Nuclear magnetic spectroscopy (NMR) is a technique used by chemists to investigate the structure of molecules. Nuclei in a molecule experience a magnetic field that depends on their position within the molecule. The strength of the magnetic field experienced by the nuclei alters the frequency of radio waves which they absorb and emit. These differences in frequency, described by the "chemical shift," are used to determine the structure of the molecule.
In NMR experiments, hydrogen atoms up to three bonds apart interact with each other in a predictable way called "J-coupling." The Karplus equation, J(phi) = (A * cos^2(phi)) + (B * cos(phi)) + C, describes how the dihedral angle "phi" between two hydrogen atoms alters the J-coupling "J." "A," "B" and "C" are constants. The equation can be plotted to obtain the Karplus curve. This can be used to understand how "J" changes with "phi."
Instructions
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1
Sketch a plot of the Karplus equation from 0 to 180 degrees, with the constants "A," "B" and "C" equal to one or reference a preexisting sketch.
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2
Draw a molecule with two hydrogen atoms that are in different chemical environments and three bonds apart.
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3
Draw your molecule so the dihedral angle "phi" is 0 degrees. Using your Karplus curve, determine the relative J-coupling value "J."
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4
Redraw your molecule so the dihedral angle "phi" is 90 degrees. Using your Karplus curve, again determine the relative J-coupling value "J." This will be smaller than for 0 degrees.
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5
Redraw your molecule so the dihedral angle "phi" is 180 degrees. Using your Karplus curve, once again determine the relative J-coupling value "J." This will be similar to the value for 0 degrees.
