# NMR Workshops on Saturdays at UM

**When: **Mondays, 7:00pm – 9:30pm

**Where:** Rm 3245, Chemistry Building

Welcome NMR Spinsters!

Taking advantage of the vast NMR experience here at UM, we have organized sessions on various NMR topics, which are held every Monday from 6:30pm to 9:30pm. The purpose is to bring the continuous flow of new students up to date, and to offer refreshers for the more seasoned spectroscopist, on the basics of NMR. Presentations in this workshop cover a range of topics, where we start from the basics of spin physics in order to understand the latest multidimensional NMR techniques in solution and solids. These meetings are open to anyone interested: from undergraduates wishing to understand a little more in depth of what is discussed at group meetings, to graduate students and postdocs wishing to sharpen their understanding or offer their perspectives. We emphasize an open format to the meetings, taking questions and encouraging group discussion of the more difficult concepts. If this sounds like something you would like to participate in, please contact Rui Huang (ruihuang@umich.edu) to be added to the email list, and keep checking this site for updates on future topics.

**Next Meeting: February 25 on "Nuclear Spin Hamiltonian". **

**Previous topics:**

**Date: **March 30, 2012

**Instructor: **Neil MacKinnon

**Topic:** Continuation of relaxation. We next turn to one of the most important NMR effects – the NOE. We will continue with a dipolar-coupled two spin system, and derive rate equations for the change in population of the four energy states as a function of transition probabilities. This will lead us to the auto and cross relaxation terms and the NOE enhancement will be discussed, in particular with respect to molecular weight.

**Date: **March 23, 2012

**Instructor: **Neil MacKinnon

**Topic: **Continuation of relaxation. We turn to an interacting two spin system and introduce the dipolar Hamiltonian, which in many cases is the dominant interaction for relaxation. Based on our knowledge of transition probabilities per unit time discussed in the previous session, we will derive the spectral density and relaxation time (T1, T2) equations commonly encountered in the literature.

**Date: **March 16, 2012

**Instructor: **Neil MacKinnon

**Topic:** Introduction to Relaxation. We will discuss auto correlation functions for particles undergoing Brownian (i.e. random) motion. This will lead us to the spectral density function, and we will discuss the frequencies of motion present as a function of molecular weight. We will then turn to a single spin system and show how relaxation may be related to random transition probabilities.

**Date: **March 2, 2012

**Instructor: **Janarthanan

**Topic: **Frequency discrimination in direct and indirect dimensions. Frequency discrimination in indirect dimension is achieved through different approaches likes States-Haberkorn-Ruben, Echo-AntiEcho, TPPI and States-TPPI. Each will be reviewed in detail with the help of a 2D NOESY experiment.

**Date: **February 17, 2012

**Instructor: **Janarthanan

**Topic: **Frequency discrimination in direct and indirect dimensions. The sign of Larmor precession frequency with respect to carrier frequency is needed to represent the peaks correctly in the processed spectra. This process called frequency discrimination is explained in terms of how it is achieved in a simple 1D experiment. Some of the basic Fourier transform properties of sin θ, cos θ and its complex combination (cos θ + i sin θ) will be reviewed.

**Date: **January 20, 2012

**Instructor: **Manoj K Pandey

**Topic: **An introduction to chemical shift anisotropy tensors. A thorough description will be given on tensors of rank 0 (scalar), 1 (vector) and 2 (dyad), supported by various examples. Anisotropic interactions in NMR, such as chemical shift and dipolar interactions, along with powder line shapes, will be discussed in detail.

**Date: **January 13, 2012

**Instructor:** Janarthanan

**Topic:** Chemical exchange (continued). The Bloch-McConnell equations will be used to simulate different scenario like protein-ligand binding interactions. An unified transition probability based approach as proposed by Prof. Alex Bain will be explained.

**Date: **December 9, 2011

**Instructor:** Janarthanan

**Topic:** Chemical exchange. Firstly, basic kinetics will be introduced to explain the formulation and usage of differential equations. Then the Bloch equations will be derived and Chemical exchange included. Simplifications for fast exchange regime will be reviewed for different binding mechanisms.

