Physical Chemistry Third Edition

1032 24 Magnetic Resonance Spectroscopy

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Figure 24.14 The Two-Dimensional COSY Spectrum of Two Coupled Protons.

results can eliminate any uncertainty. Figure 24.15 shows the HH-COSY spectrum of

methyl vinyl ketone. The couplings between protons are clearly identified from the

off-diagonal spectral features.

The HETCOR experiment is similar to the COSY experiment except that it deals with

multiplet coupling between nuclei of different types, such as protons and^13 C nuclei.

Other experiments such as the HETCOR experiment and the NOESY experiment are

discussed in the books by Farraro, Farraro and Nakamoto, and Croasman and Carlson.^8

PROBLEMS

Section 24.5: Fourier Transform NMR Spectroscopy

24.34Construct an accurate graph of the function

I(t)(cos(t)+5cos(2t))e−t/^10

This function resembles a FID signal containing two

frequencies.

24.35Find the Fourier transformI(t) of the functione−a|ω|.

24.36Find the inverse Fourier transformc(ω) of the function

I(t)e−at

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sin(bt). Construct an accurate graph of this

Fourier transform.

24.37a.Find the inverse Fourier transformc(ω)ofthe

functionI(t)e−|at|sin(bt). Ifa 1 /T 1 , this

function could represent a FID signal of a single

frequencyb/ 2 πdecaying because of the spin–lattice

relaxation.

(^8) Thomas C. Farrar,Introduction to Pulse NMR Spectroscopy, The Farragut Press, Chicago, 1989; Thomas
C. Farrar and Edwin D. Becker,Pulse and Fourier Transform NMR, Academic Press, New York, 1971;
W. R. Croasman and R. M. K. Carlson,Two-Dimensional NMR Spectroscopy—Applications for Chemists
and Biochemists, VCH Publishers, Inc., New York, 1987.