Chemistry Reference
In-Depth Information
The H
€
uckel matrix elements are:
<
¼ a
p
H
zh
z
¼
p
b
s
h
cos
H
zz
ð
:
Þ
g
2
224
:
H
h
z
h
z
¼ a
h
þ
2
b
hh
a
h
8
<
H
xx
¼ a
p
p
p
b
s
h
sin
H
yh
y
¼
g
ð
2
:
225
Þ
:
H
h
x
h
x
¼ a
h
b
hh
a
h
8
<
H
yy
¼ a
p
p
H
yh
y
¼
p
b
s
h
sin
g
ð
2
:
226
Þ
:
H
h
y
h
y
¼ a
h
b
hh
a
h
uckel theory.
29
The three lowest roots of the secular equations give the H
where
b
hh
is neglected as usual in H
€
uckel energy
of the 3a
1
1e
x
1e
y
valence electron configuration of NH
3
as a function of
angle
€
g
:
(
E
ðgÞ¼
2
«
1
ð
A
1
Þþ
2
«
1
ð
E
x
Þþ
2
«
1
ð
E
y
Þ
ð
2
:
227
Þ
¼
3
a
p
þ
3
a
h
D
2
D
1
3
where:
<
2
1
=
2
2
1
=
2
4H
zh
z
12
b
s
h
cos
2
D
1
ðgÞ¼½ða
p
a
h
Þ
þ
¼½ða
p
a
h
Þ
þ
g
>
0
:
2
1
=
2
2
1
=
2
6
b
s
h
sin
2
4H
xh
x
D
ðgÞ¼½ða
p
a
h
Þ
þ
¼½ða
p
a
h
Þ
þ
g
>
0
3
ð
:
Þ
2
228
Taking the first
g
-derivatives of the
D
s, the stationarity condition for the
energy is:
dE
d
d
D
1
d
2
d
D
3
d
1
D
1
D
6
b
s
h
sin 2
g
¼
g
g
¼
g
1
¼
0
ð
2
:
229
Þ
3
29
In the second of Equations (2.224) the minus sign accounts for the need of positive overlap
between the z AO of nitrogen and the symmetrical sum h
z
of hydrogen AOs.
