BIOINORGANIC CHEMISTRY A Short Course Second Edition

108 INSTRUMENTAL METHODS

nuclear spins are faster and some are slower, the xy magnetization starts to
fan out and lose coherence, eventually resulting in Mxy = 0. The characteristic
time for this process is called transverse relaxation orT 2. The equations gov-
erning the behavior of transverse ( Mxy ) or longitudinal ( Mz ) magnetization
and their return to equilibrium following aB 1 pulse are given by equations
3.25 (in which Mz increases from zero to its equilibrium value) and 3.26 (in
which the transverse magnetization falls from its maximum (equal toMz ) to
zero when suffi cient time has elapsed).

(M )zt=−(M )z

−

()

⎡

⎣⎢

⎤

⎦⎥

∞^1

1

exp

t

T

(3.25)

(M )xy t=(M )xy

−

(^0) ()
2
exp
t
T

(3.26)

Methods for measuring T 1 and T 2 are discussed in Chapter 5 of reference 21.
Suffi ce it to say here that understanding the method for measuring T 2 (the
Carr – Purcell pulse sequence or spin - echo method) becomes important for
discussing two - dimensional NMR spectra. When spin – spin coupling is present,
a modulation of spin echoes is produced, and it is this fact that is important
in 2 - D NMR spectroscopy. Nuclear relaxation rates and mechanisms become
important when discussing the effect of paramagnetic metal centers on NMR
spectroscopy.

3.4.10 Nuclear Overhauser Effect Spectroscopy (NOESY),

The double resonance experiment can be used to simplify a spectrum as dis-
cussed in Section 3.4.4 , or to probe correlations between different nuclei. Two
types of double resonance experiments are described. In the homonuclear
double resonance experiment the nuclei irradiated are the same isotope as
those observed: Shorthand notation for this is, for example,^1 H{^1 H}. In hetero-
nuclear double resonance, the nucleus irradiated may differ from that observed:
Observing^13 C while irradiating^1 H has the notation^13 C{^1 H}.
As stated previously, for a spin = 1/2 nuclei so that I = 1/2 and ΔE = μ B 0 / I ,
one obtains equation 3.27. Rewriting this in terms of the magnetogyric ratio,
whereγ = 2 π /h( μ /I), yields equation 3.28.

N

N

E

kT kT

I

I

+

−

=

−

( )=

−

exp exp( )

Δ 2 μB 0

(3.27)

N

NkT

I

I

+ I

−

=

−

exp( )

γB 0

(3.28)

The number of nuclei in the upper energy state, N+I, is less than that in the
lower energy state, N−I, and the probabilities of upwards and downwards
transitions are different. The spin transitions are caused by the spins S of a
nucleus, and the infl uence of these occurs directly through space. The transi-