Chemistry Reference
In-Depth Information
giving
50
% c
1
;
50
% c
2
ð
9
:
78
Þ
as relative weights of the two Kekul
e structures in square cyclobutadiene,
as it must be for completely resonant structures.
9.6.3 Butadiene (Open Chain, n
¼
2)
Butadiene, the open chain with 2n
¼
4 (two
bonds), has the canonical
structures and the superposition patterns depicted in the third and fourth
rows of Figure 9.8.
p
c
1
is the Kekul
e structure (two equivalent
short
p
bonds) and
c
2
is the Dewar structure (one long
p
bond). The complete
VB wavefunction will be
Y ¼ c
1
c
1
þc
2
c
2
ð
9
:
79
Þ
where the coefficients must be determined by the Ritz method.
The matrix elements are
8
<
3
2
K
H
11
ES
11
¼
Q
E
þ
H
22
ES
22
¼
Q
E
H
12
ES
12
¼
H
21
ES
21
¼
ð
9
:
80
Þ
:
1
2
ð
Q
E
þ
3K
Þ¼
1
2
ð
Q
E
Þþ
3
2
K
The (2
2) secular equation is
3
2
x
2
þ
3
2
x
þ
¼
0
ð
9
:
81
Þ
x
2
þ
3
2
x
2
3
¼
0
)
x
¼
3
p
3
2
x
2
þ
3
2
)
x
2
x
x
þ
¼
ð
9
:
82
Þ
