between the coupled groups is large compared to the coupling constant, i.e. ∆ν/J> ~ 7. As this ratio
becomes smaller, the inner peaks of multiplets grow at the expense of outer peaks and additional or
second-order splitting may occur. Chemical shift differences ∆ν are now measured between the 'centre
of gravity' of the multiplets. In the limiting case, where ∆ν = 0, the protons are equivalent and the
multiplet collapses to a single peak or singlet (Figure 9.32(b)). Progressive distortion of this type is
exemplified by compounds having adjacent methylene groups (Figure 9.34). The spectrum is described
as A 2 X 2 or A 2 B 2 according to the value of ∆ν/J and the degree of distortion. A significant feature, which
is an aid to interpretation, is the symmetrical appearance, even in the presence of considerable second-
order splitting. Slight distortion of multiplet intensities from first-order ('roofing' or 'leaning') is nearly
always observed but this can be useful in relating coupled groups in complex spectra.
With saturated compounds, the effect of spin-spin coupling is rarely observed for protons more than
three bonds apart. Aromatic, alkene and other unsaturated compounds, however, show more complex
splitting patterns because of longer range coupling. The ring protons of substituted aromatic compounds
are mutually coupled and mostly give second-order spectra which are difficult to interpret rigorously.
Those with similar or identical ortho or para substituents often have a symmetrical appearance similar
to an A 2 B 2 system. Vinyl groups, mono-substituted furans and related compounds with three adjacent
single protons give spectra characterized by three groups of four peaks if the chemical shift differences
are sufficiently large. Described as an AMX spectrum, the twelve-line pattern results from three
unequal coupling constants JAM,JMX and JAX, and is best understood with the aid of a splitting diagram
(Figure 9.35). This shows the individual coupling of each proton to the other two and how the three
coupling constants can be measured from the spectrum. As the chemical shifts of the three protons
become closer, the pattern distorts to ABX and finally, and in a complex manner, to ABC in which the
groups overlap. A substantial degree of distortion and second-order splitting can occur before the
pattern is unrecognizable.
Chemical Shift Reagents
In the spectra of some compounds the resonances from several groups of protons with similar chemical
shifts may overlap, thereby rendering it difficult if not impossible to interpret them satisfactorily.
Simpler spectra can be obtained by using an instrument operating at a higher frequency (field strength)
which results in increased chemical shift differences without affecting the coupling constants (see
below). However, a more powerful spectrometer may not be available and the use of chemical shift
reagents can provide a very much cheaper alternative. These reagents are coordinately unsaturated
lanthanide β-diketone complexes, in particular tris(dipivalomethanato)europium(III) and tris
(6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-