24.5 Fourier Transform NMR Spectroscopy 1031
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v 2v^1Figure 24.13 The Two-Dimensional COSY Spectrum of Two Uncoupled Protons.peaks appear only on this diagonal atν 1 ν 2 νAand atν 1 ν 2 νB, because it
turns out that the two sets of FID signals are equivalent. It is more common to make a
two-dimensional plot in which the spectral lines are represented by contours of equal
intensity, so that spectral lines appear as blobs of closely spaced contour curves, as in
Figure 24.13. Because of the use of two-dimensional plots, COSY experiments and
other similar experiments are referred to astwo-dimensional NMR.
Now consider the case that protons A and B have a nonzero coupling constantJAB.
The magnetic field at each proton has a spin–spin coupling contribution from the other
proton. This contribution is transmitted through the electrons in the bonds between
the protons and is generally significant only if there are no more than three bonds
between the protons. The contribution to the magnetic field from a coupled proton is a
time-dependent contribution because of the precession of the spins. There is a tendency
of the rate of precession of one proton to modify the precession of the other proton.
We say that magnetism is transferred from one proton to the other. The precession
of a pair of coupled protons can be represented as a combination of two precession
rates, one corresponding to the precession rate of each of the protons. Both frequencies
are encoded in the FID signal. When the FID signal is Fourier transformed, both the
frequencyνAand the frequencyνBcan appear in the same FID signal. The same is
true of the spectrum obtained by the second Fourier transform. The result is a sym-
metrical two-dimensional spectrum as shown in Figure 24.14. The multiplet splitting
still splits the spectral lines, so there are four small peaks in a square, as seen in the
diagram.
The advantage of the COSY procedure is the appearance of the off-diagonal spectral
features, which clearly identify the coupled pairs of protons. In our case of two coupled
protons, the spectrum is simple and this is not a useful advantage. In the case of more
complicated substances, overlapping multiplets can be difficult to assign, and the COSY