Chapter 6 Molecular Structure & Bonding
LUMO HOMO
p*^4 p^2 p
1
p*^3
Figure 6.27 MOs for C
H 6
viewed from the top 6
Hydrogen atoms have been omitted. Only the relative phases of the orbitals, not their relative contributions to the MOs, are shown.
so
π^2
is the highest occupied MO (HOMO) and
π^3
is the lowest unoccupied MO (LUMO).
Note that both pairs of electrons reside in bonding orbitals, consis
tent with the Lewis
structure that shows two double bonds. However,
the orbitals are delocalized over all four
carbon atoms, not localized between two atoms as shown in the Lewis structure.
As our last example, we examine the delocalized
system in benzene (Cπ
H 6
) shown in 6
Figure 6.27. Recall that the double bonds in benzene are sometimes represented by a circle (Figure 6.8b) due to resonance in the molecu
le. Although the construction of the MOs is
beyond the scope of this text, an examin
ation of them demonstrates the rules for
construction and provides a be
tter understanding of the bonding in this very important
molecule. There are six carbon atoms and six p orbitals, so there are six
MOs. The π
lowest energy MO has no nodal planes and is
a bonding orbital delocalized over all six
atoms. The highest energy orbital has a nodal plane between each pair of atoms, but, due to the symmetry of benzene, this requir
es only three nodal planes. Thus, the four
remaining MOs must contain either one or two nodal planes. In fact, two MOs have one nodal plane, and two MOs have two nodal planes. The
system has six electrons, so only π
the three bonding MOs are occupied, which gi
ves rise to the three double bonds in the
Lewis structure. The three MOs are delocali
zed over all six carbon atoms, so, consistent
with representing the double bonds with a circle, the
electron density is spread over the π
entire molecule with no localized double bonds.
6.6
CHAPTER SUMMARY AND OBJECTIVES According to the valence shell electron pa
ir repulsion (VSEPR) model, the valence
electron groups, or regions (lone pairs and
bonds) adopt positions around the atom so as σ
to minimize electron-electron repulsion. The geometries that minimize the interactions require bond angles of 109
o for four groups, 120
o for three groups, and 180
o for two
groups. Thus, the application of VSEPR theory to a Lewis structure provides an excellent way to determine the geometry of atoms around a central atom.
In valence bond theory, bonds are produced by the overlap of two orbitals on the
bound atoms. The bond that results is called a
bond if the internuclear axis is enveloped σ
by the bonding electron density or a
bond if the axis lies in a nodal plane of the bond. π
All bonds contain one and only one
bond, but multiple bonds also contain σ
bonds. The π
bond order of a bond is the sum of the
and σ
bonds that it contains. Overlap of simple π
atomic orbitals does not account for the bond
angles obtained from VSEPR, so the atomic
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