Physical Chemistry Third Edition

24.4 Nuclear Magnetic Resonance Spectroscopy 1017

left, withδ 3 .6 ppm and with area equal to twice that of the first peak. The two protons on

the second carbon are still more distant from the electronegative oxygen atom, and produce

the third peak from the left, withδ 1 .5 and twice the area of the first peak. The protons

in the methyl group are most distant from the oxygen and produce the peak withδ 0 .9 and

area three times that of the first peak.

Exercise 24.7

Sketch the low-resolution proton NMR spectrum you would expect from propanal (propionalde-

hyde).

Spin–Spin Coupling and Spin–Spin Splitting

(Multiplet Splitting)

The second molecular contribution to the magnetic field at a given nucleus is due

to other nuclei with magnetic dipoles. A magnetic dipole in one nucleus induces a

current in the electrons of the molecule, and this can produce a contribution to the

magnetic field at the second nucleus if the second nucleus is not too distant from the

first. This effect is calledspin–spin coupling. Its contribution to the field at nucleusjis

given by

Bspin–spin,j

∑n

i 1

JjiMIi (24.4-10)

where the sum includes a term for each other nucleus with nonzero spin and where

MIiis the quantum number for thezprojection of the spin angular momentum of

nucleus numberi. The coefficientJijis called thespin–spin coupling constantfor

nuclei numbersiandj.IfJijis measured in Hz (s−^1 ) instead of in tesla, Eq. (24.4-10)

is replaced by

γBspin–spin,j

2 π



∑n

i 1

JjiMIi (Jijmeasured in Hz) (24.4-11)

It is found that nucleusjaffects nucleusiin the same way that nucleusiaffects nucleus

j, so that

JijJji (24.4-12)

The ratio ofJijexpressed in frequency units (s−^1 Hz) to the instrument’s frequency

is the same as the ratio ofJij expressed in tesla to the magnetic field used in the

instrument.

In aliphatic organic compounds, two protons that are bonded to a pair of atoms that

are bonded directly together will ordinarily exhibit spin–spin coupling, but protons that

are more distant from each other than this will not usually exhibit significant spin–spin

coupling. In other words, two protons will usually have appreciable spin–spin coupling

if the number of bonds from one proton to the other is no greater than three. In aromatic

and conjugated organic compounds, spin–spin splitting frommetaorparaprotons is

observed because of the delocalized bonding.