Chemistry Reference
In-Depth Information
a
p
are in unexpected fair agree-
ment with the negative of the ionization potentials observed from exper-
imental UV photoelectron spectra of ground state HF (Lempka et al.,
1968; Potts and Price, 1972; Price, 1974):
The two lowest roots, as well as
«
p
«
2
¼ «ð
2s
Þ¼
1
:
433 E
h
;
«
3
¼ «ð
3s
Þ¼
0
:
702 E
h
;
ð
2
:
150
Þ
«
4
¼ «ð
1
pÞ¼
0
:
588 E
h
:
Therefore, the bond dissociation energy resulting from the solution
of the complete cubic H
€
uckel equation for one-term SCF/STOs and
jbj¼
0
:
114E
h
will be:
8
<
S
þ
Þ¼
S
þ
Þ
1
1
D
E
ð
HF
;
E
ð
HF
;
2
a
s
5
a
p
a
h
ð
2
:
151
Þ
¼
2
«ð
2
sÞþ
3
«ð
3
sÞþ
4
«ð
1
pÞ
2
a
s
5
a
p
a
h
:
¼
0
:
245 E
h
in complete agreement with the assumed spectroscopic value of
D
jj¼
:
245 E
h
(Huber and Herzberg, 1979).
However, if we attempt to extract, from the calculated MOs, informa-
tion on the resulting sp hybrids on F, we are faced with the problem that
such hybrids are not orthogonal and therefore not mutually exclusive,
as already observed long ago by us (Magnasco and Perico, 1967, 1968) in
obtaining localized MOs from ab initio results.
0
2.7.2.3 Introducing Hybridization into
S
Symmetry
We nowmake the orthogonal transformation
O
of the original basis to the
hybridized basis (Magnasco, 2009b; Magnasco, 2009c):
0
@
1
A
cos
v
sin
v
0
ð
lbh
Þ¼
ð
szh
Þ
sin
v
cos
v
0
ð
2
:
152
Þ
0
0
1
which corresponds to introducing the pair of orthogonal hybrids
(Figure 2.15):
(
l
¼
scos
v
zsin
v
lone pair hybrid
ð
2
:
153
Þ
b
¼
s sin
vþ
zcos
v
bond hybrid
where
v
is the hybridization (mixing) parameter. Putting
v ¼
0 gives the
previous case of no hybridization.
