Loading in 5 sec....

Molecular Structure and Dynamics by NMR Spectroscopy BCH 6745C and BCH 6745L Fall, 2008PowerPoint Presentation

Molecular Structure and Dynamics by NMR Spectroscopy BCH 6745C and BCH 6745L Fall, 2008

Download Presentation

Molecular Structure and Dynamics by NMR Spectroscopy BCH 6745C and BCH 6745L Fall, 2008

Loading in 2 Seconds...

- 504 Views
- Updated On :
- Presentation posted in: Sports / GamesEducation / CareerFashion / BeautyGraphics / DesignNews / Politics

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

Molecular Structure and Dynamics by NMR Spectroscopy BCH 6745C and BCH 6745L Fall, 2008

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Molecular Structure and Dynamics by NMR Spectroscopy

BCH 6745C and BCH 6745L

Fall, 2008

- Instructors: Arthur S. Edison and Joanna Long
- email address: art@mbi.ufl.edu & jrlong@mbi.ufl.edu
- Office: LG-187 (ground floor of the McKnight Brain Institute)
- Web page with class notes: http://edison.mbi.ufl.edu
- Office Hours: By appointment

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.

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

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

“Improved” Stern-Gerlach Experiment

(Feynman Lectures on Physics)

?

Spin ½ particle (e.g. silver atoms)

“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.

“Improved” Stern-Gerlach Experiment

(Feynman Lectures on Physics)

?

Spin ½ particle (e.g. silver atoms)

“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.

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.

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.

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.

Graphical Interpretation

Value of the angular momentum along the z-axis

Number of possible states: 2I+1

Magnitude of the angular momentum

To Summarize…

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

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

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.

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).

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?

Next Friday’s Lecture

- 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