Chemistry Reference
In-Depth Information
<
1
1
2
1
p
p
p
p
x
¼
sin
u sþ
cos
u p
x
y
1
2
1
2
1
p p
ð
2
:
111
Þ
:
y
¼
p
sin
u s þ
p
cos
u p
þ
x
y
z
¼
cos
u s
sin
u p
x
2
u
being the interbond (valence) angle. Then:
b
xh
¼ b
yh
¼ b
ph
1
p
sin
u
b
zh
¼ b
ph
cos
u
ð
2
:
112
Þ
where
b
ph
is a quantity characteristic of the bond.
The lowest roots of the secular equations will give the H
€
uckel energy
of the eight valence electrons as a function of angle
u
:
<
:
2
X
occ
E
ðuÞ¼
«
i
¼ða
s
þa
h
Þþ
3
ða
p
þa
h
Þ
i
h
i
1
=
2
h
i
1
=
2
2
16
b
sh
2
16
b
xh
ða
s
a
h
Þ
þ
ða
p
a
h
Þ
þ
h
i
1
=
2
h
i
1
=
2
2
16
b
yh
2
16
b
zh
ða
p
a
h
Þ
þ
ða
p
a
h
Þ
þ
ð
2
:
113
Þ
¼ða
s
þ
3
a
p
þ
4
a
h
Þ
h
i
1
=
2
2
16
b
sh
ða
s
a
h
Þ
þ
h
i
1
=
2
2
8
b
ph
sin
2
u
2
ða
p
a
h
Þ
þ
h
i
1
=
2
2
16
b
ph
cos
2
u
ða
p
a
h
Þ
þ
!
!
for:
d
2
E
d
u
2
dE
d
u
¼
which has an absolute minimum
0
;
5
o
>
0
2
u¼
109
:
<
:
1
2
sin
2
u
cos
2
u ¼
p
ð
2
:
114
Þ
1
p ;
5
cos
u ¼
sin
u ¼
p
Y
2
u ¼
109
:
i.e. the tetrahedral angle.
