Chemistry Reference
In-Depth Information
We start by considering that, in the first approximation, only the
appropriate 2p AO on fluorine (2p
z
, in short denoted by z) contributes
to the bonding with the 1s AOof hydrogen (in short, h). Two electrons are
placed in the undistorted
s
F lone pair s
2
, and four electrons in the two
p
F
lone pairs x
2
y
2
. As usual in elementary H
uckel theory, for the sake of
simplicity, we do not consider explicitly the overlap between basic AOs
(which are hence assumed orthonormal), but still maintain their implicit
dependence on overlap in the bond integral
17
€
(Magnasco, 2004a). The
bonding MO is then given by the Ritz method as:
jbj
z
h
l
þl
p
s ¼
zC
1
þ
hC
2
¼
ð
2
:
118
Þ
2
þ
1
where
C
2
C
1
l ¼
1
is the polarity parameter. The coefficients are obtained from the lowest
root of the 2
2H
€
uckel secular equation:
¼
H
zz
«
H
zh
0
ð
2
:
119
Þ
H
zh
H
hh
«
H
€
uckel matrix elements are:
H
zz
¼ a
p
;
H
hh
¼ a
h
;
H
zh
¼ b
ð
2
:
120
Þ
all elements being negative quantities. Roots are:
2
« ¼ða
p
þa
h
ÞD
ð
2
:
121
Þ
2
4
b
2
1
=
2
D ¼½ða
p
a
h
Þ
þ
>
0
ð
2
:
122
Þ
uckel energy for the valence electron configuration s
2
s
2
x
2
y
2
of ground state HF will be:
€
so that the H
S
þ
Þ¼
1
E
ð
HF
;
2
a
s
þ
4
a
p
þða
p
þa
h
ÞD
ð
2
:
123
Þ
The bond energy is then (Magnasco, 2003):
1
S
þ
Þ¼
1
S
þ
Þ
D
E
ð
HF
;
E
ð
HF
;
2
a
s
5
a
p
a
h
¼D ¼j
D
j ð
2
:
124
Þ
17
Orthogonal does not mean not interacting (Footnote 3). This is tantamount to keeping only the
exchange part of the exchange-overlap interaction (Magnasco, 2002, 2004a).