**Date: **November 11, 2011

**Instructor:** Manoj K Pandey

**Topic:** Discussion on the interface between classical and quantum mechanics. We will go through a basic introduction to classical and quantum physics and their correlation to one another. Historical background of the topic will be covered, starting with Newton's laws of motion, going though Planck's law and Einstein's photoelectric effect, and ending with Schrodinger wave equation. Salient features of wavefunctions and probability distribution functions will be discussed in detail.

**Date: **September 10, 2011

**Instructor: **Stéphanie Le Clair

**Topic:** The product operator analysis of the 2D heteronuclear HMQC experiment will be presented. Details of the experiment and expected spectral properties will be discussed. In addition, comparison with the HSQC experiment, with some potential benefits/limitations to each experiment will be explored.

**Date: **August 27, 2011

**Instructor: **Rui Huang and Wencheng Ge

**Topic:** The product operator analysis of the 2D heteronuclear HSQC experiment will be presented. Details of the experiment and expected spectral properties will be discussed.

**Date: **August 20, 2011

**Instructor: **Shivani Ahuja and Neil MacKinnon

**Topic:** Attention will now turn to two dimensional experiments. The general 2D pulse scheme will be discussed, followed by examination of a simple two-pulse experiment with demonstration of the origin of diagonal and cross peaks in the spectrum.

**Date: **August 13, 2011

**Instructor: **Shivani Ahuja and** **Neil MacKinnon

**Topic:** Examination of the INEPT sequence will start by a vector description given by Shivani. We will then draw parallels with the product operator analysis of INEPT, followed by refocused-INEPT. Emphasis will be given to applying what we have learned from smaller pulse sequences in solving more sophisticated experiments.

**Date: **August 6, 2011

**Instructor: **Neil MacKinnon

**Topic:** We will continue our in depth product operator analysis of the homonuclear spin-echo. After some time spent solving the problem individually, we will review the results as a group. We will also extend the result to the heteronuclear case, and examine the effect of a pi pulse applied on the S channel.

**Date: **July 23, 2011

**Instructor: **Neil MacKinnon

**Topic:** The product operator formalism has arrived! A concise summary of the rules for the application of the product operator formalism will be given, followed by our first foray into working through actual pulse sequences.

**Date: **July 16, 2011

**Instructor: **Neil MacKinnon

**Topic:** Continuing with last week’s work, we will explore the free precession of the density matrix after a pulse has been applied (i.e. coherences have been generated). We will introduce the ‘rotation sandwich’ method for rotation calculations, and prove it is equivalent to the full density matrix representation. This will be our first application of the product operator formalism.

**Date: **July 9, 2011

**Instructor: **Neil MacKinnon

**Topic:** After a quick review of resonance offset effects determined from the rotating-frame transformation of the RF-field Hamiltonian, we will continue with our description of a two-spin interacting system. We will derive the free precession propagator and examine what happens to the populations and coherences of a generalized density matrix. We will then apply a pulse to the thermal equilibrium density matrix and examine the results.

**Date: **June 18, 2011

**Instructor: **Shivani Ahuja

**Topic:** What do you do if you see no signal? A continuation of spectrometer troubleshooting, building on last week’s lesson. First, the important distinction between Varian and Bruker power level definitions will be detailed. We will then visit an actual spectrometer and learn where signals are generated, and trace the signal using an oscilloscope through the various components from the SGU to the pre-amplifier.

**Date: **June 11, 2011

**Instructor: **Shivani Ahuja

**Topic:** What do you do if you see no signal? A brief review of our previous work, followed by a hardware discussion geared towards spectrometer troubleshooting. The responsibility of various spectrometer components will be discussed, including pulse generation, timing, and amplification.

**Date: **May 28, 2011

**Instructor: **Neil MacKinnon

**Topic:** After last week’s review session, several questions arose which warrant further clarification. Specifically, we will show how to transform the Hamiltonian into the rotating frame utilizing our understanding of rotation operators. The importance of such a transformation will be highlighted with the RF-field Hamiltonian, where explicit time dependence is removed.

