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

1. 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

2. 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.

3. 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

4. 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

5. “Improved” Stern-Gerlach Experiment (Feynman Lectures on Physics) ? Spin ½ particle (e.g. silver atoms)

6. “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.

7. “Improved” Stern-Gerlach Experiment (Feynman Lectures on Physics) ? Spin ½ particle (e.g. silver atoms)

8. “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.

9. 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.

10. 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.

11. 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.

12. Graphical Interpretation

13. Value of the angular momentum along the z-axis Number of possible states: 2I+1 Magnitude of the angular momentum To Summarize…

14. 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

15. 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

16. 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.

17. 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).

18. 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?

19. 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