**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