Advanced Nuclear Magnetic Resonance

1
Advanced Nuclear Magnetic Resonance Spectroscopy
Guillermo Moyna - Spring 1999
Ala-Arg-Pro-Tyr-Asn-Phe-Cpa-Leu-NH2
Cpa
Ala
Pro
2

• 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

3

• 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 electro-
• magnetic 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

4

• 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

5

• 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
• Since they have a magnetic moment, when we apply
  a strong
• external magnetic field (Bo), they orient
  either against or with it

g h / 4p
Bo
6

• Energy and populations
• Upon application of the external magnetic field
  we create an
• energy difference between nuclei aligned and
  against Bo
• Each level has a different population (N), and
  the difference
• between the two is related to the energy
  difference by the
• Boltzmman distribution

b
Bo gt 0
DE h n
a
Bo 0
7

• 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

g13C 6,728 rad / G g1H 26,753 rad / G
1H is 64 times more sensitive than 13C just
because of the g
8

• Energy and frequency
• Since energy is related to frequency, we can do
  some
• insightful math
• DE h n
• n g Bo / 2p
• DE g h 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 IR m-wave
radio
10-10 10-8 10-6 10-4 10-2
100 102
wavelength (cm)
9

• 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
• 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

l
Bo
Bo
m
or...
m
10

• 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
• The best way to picture it is to imagine a
  spinning wooden top
• under the action of gravity.

wo
m
Bo
11

• 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
• We can decompose each little m in a z
  contribution and an
• ltxygt plane contribution. The components in the
  ltxygt plane

z
z
Mo
x
x
y
y
Bo
Bo
12

• 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.