Chemistry Reference
In-Depth Information
f
i
, n
i
the number
of electrons in the ith AO
x
i
in the separated atoms, we define the bond
energy as:
If n
i
is the number of electrons occupying the ithMO
X
X
occ
occ
n
i
a
i
D
E
¼
n
i
«
i
ð
2
:
62
Þ
i
i
which, for homonuclear diatomics, reduces to the expression used in
Section 2.1:
X
X
occ
occ
D
E
¼
n
i
ð«
i
aÞ¼
n
i
D«
i
ð
2
:
63
Þ
i
i
The filling of electrons into the MO levels has now more possibilities
than in the previous homonuclear case. These cases are fully described
elsewhere (Magnasco, 2003).
Apart from their asymptotic form for 0
< jbj < a
2
a
1
(Equations 2.20
and 2.23 in Section 2.1), the general expressions for the orbital interaction
energies of the heteropolar MOs are rather complicated in the case of
nonorthogonal AOs. For the sake of simplicity, we shall content ourselves
with the simpler expressions occurring in the case of orthogonality
between the interacting AOs
x
1
and
x
2
. Under this assumption, Equations
(2.58) simplify to:
<
:
x
1
þl
x
2
1
f
1
¼
p
bonding MO
2
þl
ð
2
:
64
Þ
x
2
lx
1
1
f
2
¼
p
antibonding MO
2
þl
with the orbital energies:
a
1
þa
2
2
2
;
a
1
þa
2
2
þ
2
«
1
¼
«
2
¼
ð
2
:
65
Þ
where now:
2
4
b
2
1
=
2
D ¼½ða
2
a
1
Þ
þ
>
0
ð
2
:
66
Þ
We observe that, in this case, the splitting of the molecular levels upon
interaction is symmetric with respect to the arithmetic mean of the atomic
levels (Figure 2.13).
Table 2.7 collects the bond energies
E for the eight possible ways of
filling electrons into the MO levels resulting for a heteronuclear
s
system
D
