Chemistry Reference
In-Depth Information
55
does satisfy the stationarity equation with an accuracy better
v ¼
7
:
10
5
. In the following, however, we shall content ourselves with
the rounded value
v
than 1
8
, which means 2% mixing of s into the bond
hybrid (98% p). In the range 7
v
8
jbj
has the practically constant
value
7 kcal mol
1
jbj¼
0
:
1142 E
h
¼
71
:
:
2.7.2.4 Charge Distribution in the Hybridized Basis
We now analyse the charge distribution in ground state HF resulting from
the
s
bond orbitals in the hybridized basis (Figure 2.15):
2
s
l
¼
scos
v
zsin
v
ð
2
:
164
Þ
b
h
l
þl
ssin
vþ
zcos
vþl
h
3
s
p
¼
p
ð
:
Þ
l
2
165
2
2
þ
1
þ
1
We have for the electron density (Magnasco, 2007, Magnasco, 2009a):
<
2
2
P
ðrÞ¼
2
½
2
s ðÞ
þ
2
½
3
s ðÞ
z
2
sin
2
v
s
2
cos
2
vþ
¼
2
½
sz sin2
v
Þ
1
2
s
2
sin
2
vþ
z
2
cos
2
vþ
2
h
2
þðl
þ
1
ð
szsin 2
vþl
Þ
s
2
2 cos
2
vþ
z
2
2 sin
2
vþ
h
2
2
2sin
2
v
l
2
2cos
2
v
l
l
:
¼
þ
þ
2
2
2
þ
1
þ
1
l
þ
1
sz
2
2sin2
v
l
þ
2
l
þ
1
ð
2
:
166
Þ
where the first three terms contribute to the heteropolar dipole (
m
H
), the
last term being the contribution from the so called atomic dipole
m
A
(Coulson, 1961). There is no contribution from the size effect (or homo-
polar) dipole moment, since we are neglecting explicit overlap between
our AOs. Of course, the conservation relation holds:
ð
d
r
P
ðrÞ¼
4
ð
2
:
167
Þ
