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NOTE FOR INSTRUCTORS:

For this class we use the online version of GAMMA. There is no special
file to download.

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GOALS:

1) Get hands on experience with the online version of GAMMA

2) Study the effect of strong coupling in AB and ABX spin systems
 

BACKGROUND:
 

    GAMMA is a program written in C++ by Scott Smith, who is now at the National High Magnetic Field Laboratory in Florida.  It works using density matrices and rotation operators much as we described in class.  Defining a spin system sets up rotation operators and an equilibrium density matrix in the proper basis set.  Pulses are applied using x or y rotation operators in matrix form, evolution is represented using z rotation operators which include the effects of chemical shift offset and scalar couplings, and an FID is constructed by taking the trace of the product of the resulting density matrices multiplied by matrix representations of x and y magnetization operators.
    Today we will use the online version of GAMMA for simple applications.  For more complex applications, we could install executables on individual workstation, and this would give us access to powerful programming tools used by NMR experimentalists and theoreticians to build magnetic resonance programs.  The name GAMMA actually comes from the symbol used to represent a matrix that describes the changes in density matrix elements due to spin relaxation.  We did not discuss this application, but it is the primary reason GAMMA was written.

Reference:

"Computer Simulations in Magnetic Resonance. An Object Oriented Programming Approach", S.A. Smith, T.O. Levante, B.H. Meier, and R.R. Ernst, J. Magn. Reson., 106a, 75-105, (1994).
 
 

LETS GET STARTED WITH A SIMPLE EXAMPLE:

To get started open a web browser on your PC or workstation.  Go to the following URL: http://gamma2.magnet.fsu.edu/index.html (note the main site is corrupted and does not work at this time).  Select online programs from the menu at the left.  Then select NMR of liquids.  Then select simple FID.  You will need to enter parameters into the menu displayed:

Example: AX spin system, H5 (5.5 ppm) and H6 (7.3 ppm) in Uridine J = 15.0 Hz

        No. Spins = 2
        Frequency Units: ppm
        Isotopes = 1H for spin 1 and spin 2
        Shifts = spin1 : 7.3, spin2 : 5.5
        [You donít need to fill in the whole table of parameters;
           the program will ignore any parameters that donít correspond
           to spins beyond the number you enter at the top
           (ie chemical shift of spin 3 or coupling between spin 2 and spin 3
           is not used when you specify a 2 spin system).]
        Js (Hz) = spin1-spin2: 15.0
        Spectrometer Frequency: 500 MHz
        Pulse/Detect Channel: 1H
        X-Approx. = Yes
        Block Size: 4K
        Spectral Width = 16 ppm, SQT linewidth = 4 Hz

        Submit your request: RUN SIMULATION

        A new page will appear with the FID and several options. Click on "NMR spectrum".
        Select NMR spectrum (this does an FT); you should get a new page with the spectrum in the frequency domain.

Note: the Freqeuncy axis goes from -8 to +8 ppm and you see peaks at 5.5 and 7.3 ppm. Regrettably, there is no flexibility for expanding the spectrum using the web page application. (Using GAMMA from your individual workstation, you could route the output to various NMR processing packages including Felix)
 

EFFECT OF STRONG COUPLING IN AB AND ABX SPIN SYSTEMS:

We will use GAMMA to illustrate the effects of strong coupling in AB and ABX spin systems.  Note that even though we discussed a correlation between specific density matrix elements and particular lines of an AX (first order) spin system in class, this one to one correlation does not hold for second order systems (AB, ABX, etc).  Mixtures of elements such as sigma12 and sigma13 are actually what evolve at a discrete frequency.  We donít actually need to know the exact nature of the association since we calculate the entire FID directly.  The approach is completely general regardless of how complex the evolution Hamiltonian.
 

A) First look at the effect of chemical shift separation of the two resonances in the AB system. I suggest entering the following parameters to start:

2 spins, 1H for both
500 MHz operation with 1H pulse and detect.
do not use the X approximation - this would always give a 1st order spectrum.
shifts: -0.1 and 0.1 ppm
J : 12.0 Hz
points: 1024, spectral width 0.3 ppm an linewidth 1.0 Hz

Simulate the FID and a new page will appear with the FID and several options.
Select NMR spectrum (this does an FT); you should get a new page with the spectrum in the frequency domain. You see two split peaks in the spectrum.  You will be asked to analyze the most downfield peak.
Return to the option page and select transition table.

Note the separation of the two downfield lines, their midpoint, and their intensities and complete the first row of the table in Questions 1.

Simulate FIDs using shifts of +/- 0.6, and +/- 0.03 and complete lab problem set questions 1 and 2.
 

B) Look at the effect of A-B chemical shift separation on Jax and Jbx couplings as measured from splittings of the X multiplet in an ABX three spin system.

Try the following parameters as a start:
shifts: -0.16 (spin 1) , -0.15 (spin 2), 0.15 (spin 3)
couplings: 16.0 (spin1-2), 8.0 (spin 1-3), 1.0 (spin 2-3)
points 1024, dwell 0.005 (spectral width 0.4), linewidth 0.5

Answer questions 3 and 4 of problem set.
Increase and decrease the shift difference between spins 1 (A)  and 2 (B) to see when Js can be measured.
 

LAB PROBLEM SET #5:
 

1.  Complete the following table:
 
 

	Peak Intensities of the two lines of downfield signal	Midpoint of the two lines of downfield signal (ppm)	Separation of the two lines of most downfield signal (Hz)
Two-spin simulation with delta=0.1 and -0.1 ppm and J = 12.0 Hz
Two-spin simulation with delta=0.6 and -0.6 ppm and J = 12.0 Hz
Two-spin simulation with delta=0.03 and -0.03 ppm and J = 12.0 Hz

2.  Compare the values obtained in second order spectra (question 1) with those obtained in a first order spectra.  Does the splitting give J ?  Does the midpoint of the doublet give the shift?  Are the peak intensities of each line of the doublet equal ?
 

3.  For the ABX three-spin simulation, measure splittings of peak around 0.15 ppm using the table of transitions and compare them to input Js.
 

4.  For the ABX three-spin simulation, it is very difficult to measure chemical shift and couplings for the two spins aroun -0.15 ppm.  Suggest and experimental approach that would help relieve some of the second order effect for these two spins.