The magnitude of A is given by this relationships and where A is the energy of the interaction, μn is the nuclear magnetic moment, μe is the electron magnetic dipole moment, Ψ(0) is the value of the electron wavefunction at the nucleus, and
[1] It has been pointed out that it is an ill-defined problem because the standard formulation assumes that the nucleus has a magnetic dipolar moment, which is not always the case.
[2] Roughly, the magnitude of A indicates the extent to which the unpaired spin resides on the nucleus.
Thus, knowledge of the A values allows one to map the singly occupied molecular orbital.
This field acquires a simple expression when the distance r between the two dipoles goes to zero, since
Simplified view of the Fermi contact interaction in the terms of nuclear (green arrow) and electron
spins
(blue arrow).
1
: in
H
2
,
1
H
spin polarizes electron spin antiparallel. This in turn polarizes the other electron of the
σ-bond
antiparallel as demanded by
Pauli's exclusion principle
. Electron polarizes the other
1
H.
1
H nuclei are antiparallel and
1
J
HH
has a positive value.
[
3
]
2
:
1
H nuclei are parallel. This form is unstable (has higher energy E) than the form 1.
[
4
]
3
: vicinal
1
H J-coupling via
12
C
or
13
C
nuclei. Same as before, but electron spins on
p-orbitals
are parallel due to
Hund's 1. rule
.
1
H nuclei are antiparallel and
3
J
HH
has a positive value.
[
3
]
1
H NMR spectrum of 1,1'-dimethyl
nickelocene
, illustrating the dramatic chemical shifts observed in some paramagnetic compounds. The sharp signals near 0 ppm are from solvent.
[
5
]
