Molecular Structure and Dynamics by NMR Spectroscopy

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Molecular Structure and Dynamics by NMR
Spectroscopy BCH 6745C and BCH 6745L Fall, 2006

• Instructors Arthur S. Edison and Joanna Long
• email address art_at_mbi.ufl.edu
  jrlong_at_mbi.ufl.edu
• Office LG-187 (first floor of the McKnight
  Brain Institute)
• Web page with class notes http//edison.mbi.ufl.
  edu
• Office Hours By appointment

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Recommended Materials

• High-Resolution NMR Techniques in Organic
  Chemistry, Timothy D. W. Claridge, Elsevier,
  1999. ISBN 0 08 042798 7 (good practical
  resource)
• 2) "NMR of Proteins and Nucleic Acids", by Kurt
  Wuthrich (ISBN 0-471-82893-9) (Old standard very
  useful and practical)
• 3) "Protein NMR Spectroscopy Principles and
  Practice by John Cavanagh, Arthur G., III
  Palmer, Wayne Fairbrother (Contributor), Nick
  Skelton (Contributor) (Great theoretical and for
  serious student)
• 4) "Spin Dynamics Basics of Nuclear Magnetic
  Resonance, by Malcolm H. Levitt
• 5) "NMR The Toolkit" (Oxford Chemistry Primers,
  92)by P. J. Hore, J. A. Jones, Stephen Wimperis
• 6) "Spin Choreography Basic Steps in High
  Resolution NMR" by Ray Freeman
• 7) Mathematica or Matlab.

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Todays Lecture

• Friday, Nov 29 Behavior of nuclear spins in a
  magnetic field I
• Stern-Gerlach
• Improved Stern-Gerlach
• Brief Angular momentum review
• Rabbi experiment

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Stern-Gerlach Experiment
2I1 Energy Levels
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Improved Stern-Gerlach Experiment (Feynman
Lectures on Physics)
?
Spin ½ particle (e.g. silver atoms)
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Improved Stern-Gerlach Experiment (Feynman
Lectures on Physics)
Spin ½ particle (e.g. silver atoms)
Once we have selected a pure component along the
z-axis, it stays in that state.
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Improved Stern-Gerlach Experiment (Feynman
Lectures on Physics)
?
Spin ½ particle (e.g. silver atoms)
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Improved Stern-Gerlach Experiment (Feynman
Lectures on Physics)
back
out
Spin ½ particle (e.g. silver atoms)
Whatever happened along the z-axis doesnt matter
anymore if we look along the x-axis. It is once
again split into 2 beams.
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What is spin?
Spin is a quantum mechanical property of many
fundemental particles or combinations of
particles. It is called spin because it is a
type of angular momentum and is described by
equations treating angular momentum.
Angular momentum is a vector. Ideally, we would
like to be able to determine the 3D orientation
and length of such a vector. However, quantum
mechanics tells us that that is impossible. We
can know one orientation (by convention the
z-axis) and the magnitude simultaneously, but the
other orientations are completely unknown.
Another way of stating the same thing is that the
z-component (Iz) and the square of the magnitude
(I2) simultaneously satisfy the same
eigenfunctions.
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What is spin?
When a particle is in state f, we can know the
z-component
and also the magnitude at the same time.
m and I are quantum numbers. For a give I (e.g.
½), m can take values from I to I. Thus, there
are 2I1 states.
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More Specifically
A spin ½ particle has 2 states which can be
called up and down, 1 and 2, Fred and
Marge, We will usually refer to them as
a and b. The Stern-Gerlach experiment shows
that these states have different energies in a
magnetic field (B0), but they are degenerate in
the absence of a magnetic field.
The states have different energies but have the
same magnitude of the angular momentum.
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Graphical Interpretation
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To Summarize
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Spin angular momentum is proportional to the
magnetic moment
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Now we can find the energy of a magnetic moment
in a magnetic field
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The Stern-Gerlach experiment can now be understood
The force on a particle with a magnetic moment in
a magnetic field is proportional to the
derivative (gradient) of the magnetic field in
the direction of the force. No gradient, no
force.
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I. I. Rabi molecular beam experiment to measure
g (Feynman Lectures on Physics)
B0
z
The coil produces a magnetic field along the
x-axis (going into the board).
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The Boltzmann equation tells us the population of
a state if we know its energy

• Homework due next Wed
• What is the ratio of the number of spins in the a
  state to the b state in no magnetic field?
• 2) What is the ratio of the number of spins in
  the a state to the b state at room temperature in
  a magnetic field of 11.7 T (500 MHz) for 1H?
• 3) What is the ratio of the number of spins in
  the a state to the b state at room temperature in
  a magnetic field of 11.7 T (500 MHz) for 13C?
• 4) What is the ratio of the number of spins in
  the a state to the b state at room temperature in
  a magnetic field of 21.1 T (900 MHz) for 1H?

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Next Mondays Lecture
2) Mon, Oct 2 Behavior of nuclear spins in a
magnetic field II a. Teach Spin apparatus b.
Bloch equations c. Phenomenological introduction
to T1 and T2 c. RF Pulses