Chapter 6 Molecular Structure & Bonding
(b) out-of-phase combination = * MO
s
(a) in-phase combination =
MOs
= =
Figure 6.19
σ bonds from end-on combinations of p orbitals
+
b) out-of-phase
= * orbitalp
=
+
a) in-phase= orbital
p
=
Nodal plane perpendicular to bondingaxis makes the orbital antibondingNodal planes containing the bondingaxis makes the orbital a orbital
p
Figure 6.20
π bonds from side-on combinations of p orbitals
DE
DE*
ss
s* s
Energy
= =
Figure 6.21 MO diagram for combining two s orbitals
While the color of each AO in diagrams su
ch as Figure 6.18 represents its phase in the
combination, the
size of the sphere represents its relative contribution to the MO
. The fact
that the two AOs are the same size in Figure 6.18 means that the two AOs contribute equally to the MO, which means that the electr
on density in the MO is distributed equally
over both atoms. MOs can be represented by e
ither the resulting combination as shown on
the right of Figure 6.18 or as the combining orbitals as shown on the left of Figure 6.18. We will use the latter method, where spheres
showing the sign and relative magnitude of
the contributing AOs will be shown rather than the resulting MO.
As shown in Figure 6.18,
and σ
- MOs are formed from the combination of two s σ
orbitals on different atoms. However,
σ
interactions are also pr
oduced by the head-on
combination of p orbitals. The combination of
orbitals that mixes lobes of the same phase
(Figure 6.19a) increases electron density
on the bonding axis, so it is a
bonding orbital. σ
The combination in which lobes of opposite phase interact (Figure 6.19b) annihilates electron density between the two atoms to produce a nodal plane perpendicular to the bonding axis, so it is a
- antibonding orbital. σ
The side-on combination of two p orbitals (Figure 6.20) results in no electron density
on the bonding axis, so both co
mbinations are classified as
. The combination of orbitals π
of the same phase increases electron density
between the bound atoms, so it is the
π
bonding orbital. The combination in which
lobes of opposite phase interact produces a
nodal plane perpendicular to the bonding axis, so it is an antibonding
- orbital. π
DIATOMIC MOLECULES The two nuclei in a
homonuclear diatomic molecule
are nuclei of the
same
element, so
the interacting atomic orbitals (AOs) are id
entical and contribute equally to the MO.
Consequently, the electron density in each MO
is symmetric and the bonds are nonpolar.
Each MO is characterized by an energy level, and electrons occupy the molecular orbitals in the same manner that they do atomic orbitals;
i.e.
, they fill the molecular orbitals at
lowest energy while obeying both Hund’s ru
le and the Pauli Exclusion Principle.
The energies of the
and σ
- orbitals relative to the s orbσ
itals used to construct them
are shown in an MO diagram. Three important characteristics of MO diagrams like those in Figure 6.21 are:
- The energy of bonding interactions is
lower than that of the atomic orbitals (
E). Δ
- The energy of antibonding orbitals is
higher than that of the atomic orbitals (
E*). Δ
3.
E* > Δ
E. Δ
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