Fast Course in NMR Lecture 1 Jan/Feb, 2016 Instructor: Art Edison Email address: [email protected] Office: CCRC 1040 Web page with class notes: http://edison.ccrc.uga.edu/ A. S. Edison University of Georgia 2016 Overview Brief Introduction to: Spin Classical motion in a magnetic field (Bloch) Parameters that are measured

Product operators Data collection and Fourier transform 2D NMR Homonuclear 2D Heteronuclear 2D A. S. Edison University of Georgia 2016 Overall goal: To get everyone acquainted with the basic physics and principles of NMR. What isnt covered: Details of any specific application like metabolomics, proteins, etc. In depth coverage of any of the basics, which would require a much longer class.

A. S. Edison University of Georgia 2016 Recommended Materials 1) 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(good practical resource) 2) "NMR of Proteins and Nucleic Acids", by Kurt Wuthrich (ISBN 0-471-82893-9) (Old standard; out of date but still useful and practical) 3) "Protein NMR Spectroscopy: Principles and Practice by John Cavanagh, Arthur G., III Palmer, Wayne Fairbrother (Contributor),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) 5) Understanding NMR Spectroscopy, second edition, James Keeler (highly recommended by some of my students and postdocs) 4) NMR Data Processing Jeff Hoch and Alan Stern (Great book on processing, FT, and alternatives) 5) The Nuclear Overhauser Effect in Structural and Conformational Analysis, Second Ed. David Neuhaus and Michael Williamson (The best reference for the NOE)

6) "Spin Dynamics: Basics of Nuclear Magnetic Resonance, by Malcolm H. Levitt 7) "Spin Choreography: Basic Steps in High Resolution NMR" by Ray Freeman 8) Principles of Nuclear Magnetic Resonance in One and Two Dimensions by Ernst, Bodenhausen, and Wokaun (The New Testament) 9) Principles of Nuclear Magnetism by Abragam (The Old Testament) Physics: The Feynman Lectures on Physics (Addison Wesley) Modeling/self study: Mathematica or MATLAB. A. S. Edison University of Georgia 2016 What is spin? 5 min to jot a few notes to yourself A. S. Edison University of Georgia

2016 Todays Lecture Behavior of nuclear spins in a magnetic field I Stern-Gerlach Improved Stern-Gerlach Brief Angular momentum review Rabbi experiment A. S. Edison University of Georgia 2016 Stern-Gerlach Experiment Any particle with spin

B =0 z Spin particle (e.g. 107Ag or 1H) B 0 z Spin 1 particle (e.g. 2H) B 0 z

Spin 3/2 particle (e.g. 7Li) B 0 z 2I+1 Energy Levels https://phet.colorado.edu/sims/stern-gerlach/stern-gerlach_en.html A. S. Edison University of Georgia 2016 Improved Stern-Gerlach Experiment (Feynman Lectures on Physics) ?

B 0 z Spin particle (e.g. silver atoms) B 0 z A. S. Edison University of Georgia 2016 Improved Stern-Gerlach Experiment (Feynman Lectures on Physics) B

0 z Spin particle (e.g. silver atoms) B 0 z Once we have selected a pure component along the z-axis, it stays in that state. A. S. Edison University of Georgia 2016

Improved Stern-Gerlach Experiment (Feynman Lectures on Physics) ? B 0 x Spin particle (e.g. silver atoms) B 0 z A. S. Edison University of Georgia 2016

Improved Stern-Gerlach Experiment (Feynman Lectures on Physics) back out B 0 x Spin particle (e.g. silver atoms) B 0 z

Whatever happened along the zaxis doesnt matter anymore if we look along the x-axis. It is once again split into 2 beams. A. S. Edison University of Georgia 2016 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. A. S. Edison University of Georgia 2016 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=(- I ,- I + 1,..., I - 1, I ) m and I are quantum numbers. For a given I (e.g. ), m can take

values from I to +I. Thus, there are 2I+1 states. A. S. Edison University of Georgia 2016 More Specifically A spin 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. b

B0=0 a B0>0 The states have different energies but have the same magnitude of the angular momentum. A. S. Edison University of Georgia 2016 Graphical Interpretation A. S. Edison University of Georgia 2016

To Summarize Value of the angular momentum along the z-axis m=( - I ,- I + 1,..., I - 1, I ) Number of possible states: 2I+1 Magnitude of the angular momentum A. S. Edison University of Georgia 2016 Spin angular momentum is proportional to the magnetic moment The magnetic moment (m) is a vector parallel to the spin angular momentum. The gyromagnetic (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. m=(- I ,- I + 1,..., I - 1, I ) A. S. Edison University of Georgia 2016 Now we can find the energy of a magnetic moment in a magnetic field 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 zaxis. 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 A. S. Edison University of Georgia 2016 The Stern-Gerlach experiment can now be understood E B Fz ==m cos q =maz z z 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. A. S. Edison

University of Georgia 2016 I. I. Rabi molecular beam experiment to measure g (Feynman Lectures on Physics) B0 z OVEN Detector B >0 z B =0 Slit

z Frequency Generator w 0 =- gB0 w0 w B <0 z Slit The coil produces a magnetic field along the x-axis (going into the board). http://mri-q.com/who-discovered-nmr.html

When the frequency reaches resonance, particles no longer reach the detector. A. S. Edison University of Georgia 2016 What is spin? Discussion A. S. Edison University of Georgia 2016 The Boltzmann equation tells us the population of a state if we know its energy Eb - Ea

Na =e Nb kBT Self Study: 1) 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? 5) What is the ratio of the number of spins in the a state to the b state at 1 mK in a magnetic field of 11.7 T for 1H? A. S. Edison University of Georgia

2016 Next Lecture 2) Behavior of nuclear spins in a magnetic field II a. Bloch equations b. Phenomenological introduction to T1 and T2 c. RF Pulses A. S. Edison University of Georgia 2016