Chemistry Reference
In-Depth Information
calculation shows that the real MOs are
<
1
f
1
¼
p ðx
1
þx
2
þx
3
þx
4
þx
5
þx
6
Þ
1
2
ðx
1
x
3
x
4
þx
6
Þ/
x
f
2
¼
1
f
3
¼
1
p ðx
1
þ
2
x
2
þx
3
x
4
2
x
5
x
6
Þ/
y
ð
7
:
96
Þ
:
1
x
5
þx
6
Þ/
x
2
y
2
f
4
¼
1
p ðx
1
2
x
2
þx
3
þx
4
2
1
2
ðx
1
x
3
þx
4
x
6
Þ/
xy
f
5
¼
1
p
ðx
1
x
2
þx
3
x
4
þx
5
x
6
Þ:
f
6
¼
The first degenerate MOs transform as (x,y) and are
bonding
(HOMOs); the second degenerate MOs transform as (x
2
y
2
, xy) and
are antibonding (LUMOs). These degenerate MOs have one and two
nodal planes respectively. The highest antibonding MO,
f
6
, has three
nodal planes. The six real MOs for the
electron system of benzene are
sketched in the drawings of Figure 7.7, where the same assumptions were
made as for cyclobutadiene.
The
p
r
a
and
r
b
components of the distribution function for benzene are
equal:
2
2
2
3
r
a
¼ r
b
¼ f
1
þf
2
þf
!
!
þx
!
1
6
þ
1
4
þ
1
12
1
6
þ
4
12
1
6
þ
1
4
þ
1
12
1
2
3
¼ x
þx
ð
7
:
97
Þ
!
!
þx
!
1
6
þ
1
4
þ
1
12
1
6
þ
4
12
1
6
þ
1
4
þ
1
12
2
4
2
5
2
6
þx
þx
so that
1
2
ðx
r
a
¼ r
b
¼
2
2
2
2
2
2
1
þx
2
þx
3
þx
4
þx
5
þx
6
Þ
ð
7
:
98
Þ
