BIOINORGANIC CHEMISTRY A Short Course Second Edition

102 INSTRUMENTAL METHODS

and so on, would be gained. However, when a magnetic fi eld is applied during
an NMR experiment, electrons surrounding nuclei in the molecules under
study set up a secondary magnetic fi eld. The secondary fi eld opposes the main
fi eld, reducing the nuclear frequency. The magnitude of the frequency change
is proportional toB 0. This is important in that there will be larger separations
between resonant frequencies at higher magnetic fi eld strengths, allowing one
to detect fi ner differences between the different protons in any liquid sample.
The effect of electrons surrounding the nucleus on the nucleus in the applied
magnetic fi eld is termed screening (or shielding). Taking equation 3.20 and
introducing the screening constant, σ , one fi nds equation 3.21 :

ν

γ

π

=( ) −σ

2

B 0 () 1 (3.21)

The screening constant, σ , is dimensionless and usually recorded in parts per
million (ppm). Contributors to σ , opposite in sign, are σd (the diamagnetic
term) andσp (the paramagnetic term). The diamagnetic term depends upon
the density of circulating electrons — the number of electrons surrounding the
nucleus of interest. The paramagnetic effect in this context does not imply the
presence of unpaired electrons (to be discussed below) but is substantial, and
dominates, for heavier atoms with many electrons in outer orbitals involved
in chemical bonding. Several factors affect σp :

1. The inverse of the energy separation, ΔE , between ground and excited
   electronic states of the molecule. This means that there will be a correla-
   tion between NMR spectra and absorption in the visible and ultraviolet
   spectral regions.


2. The relative electron density in p orbitals involved in bonding.


3. The value of 〈 1/ r^3 〉 , the average inverse cube distance from the nucleus
   to the electronic orbitals involved.

Figure 3.11 Rotating Frame when B 1 is applied in the form of a 90 ° pulse. (Adapted
with permission of Nelson Thornes Ltd. from Figure 1.6 of reference 21 .)

x

y

x

y

z

Bo

Mz

90 o pulse z

Bo

Mxy

time = zero

staticMz

rotatingMxy

ofB 1

B 1