Biomedical Engineering Reference
In-Depth Information
Table 17.5
Experimental results for XCN
Molecule
R
(C N)/pm
14
N QCC/MHz
HCN
115.5
−
4.58
FCN
115.9
−
2.67
ClCN
115.9
−
3.63
Table 17.6
HF/6-311G** results for XCN
Molecule
R
(C N)/pm
14
N QCC/MHz
HCN
112.7
−
4.53
FCN
112.5
−
2.95
ClCN
112.8
−
3.85
The agreement with experiment is good to within a few percent. What chemical insight
these calculations give into the reason why the three coupling constants are so different is
not clear!
17.11 Hyperfine Interactions
We considered a simple two-state system in Chapter 7; I took for granted you were famil-
iar with electron and nuclear spin, and had come across nuclear magnetic resonance and
electron spin resonance.
Atomic and molecular magnetic dipoles have to obey the quantum mechanical laws of
angular momentum, and each dipole can make only a number of allowed orientations with
an applied magnetic field. Each orientation corresponds to a different energy and absorption
of a suitable photon may cause a change in orientation. This is the physical basis of the
magnetic resonance experiment.
The energy level differences are tiny in comparison to electronic ones, and it is conven-
tional to discuss such hyperfine effects as perturbations on the electronic energy levels.
In the electron spin resonance experiment, there are two terms of interest. First there is a
classical electron spin dipole-nuclear spin dipole term
g
α
β
α
3 (
R
α
i
.
S
i
)(
R
α
i
.
I
α
)
g
e
β
e
i
−
R
α
i
(
S
i
.
I
α
)
(17.31)
R
α
i
α
that averages to zero for tumbling species in the gas phase or in solution.
Second there is the
Fermi contact term
4π
3
g
e
β
e
i
g
α
β
α
I
α
.
S
i
δ (
R
α
i
)
(17.32)
α
