Biomedical Engineering Reference
In-Depth Information
Figure 17.9
ROHF calculation on the vinyl radical
good in either case, and a further major problem with the UHF model is that it does not
necessarily give a pure spin state
S
2
Ψ
UHF
=
1)
h
2
4π
2
Ψ
UHF
In general, if there are
p
electrons of α spin and
q
electrons of β spin, the UHF wavefunction
can contain spin components ranging from
s
s
(
s
+
1
2
(
p
q
) to
2
(
p
=
−
+
q
). The expectation
value
S
2
Ψ
UHF
S
2
Ψ
UHF
dτ d
s
=
is taken as a measure of the spin impurities. In this calculation it came out as 0.9901 instead
of the pure doublet value 3/4.
Table 17.7
Hyperfine coupling constants (in mT) for vinyl radical
C
1
H
1
C
2
H
2
H
3
Experiment
10.76
(
−
)
1.33
(
−
)
0.86
6.81
3.41
ROHF
11.49
2.37
1.19
2.20
1.32
UHF
17.75
−
1.33
−
4.22
6.53
4.56
17.12 Problem Set
A set of problems, together with solutions, is available on the associated website.