**Date: **May 21, 2011

**Instructor: **Shivani Ahuja

**Topic:** After a brief hiatus, a chance for review! Discussion will be focused on reworking notes from Mar. 26’s meeting to refresh our memories, helping to ensure a firm understanding is developed.

**Date: **Apr. 2, 2011

**Instructor: **Neil MacKinnon

**Topic:** We will wrap up our description of the non-interacting spin-1/2 ensemble, and move on to a two spin-1/2 system which is allowed to interact. We will examine the relevant Hamiltonian and construct the appropriate basis set, operators and density matrix for this system.

**Date: **Mar. 26, 2011

**Instructor: **Neil MacKinnon

**Topic:** With our understanding of rotation operators, we will now increase the complexity of our system from an isolated spin-1/2 to an ensemble of non-interacting spin-1/2. Density matrix formalism will be introduced, and examination of the response of our ensemble to free precession and RF pulses will be explored.

**Date: **Mar. 12, 2011

**Instructor: **Shivani Ahuja

**Topic:** Welcome back from spring break! As promised, we will hold a review session covering all quantum mechanical treatments to date. Problems will also be provided to work through during the class.

**Date:** Feb. 26 – Mar. 5, 2011

Spring Break! We will be taking a short hiatus for spring break. We will be reconvening on March 12, 2011 where we will offer a review session (including problems to work through) on the material we have covered.

**Date**: Feb. 12, 2011

**Instructor**: Neil MacKinnon

**Topic**: Continuation of quantum mechanical description. Rotation operators will be discussed, and their importance in describing precession demonstrated. A two-spin system will be introduced.

**Date**: Feb. 5, 2011

**Instructor**: Neil MacKinnon

**Topic**: Attention now turns to a quantum mechanical description of NMR. While not meant to be a general introduction to quantum mechanics, some basic tools necessary for a description of NMR will be introduced. Focus will be on a single spin and derivation of matrix formalism of wavefunctions and operators.

**Date**: Jan. 29, 2011

**Instructors**: Rui Huang, Shirley Lee and Neil MacKinnon

**Topic**: Wrap-up of review. New material will include the introduction of chemical shift and J-coupling interactions and mechanisms.

**Date**: Jan. 22, 2011

**Instructors**: Rui Huang and Shirley Lee

**Topic**: This week will be a review of all topics covered to date.

**Date**: Jan. 15, 2011

**Instructor**: Vivekanandan Subramanian

**Topic**: Continuation of examination of spectrometer hardware. Focus will be devoted to pulse generation, transmission to the probe, and signal reception. Quadrature detection and analog-to-digital conversion will also be discussed.

**Date**: Dec. 4, 2010

**Instructor**: Shivani Ahuja

**Topic**: Attention will now turn to spectrometer hardware. In this session, presentation of probe design with particular focus on circuit tuning and matching will be done. An actual probe will be on hand, and the tuning and matching will be monitored on an oscilloscope.

**Date**: Nov. 20, 2010

**Instructor**: Shivani Ahuja

**Topic**: Continuation of FT, with specific attention to FID processing and window functions. The application of various window functions and the resulting spectral effects will be discussed.

**Date**: Nov. 6, 2010

**Instructor**: Shivani Ahuja

**Topic**: The mathematics of the Fourier transform (FT) will be introduced, along with its importance to pulsed NMR experiments. This will lead naturally to line shape equations (Lorentzian/Gaussian).

**Date**: Oct. 30, 2010

**Instructor**: Neil MacKinnon

**Topic**: Continuation of classical description of magnetization precession, this time in the presence of an applied excitation field (B1). Rotating frame of reference will be introduced, and effects of on-resonance versus off-resonance B1 fields will be discussed.

**Date**: Oct. 23, 2010

**Instructor**: Neil MacKinnon

**Topic**: Introduction to classical description of nuclear magnetism. Development of bulk magnetization and precession within a large static magnetic field (Bo) will be derived (Bloch Equations).