Chemistry Reference
In-Depth Information
Figure 2.26
Energy levels (left) and H
€
uckel MOs (right) for the allyl radical ground
state
ð
N
¼
3
Þ
secular equation gives:
¼
x 10
1
x
2
D
3
¼
x
1
x
ð
2
Þ¼
0
ð
2
:
261
Þ
01
x
with the ordered roots:
p
;
p
¼
¼
;
¼
ð
:
Þ
x
1
x
2
0
x
3
2
262
and the MOs:
8
<
p
x
2
þx
3
2
x
1
þ
f
1
¼
x
1
x
3
2
p
f
2
¼
ð
2
:
263
Þ
:
p
x
2
þx
3
2
x
1
f
3
¼
Figure 2.26 gives the diagram of the energy levels as occupied by
electrons for the ground state of the allyl radical and the related H
uckel
€
.
32
molecular orbitals
f
s
ðf
2
¼
HOMO
; f
3
¼
LUMO
Þ
The electron distribution of the
p
electrons in the allyl radical ground
state is:
<
:
P
ðrÞ¼
contribution from
a
and
b
spin
¼ r
a
ðrÞþr
b
ðrÞ
¼ x
1
ðrÞþx
2
ðrÞþx
3
ðrÞ;
ð
2
:
264
Þ
32
This is true for the allyl radical
ð
N
¼
3
Þ
and for the allyl anion
ð
N
¼
4
Þ
, but
f
1
¼
HOMO
;
f
2
¼
LUMO for the allyl cation (N
¼
2).
