BCMB/CHEM 8190

PROBLEM SET 4

1. Write an expression for the density matrix at the beginning of acquisition using rotation operators and the equilibrium density matrix for the following pulse sequence and a single spin 1/2 nucleus: 90x - t - 180y - t - acquire Find the value of Mx and My from the resulting density matrix.

2. Use the program GAMMA to simulate a 1D spectrum for a ABX spin system with the following parameters:  A shift, -0.15ppm, B shift, -0.05ppm, X shift 0.15 ppm, spectrometer frequency 500 MHz, AX coupling 8.0 Hz, BX coupling 2.0 Hz, AB coupling 12 Hz.  What error in AX coupling do you make by using the difference in peak position for the X multiplet?  Change the B shift to -0.14 ppm. What is the error now?  Use the on line version that can be found at http://gamma2.magnet.fsu.edu.

3.  a) In product operator notation, show the effect of a short
       (hits both  spins) 90 degree rf pulse about the + y axis on the density matrix      
       represented by the I1xI2z product operator.
 
     b) Show the density matrix equivalent (fill in elements of matrix) of the result in a two 
       spin 1/2 system and sketch the spectrum that would result    
       from observing x magnetization.
 
4.  Use density matrix representations (two spin 1/2 particles) of 
    the (I1xI2x + I1yI2y) operator to identify the coherence order 
    it represents.