Chemistry Reference
In-Depth Information
Taking the lowest root, we obtain for the ground state
12
5
K
¼
Q
þ
2
E
¼
Q
þ
:
4K
ð
9
:
114
Þ
giving as resonance energy for the two Kekul
e structures
K
¼
12
5
3
2
9
10
K
<
D
E
¼
E
ð
2K
Þ
E
ð
K
Þ¼
0
ð
9
:
115
Þ
.
Resonance between the three Dewar structures
Y ¼ c
3
c
3
þc
4
c
4
þc
5
c
5
ð
9
:
116
Þ
x
4
þ
3
2
x
4
þ
3
2
x
x
4
þ
3
2
x
4
þ
3
2
x
¼
0
ð
9
:
117
Þ
x
4
þ
3
2
x
4
þ
3
2
x
Expanding the determinant gives the cubic equation in x:
x
3
þ
2x
2
2
4x
8
¼ð
x
þ
2
Þ
ð
x
2
Þ¼
0
)
x
¼
2
ð
twice
Þ;
x
¼
2
ð
9
:
118
Þ
The lowest root is
E
¼
Q
þ
2K
ð
9
:
119
Þ
giving as resonance energy between the three Dewar structures
K
¼
3
2
1
2
K
<
D
E
¼
E
ð
3D
Þ
E
ð
K
Þ¼
2
0
ð
9
:
120
Þ
The resonance between the three Dewar structures, each having a long
bond, is therefore sensibly less than the resonance between the two
Kekul
e structures (0.5 instead of 0.9).
