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Encyclopedia of Physical Science and Technology EN010C-493 July 19, 2001 20:30

716 Nuclear Magnetic Resonance (NMR)

netic moment. This is to say that the observed signal in
the time domain, such as shown in Fig. 2, is the signal
13
associated with C in adamantane resulting from a single
pulse excitation (Fig. 7). The time-dependent state lead-
ing to this time-dependent signal is a superposition of two
states differing by unity in the quantum number describ-
ing the nuclear angular momentum. The observed signal,
of course, is the average over all the spins in the sample,
and thus may be said to be a coherent magnetization of all
spins in the ensemble of molecules being observed. An-
other way of speaking of this signal is that it represents a
single quantum coherence.
It is possible for systems of nuclear spins to have states
that differ by greater than unity in that quantum number
for angular momentum. There are at least two ways in
which this may come about
1
FIGURE 8 Two-dimensional plot of 13 C NMR. The peaks along The first way is two or more spins may couple together
2
the ω 1 axis (at the top of the figure) are the 13 C resonances to form a spin greater than . For example, two spins 1
1
taken without decoupling the protons from the carbons. Overlap- 2 2
ping peaks make spin–spin coupling multiplicities hard to deter- may couple to form a system with spin unity. In this case,
mine. The peaks along the ω 2 axis are the 13 C resonances ob- there are 2S + 1 = 3 states describing this coupled system,
tained when the protons are decoupled from the carbons, thus and there can be two states that differ by two in angular
eliminating spin–spin coupling multiplicities. The peaks in the 2-D momentum. If an excitation is provided which produces
area clearly show which chemically shifted carbons have two or a time-dependent state that is a superposition of the two
three protons attached. A triplet represents two attached protons,
a quartet three. states differing by two in angular momentum, then with
that superposition being coherent over the ensemble of
spins being observed, we speak of a double quantum co-
to how many protons. For example, the chemical shifted 1
herence. Extending the argument to many coupled spins
carbon labeled “a” at a frequency of roughly 0.45 kHz on 2
leads to the idea that multiple quantum coherences may be
the ω 1 axis is clearly split into a quartet in the 2-D plot.
produced by suitable excitation. In fact, the highest order
This uniquely identifies this carbon as being attached to
of coherence being observed is one means of counting the
three chemically equivalent protons, or as a CH 3 group.
number of spins that are coupled. As one example of the
The chemically shifted carbons labeled “b” and “c” on the
use of such an idea on which the author has worked, con-
ω 1 axis are J-split into triplets, which clearly indicates,
sider the problem of determining how many protons there
as with the previously discussed case of adamantane, that
in a fragment of ethylene adsorbed on a metal catalyst
they are methylene carbons.
during any part of the processes involving adsorption and
This is one of the simplest 2-D experiments possible,
reaction. These are disordered systems, with no coherence
and there is an entire catalogue of such experiments which
length amenable to analyses by X-rays. One possibility
canbeused,forexample,totraceconnectivitiesofcarbon–
is to count the maximum number of coupled protons re-
carbon bonds through a chemical structure. The latter is
sulting from such an adsorption and subsequent reaction.
especially useful in complicated structures, such as are
In this case, it was found that at a particular time in the
found in molecules such as steroids and proteins, of great
reaction sequence, there were six coupled protons in the
interest to biochemistry and the medical profession.
C n H m fragment bound to the surface, which indicated that
the fragment could be (Ru) CH 2 CH CH CH 2 (Ru),
where the Ru in parenthesis stands for the metal in the
VII. MULTIPLE QUANTUM NMR
catalyst particle.
A. Coupled Spins 1 The multiple quantum spectrum associated with this
2 six-quantum coherence is shown in Fig. 9. The intensities
In the discussion thus far, we have been dealing with what of the peaks associated with higher orders of coherence
is termed “single quantum” NMR. This term is used be- drop off roughly as a Gaussian curve, and the highest order
cause the quatum mechanical states that result in the ob- of coherence developed depends upon the time allowed for
served signal differ by unity, that is, by a “single” quantum this development. In the present example, only five peaks
of angular momentum, in the quantum number that relates were developed no matter how long time was allowed
to the nuclear angular momentum, and thus to the mag- for higher coherences to develop, indicating that with the