy
levels. This corresponds to negative spin temperatures!!
NMR imaging
Most of us familiar with Dentist, who take pictures of
teeth bones with X-ray. This method is imminently
suited for imaging bones as it relies on large density
difference between bones
and soft tissues. In midseventies, it became clear
that NMR can also be used
for imaging, especially
imaging of soft-tissues,
which led to the birth of
MRI scans. An image of a
human brain is shown to the
left. This remarkable ability
of NMR to image soft tissues
has revolutionalized medical diagnostics. It works on the
following simple principle. Energy gap between the up
and down spins depends on the strength of the applied
magnetic field. So if we apply a linear magnetic field
gradient to a non-uniform sample, different nuclei at
different location will resonate at different frequencies:
 ( z )   0  kz
However, the detected NMR signal is proportional to the
number nuclei present at a given slice of uniform
magnetic field. Hence, by applying gradients in three
spatial directions, we can construct a three-dimensional
image of an object, such as brain/heart etc. Today it’s not
difficult to construct the image of the entire human body.
Before too long, spatial resolution would approach few
microns enabling early detection of tumors.
Chemical applications: Chemical shift
Just as discussed before, the spectral position of a given
nucleus depends on the external field. Additionally
presence other nuclei or spatial electron distribution, in
molecules, gives rise to small local field at given
nucleus. We call this shielding effect.
Instead of quoting precise frequency position, we use a
common reference such TMS (Tetra-methyl silane)
proton signal position and calculate the relative positions
of other types of nuclei by defining the chemical shift
scale as follows:
Some typical values of chemical shifts of protons are
shown below.
Thus, one of the earliest applications of NMR
spectroscopy was in identification of organic molecules.
Chemical applications: J coupling
Just as the electronic environment affects local magnetic
environment of a given nucleus, it can also be affected
by neighboring nuclei. Recall, each nucleus acts like a
tiny magnet. Depending on the orientation of nuclear
spin, the magnetic field felt by a given nucleus is
different. This has an effect of splitting the energy levels.
J-coupling
The Combination of J-coupling and chemical shift can
give rise to some unusual second order effects in spectra.
Consider two nuclei having chemical shifts of vA and vB,
with coupling constant JAB. If JAB is large compared to
frequency difference between the chemical shifts of the
two nuclei one gets a simple 1st order spectrum;
however as the ratio of the two frequencies become
comparable then situation is more complex as shown
below:
In addition, the magnitude of the j-coupling depends on the
distance and the angle between the bonds. For example,
In this case J varies with angle as follows:
Thus NMR spectroscopy has revolutionalized molecular
structure determination.
2D NMR spectroscopy
In conventional spectroscopy we deal with intensity versus
frequency or wavelength representation. Fortunately in
NMR we can perform a “two dimensional” experiment. In
this case we apply two RF pulses and Fourier transform the
signal with respect to two time intervals; one with respect
to the time of collection of signal after the second pulse,
commonly referred as t2, and also as a function of the time
interval between the two pulses. Resulting 2-D spectrum is
shown below:
This is called as COSY (COrrelated SpectroscopY). Cross
peaks arise between the nuclei that are coupled through j
coupling. This is a very common technique used to
establish the molecular connectivity. Few examples are
shown below.
COSY spectroscopy of amino acids