Chemistry Reference
In-Depth Information
giving
1
1
2
c
1
þ
c
1
¼
2c
1
)
c
1
¼
p
;
p
c
2
¼
0
;
c
3
¼
c
1
;
c
2
¼
0
;
c
3
¼
ð
7
:
61
Þ
which is the second column of matrix (7.57).
(c) x
3
¼
p
<
:
p
c
1
þ
c
2
¼
0
1
:
p
c
2
þ
c
3
¼
0
2
:
c
1
þ
p
c
3
¼
0
c
1
þ
c
2
þ
c
3
¼
1
c
2
þ
ð
7
:
62
Þ
3
:
c
2
¼
p
c
1
1
:
gives now
:
1
3
:
gives
:
c
3
¼
p
c
2
¼
c
1
so that it is immediately obtained that
p
2
1
2
;
1
2
ð
7
c
1
þ
2c
1
þ
c
1
¼
4c
1
¼
1
)
c
1
¼
c
2
¼
;
c
3
¼
:
63
Þ
2
which is the third column of matrix (7.57).
It is of interest to evaluate charge and spin density distributions in
the allyl radical, asssuming that the unpaired electron has
a
spin
. It is convenient to write explicitly the three MOs as
1
2
S
¼
M
S
¼
p
2
p
2
1
2
ðx
1
þ
1
1
2
ðx
1
f
1
¼
x
2
þx
3
Þ; f
2
¼
p ðx
1
x
3
Þ; f
3
¼
x
2
þx
3
Þ
ð
7
:
64
Þ
r
a
and
r
b
components of the
We then have the following for the
distribution function:
1
4
x
2
4
x
1
4
x
2
4
x
2
4
x
3
4
x
2
4
x
3
4
x
r
a
¼ f
2
2
2
2
2
2
2
2
2
2
3
1
þf
2
¼
1
þ
2
þ
3
þ
1
þ
3
¼
1
þ
2
þ
ð
7
:
65
Þ
