Physical Chemistry Third Edition

1018 24 Magnetic Resonance Spectroscopy

The spin–spin coupling leads to a splitting of spectral lines into multiple lines that can

be seen in a high-resolution spectrum. This splitting is known asspin–spin splittingor

multiplet splitting. For example, in a molecule that contains no magnetic nuclei except

for two protons that have significantly different shielding constants, the field at proton

number 1 is

B 1 B 0 (1−σ 1 )+J 12 MI 2 (24.4-13)

where J 12 is measured in tesla. The field at proton number 2 is

B 2 B 0 (1−σ 2 )+J 21 MI 1 (24.4-14)

There will be one value ofB 0 at which the protons withMI 2  1 /2 will resonate and

another value at which the protons withMI 2 − 1 /2 will resonate. Two lines will

occur for proton number 1, corresponding to the two different values thatMIcan have

for the other proton. Similarly, two lines will occur for proton number 2. We say that

there are two doublets. The two lines of each pair will be split by an amount equal

toJ 12 , which is equal toJ 21 and the difference between the centers of the two pairs

will be equal toσ 1 −σ 2. This spectrum is called afirst-orderspectrum, and applies if

B 0 (σ 1 −σ 2 ) is fairly large compared withJ 12.

EXAMPLE24.13

A typical value ofJijis 10 s−^1 10 Hz. For an NMR spectrometer withνspec200 MHz

(2. 00 × 108 s−^1 ), find the ratio ofJijto a difference in chemical shifts of 1.5 ppm.

Solution

We expressδ 1 −δ 2 in frequency units:

(1. 5 × 10 −^6 )(2. 00 × 108 s−^1 )300 s−^1

which is much larger than 10 s−^1 so that the first-order analysis is justified.

IfB 0 (σ 1 −σ 2 ) is not large compared withJ 12 , the two lines for each proton are

not of equal area, and the difference between the centers of the pairs is not equal to

(σ 1 −σ 2 ), but is equal to

√

(σ 1 −σ 2 )^2 +(J 12 /B 0 )^2 , whereJ 12 is measured in tesla. In

addition, the line in each pair closer to the other pair of lines will have a larger intensity

than the other line.^3 This is called asecond-order spectrum. In the limit thatσ 1 −σ 2

approaches zero, the distance between the centers of the pairs approachesJ 12 /B 0 , the

two inner lines coalesce into one line, and the outer lines disappear. Although spin–spin

coupling occurs, spin–spin splitting is not observed between two protons that have the

same chemical shift.

Some nuclei other than protons exhibit spin–spin coupling with protons, but nuclei

with values ofIgreater than 1/2 do not ordinarily give spin–spin splitting. For example,

(^14) N, withI1, and (^35) C and (^37) Cl, withI 3 /2, do not split proton NMR lines.
Splitting does occur between protons and^19 For^13 C, which haveI 1 /2. In organic
(^3) J. D. Roberts,Nuclear Magnetic Resonance, McGraw-Hill, New York, 1959, p. 55ff.