Molecular Structure and Dynamics by NMR Spectroscopy
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Molecular Structure and Dynamics by NMR Spectroscopy BCH 6745C and BCH 6745L Fall, 2008 Instructors: Arthur S. Edison and Joanna Long email address: [email protected] & [email protected] Office: LG-187 (ground floor of the McKnight Brain Institute)

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Molecular Structure and Dynamics by NMR Spectroscopy

BCH 6745C and BCH 6745L

Fall, 2008

  • Instructors: Arthur S. Edison and Joanna Long

  • email address: [email protected] & [email protected]

  • Office: LG-187 (ground 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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Today’s Lecture

  • Wed, Oct 1: Behavior of nuclear spins in a magnetic field I

    • Stern-Gerlach

    • “Improved” Stern-Gerlach

    • Brief Angular momentum review

    • Rabbi experiment


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Any particle with spin

Spin ½ particle (e.g. 107Ag or 1H)

Spin 1 particle (e.g. 2H)

Spin 3/2 particle (e.g. 7Li)

Stern-Gerlach Experiment

2I+1 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 doesn’t 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 given I (e.g. ½), m can take values from –I to +I. Thus, there are 2I+1 states.


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b

B0=0

a

B0>0

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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Value of the angular momentum along the z-axis

Number of possible states: 2I+1

Magnitude of the angular momentum

To Summarize…


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The magnetic moment (m) is a vector parallel to the spin angular momentum. The gyromagneto (or magnetogyro) ratio (g) is a physical constant particular to a given nucleus.

Therefore, the value of the z-component of m takes the following values.

Spin angular momentum is proportional to the magnetic moment


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The magnetic field (B) is also a vector. The dot product of 2 vectors (e.g. m and B) is a scalar.

In NMR we start with a large static field, B0, that is defined as the component of B along the z-axis. Thus, the only term that survives the dot product is the value of m along the z-axis (mz).

Em is the value of the energy for a particular value of the quantum number m

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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w0

w

When the frequency reaches resonance, particles no longer reach the detector.

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 14.1 T (600 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 Friday’s Lecture we know its energy

  • 2) Fri, Oct 3: 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


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