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Advanced Nuclear Magnetic Resonance
Spectroscopy
Ala-Arg-Pro-Tyr-Asn-Phe-Cpa-Leu-NH2
Cpa
Ala
Pro
Guillermo Moyna - Spring 1999
Why bother learning NMR?
• Structural (chemical) elucidation
• Natural product chemistry.
• Synthetic organic chemistry. Analytical tool of choice of
synthetic chemists.
• Study of dynamic processes
• Reaction kinetics.
• Study of equilibrium (chemical or structural).
• Structural (three-dimensional) studies
• Proteins.
• DNA. Protein/DNA complexes
• Polysaccharides
• Drug design
• Structure Activity Relationships by NMR
• Medicine - MRI
The gory details
• Absorption (or emission) spectroscopy, as IR or UV. Detects
the absorption of radiofrequencies (electromagnetic radiation)
by certain nuclei in a molecule.
• Unfortunately, some quantum mechanics are needed to
understand it (a lot to really understand it…).
• Only nuclei with spin number (I)  0 can absorb/emit electromagnetic radiation.
• Even atomic mass & number  I = 0 (12C, 16O)
• Even atomic mass & odd number  I = whole integer
(14N, 2H, 10B)
• Odd atomic mass  I = half integer (1H, 13C, 15N, 31P)
• The spin states of the nucleus (m) are quantified:
m = I, (I - 1), (I - 2), … , -I
• Properly, m is called the magnetic quantum number.
Background (continued)
• For 1H, 13C, 15N, 31P (biologically relevant nuclei) then:
m = 1/2, -1/2
• This means that only two states (energy levels) can be
taken by these nuclei.
• Another important parameter of each particular nuclei is
the magnetic moment (m), which can be expressed as:
m = g I h / 2p
• It is a vector quantity that gives the direction and magnitude
(or strength) of the ‘nuclear magnet’
• h is the Planck constant
• g is the gyromagnetic ratio, and it depends on the
nature of each nuclei.
• Different nuclei have different magnetic moments.
Effect of a magnetic field (for I = 1/2)
• In the ground state all nuclear spins are disordered, and there
is no energy difference between them. They are degenerate:
= g h / 4p
• Since they have a magnetic moment, when we apply a strong
external magnetic field (Bo), they orient either against or with it:
Bo
• There is always a small excess of nuclei (population excess)
aligned with the field than pointing against it.
Energy and populations
• Upon application of the external magnetic field we create an
energy difference between nuclei aligned and against Bo:
b
DE = h n
Bo > 0
a
Bo = 0
• Each level has a different population (N), and the difference
between the two is related to the energy difference by the
Boltzmman distribution:
N a / Nb = e
DE / kT
• The DE for 1H at 400 MHz (Bo = 9.5 T) is 3.8 x 10-5 Kcal / mol
Na / Nb = 1.000064
• The surplus population is small when compared to UV or IR.
Energy and sensitivity
• The energy (for a single spin) is proportional to the magnetic
moment of the nuclei and the external magnetic field:
E = - m . Bo  E(up) = g h Bo / 4p --- E(down) = - g h Bo / 4p
DE = g h Bo / 2p
• This has implications on the energy (i.e., the intensity of the
signal and sensitivity) that each nuclei can absorb:
• Bigger magnets (bigger Bo) make more sensitive NMR
instruments.
• Nuclei with larger g absorb/emit more energy and are
therefore more sensitive. Sensitivity is proportional to
m, to Na - Nb, and to the ‘coil magnetic flux’, which are
all dependent on g. Therefore, it is proportional to g3.
g13C = 6,728 rad / G
g1H = 26,753 rad / G
1H
is ~ 64 times more sensitive
than 13C just because of the g
• If we consider natural abundance,
6400 times less sensitive...
13C
(~1%) ends up being
Energy and frequency
• Since energy is related to frequency, we can do some
insightful math…
DE = h n
DE = g h Bo / 2p
n = g Bo / 2p
• For 1H in normal magnets (2.35 - 18.6 T), this frequency is
in the 100-800 MHz range. For 13C, 1/4 of that…
g-rays x-rays UV VIS
10-10
10-8
IR
m-wave radio
10-6 10-4
10-2
wavelength (cm)
100
102
• To explain certain aspects of NMR, we need to refer to
circular motion. Hz are not the best units to do so. We define
the precession or Larmor frequency, w:
w = 2pn

wo = g Bo (radians)
Precession and spinning tops
• What precession is wo associated with? One thing that we
left out from the mix is the angular momentum, l, which
is associated with all nuclei:
l
• Crudely, we can think of the nuclei as being spinning around
its z axis. If we now consider those nuclei that have also a
non zero m, we have little spinning atomic magnets.
• Now, if we bring about a big Bo, there will be an interaction
between m and Bo that generates a torque. No matter which
is the original direction of m, it will tend to align with Bo:
m
Bo
Bo
or...
m
Precession (continued)
• Now it starts getting exciting (?). Since the nuclei associated
with m is spinning due to l, there are two forces acting on it.
One that wants to bring it towards Bo, and one that wants to
keep it spinning. m ends up precessing around Bo:
wo
m
Bo
• The best way to picture it is to imagine a spinning wooden top
under the action of gravity.
• The frequency at which m precesses around Bo is the same
as the one derived from energetic considerations.
• Although there is no apparent connection between these two
frequencies, the relationship comes about automatically if we
do a rigorous quantum mechanical derivation. Some of the
phenomena are a black box for the classical NMR model...
Bulk magnetization
• We see the effects on macroscopic magnetization, Mo, which
is directly proportional to the population difference (Na - Nb),
in which contributions from different ms have been averaged:
z
z
Mo
x
y
x
y
Bo
Bo
• We can decompose each little m in a z contribution and an
<xy> plane contribution. The components in the <xy> plane
are randomly distributed and cancel out. For the ones in z,
we get a net magnetization proportional to Na - Nb.
• Since this is (more or less) the situation in a real sample, we
will from now on use Mo in all further descriptions/examples.
• There is an important difference between a m and Mo. While
the former is quantized and can be only in one of two states
(a or b), the latter tells us on the whole spin population. It
has a continuous number of states.
Next class topics
• Bulk magnetization and vector models.
• Simple excitation of average magnetization.
• Laboratory and rotating frames.
• Chemical shift (d)
• Spin-spin coupling (J). Energy diagrams for systems
of two coupled spins.