Chemistry Reference
In-Depth Information
difference between the s and p states is large, i.e. for elements from the right-hand end of
the second row (see Figure 7.13).
If the s and p states are closer in energy, then mixing of the MOs formed from s and p
z
can occur. Figure 7.29 shows how this affects the MO diagram for the diatomic molecule.
The lowest energy valence orbital, 3
σ
g
+
, is shifted down in energy because mixing with the
p
z
-orbitals in 5
σ
g
+
leads to an increased orbital overlap in the hybrid state. The antibonding
σ
u
+
, is also shifted down in energy since the sp hybridization gives a weaker
overlap in the internuclear region and so this orbital becomes only weakly antibonding.
counterpart, 4
σ
u
+
) -
c
2
(6
σ
u
+
)
c
1
(4
σ
u
+
6
π
g
π
g
2
2
p
z
p
x
p
y
2p
σ
g
+
) -
c
1
(5
σ
g
+
)
c
2
(3
π
u
π
u
1
1
σ
g
+
5
σ
u
+
4
2s
σ
u
+
) +
c
2
(6
σ
u
+
)
c
1
(4
σ
g
+
3
σ
g
+
) +
c
2
(5
σ
g
+
)
c
1
(3
Figure 7.29
The effect of hybridization on the MO diagram of A
2
molecules. The orbital
labels of the
hybrids are referred to using the same numbering system as for the nonhybrid
case, i.e. starting from
3
σ
σ
g
+
as the lowest energy state; they are numbered in order of energy.
σ
g
+
state, but, since this is bonding when formed
purely from p
z
-orbitals, the loss of overlap density causes its energy to increase. Finally,
the antibonding character of the 6
A similar effect can be seen for the 5
σ
u
+
is increased on sp-hybridization.
The coefficients in the hybrids shown in Figure 7.29 will depend on the energy differ-
ence between the orbitals of matching symmetry. This, in turn, depends on the separation
of the AOs in the atomic states shown in grey in Figure 7.29. For closely spaced s and p
orbitals, coefficient
c
2
will be relatively large and sp-mixing gives the MO diagram to the
right of the figure. When the AOs of the parent atoms are widely spaced,
c
2
will tend to
zero and we recover the MO diagram in the centre of Figure 7.29 (remember that multi-
plying the entire MO by
−
1 does not change the energy of the orbital, only reverses the
phase pattern).
Perhaps the most important effect from hybridization is the change in the relative posi-
tioning of 5
π
u
. Symmetry alone cannot determine which molecules will have the
orbital ordering with 5
σ
g
+
and 1
σ
g
+
above 1
π
u
(significant sp-hybrids) and which will have 5
σ
g
+
