Chemistry Reference
In-Depth Information
E
-
E
Li
E
H
E
+
Figure 2.8
Energy level diagram for a diatomic molecule formed between lithium (on
the left) and hydrogen (on the right). The isolated-atom energy levels
interact to give bonding and anti-bonding energy levels at
E
+
and
E
−
respectively, where
E
+
and
E
−
are defined by eq. (2.29).
The energy gap,
E
g
, between the highest occupied molecular orbital
(known as the HOMO) and the lowest unoccupied molecular orbital
(LUMO) is then given by
2
+
(
E
H
−
E
Li
)
U
2
E
g
=
2
4
or
E
g
=
(
2
2
2
U
)
+
(
E
H
−
E
Li
)
(2.30)
We rewrite this as
E
g
=
E
h
+
C
2
(2.30a)
to emphasise that there are two contributions to the energy gap, the cova-
lent bonding contribution
E
h
2
(where the subscript 'h' denotes
homopolar), and the ionic contribution,
C
2
=
(
2
U
)
2
, due to the dif-
ference in atomic orbital energy, which is often described by chemists in
terms of the difference in electronegativity of the two atoms. For any bond,
we can then define the bond covalency,
=
(
E
H
−
E
Li
)
α
c
, and polarity,
α
p
,by
2
U
E
h
E
g
α
=
=
c
2
2
(
2
U
)
+
(
E
a
−
E
c
)
and
|
E
a
−
E
c
|
C
E
g
α
=
=
(2.31)
p
2
2
(
2
U
)
+
(
E
a
−
E
c
)
where
E
a
and
E
c
refer to the orbital energies of the two atoms. We then
have for all bonds that
2
c
2
p
α
+
α
=
1
(2.32)
