Chemistry Reference
In-Depth Information
and fourth row of Figure 7.3) are
<
:
f
1
¼
0
:
x
1
þ
0
:
601
ðx
2
þx
3
Þþ
0
:
x
4
371
371
f
2
¼
0
:
601
x
1
þ
0
:
371
ðx
2
x
3
Þ
0
:
601
x
4
ð
7
:
74
Þ
f
3
¼
0
:
601
x
1
0
:
371
ðx
2
þx
3
Þþ
0
:
601
x
4
f
4
¼
0
:
371
x
1
0
:
601
x
2
þ
0
:
601
x
3
0
:
371
x
4
with the first two being bonding MOs (
f
2
¼
HOMO) and the last two
antibonding MOs (
f
3
¼
LUMO).
Proceeding as we did for allyl, it is easily seen that the electron charge
distribution is uniform (one
p
electron onto each carbon atom, alternant
hydrocarbon) and the spin density is zero, as expected for a state with
S
¼
M
S
¼
0, since the two bonding MOs are fully occupied by electrons
with opposite spin. The delocalization energy for linear butadiene is
D
E
p
ð
butadiene
Þ
2
D
E
p
ð
ethylene
Þ¼
4
:
472
4
¼
0
:
472
ð
7
:
75
Þ
and, therefore, is sensibly less than the conjugation energy of the allyl
radical.
7.4.4 Cyclobutadiene (N
¼
4)
The H
€
uckel secular equation for the square ring with N
¼
4is
x 101
1
x 10
¼
x
4
4x
2
¼
x
2
ð
x
2
D
4
¼
4
Þ¼
0
ð
7
:
76
Þ
01
x
1
1 01
x
where the boldface elements are the only ones differing from those of the
linear chain (1 and 4 are now adjacent atoms). The roots of Equation 7.76
are x
1
¼
2, x
2
¼
x
3
¼
0 (doubly degenerate), and x
4
¼
2 (right in the
bottom row of Figure 7.2).
