Chemistry Reference
In-Depth Information
uckel theory, we put
b
sh
¼ b
s
h
¼ b
, a parameter
characteristic of the N
If, in the spirit of H
€
H bond, the coefficients become after dividing
by
b
2
:
<
24
b
2
cos
2
v ð
cos
2
vþ
A
¼
2
Þ
24
b
2
sin2
v ð
cos
2
vþ
B
¼
2
Þ
8
<
9
=
3
b
2
1
4 sin
2
v
h
i
2
2
2
cos
4
v ða
p
a
h
Þ
6
b
2
C
¼
4
ða
b
a
h
Þ
þ
2
ð
sin2
vÞ
þ
þ
:
;
:
2
4 sin2
v
cos
2
v ½ða
p
a
h
Þ
6
b
2
D
¼
þ
2
2
6
b
2
¼ð
sin2
vÞ
½ða
p
a
h
Þ
þ
:
E
ð
2
:
242
Þ
As before, we now examine the following two particular cases.
(i) For
v ¼
0 (no hybridization),
a
b
a
h
¼ a
p
a
h
, coefficients B, D, E
72
b
2
24
b
2
, and Equation (2.241) gives:
vanish, A
¼
;
C
¼
8
<
1
p
Y
g ¼
74
3x
2
¼
1
;
x
¼
cos
g ¼
54
:
ð
2
:
243
Þ
p
p
Y
2
:
2
3
1
90
p
p
Y
sin
g ¼
sin
u ¼
sin
u ¼
2
u ¼
as it must be.
(ii) If we put:
a
b
a
h
¼ a
p
a
h
¼
0
ð
2
:
244
Þ
(which is tantamount to assuming nonpolar bonds) dividing through-
out by 6
b
2
, the coefficients will depend only on
v
, becoming:
<
4 cos
2
v ð
cos
2
vþ
A
¼
2
Þ
cos
2
vþ
B
¼
4 sin 2
v ð
2
Þ
2
8 sin
2
v
4 cos
4
v
ð
2
:
245
Þ
C
¼ð
sin 2
vÞ
þ
:
4 sin 2
v
cos
2
v
D
¼
2
E
¼ð
sin 2
vÞ
