BioPHYSICAL chemistry

a proton. The spins of the H 2 may be up/up,
up/down, down/up, or down/down. Since the
up/down and down/up configurations lead to
the same energy, these two lines overlap and
what is observed are three lines of which the mid-
dle is twice as large as the two side lines. This
is called a 1:2:1 triplet and is shown in Figure 16.4.
Threeinteracting protons will lead to a 1:3:3:1
pattern and larger numbers can be determined
easily using Pascal’s triangle.
In an NMR spectrum, the presence of two close
peaks may arise from spin–spin coupling but
it may also be accidental and simply due to the
complexity of the spectrum. These two cases
can be distinguished experimentally by changing
the field strength. If the two lines arise from the
spin–spin interaction then altering the field will
not change the splitting. If they are two separate
lines, their separation willbe proportional to the field strength. However,
this is normally not done as the use of two-dimensional NMR will also
yield the same information as described below. Instead, another means
of identifying whether peaks arise from a single spin but are split is to
measure the total area of the peaks, as this should be directly proportional
to the number of spins, although broadening of a peak due to a factor
such as proton exhangemay make assignment of the areas problematic.

Pulse techniques

NMR experiments can be performed using a conventional continuous-
wave instrument but modern instruments use radiofrequency pulses due
to improved signal-to-noise features and versatility. The use of the pulse
techniques arises from the ability to align magnetic dipoles due to the
presence of an external magnetic field. In the absence of the external field,
there is no preferred direction for the dipoles and they will lie at random
angles on a cone such that their projection is +1/2 or −1/2 (Figure 16.5).
In the presence of the field, there is a net magnetization, M, along the z
direction and the spins start precessing along that direction.
Now consider the effect of a radiofrequency pulse that has a field strength
B 1. If this field is given a frequency that matches the Larmor frequency,
the magnetization vector will begin to precess around the direction of B 1
(Figure 16.6). As the spins precess their direction changes from alongz to
a cone around B 1. The duration of the pulse then will determine the final
direction of the spins, with a 90° pulse resulting in magnetization moving
from the z direction to the x−yplane. After the 90° pulse, the magnetiza-
tion vector is in the x−yplane. As time passes, the individual spins precess

CHAPTER 16 MAGNETIC RESONANCE 349

Resonance

for Spin A

J: Interaction strength

between Spin A and B

Resonance

for Spin B

A

B

J

A

B

A

B

A

B

J

Figure 16.4An NMR spectrum with each

resonance, due to spin A or B, split into two

lines due to interactions with the nearby spin.