21.5 The Valence-Bond Description of Polyatomic Molecules 883
This wave function is probably superior to that used in Chapter 20 without hybrid orbitals,
since it allows the lone pair electrons to be farther from each other on the average, and thus
probably more nearly resembles the energy-localized wave function.Exercise 21.10
Construct an LCAOMO wave function for diatomic fluorine using the hybrid orbitals.Valence-bond descriptions of multiple bonds are also similar to the simple LCAOMO
description. A double bond consists of a sigma bond and a pi bond, and a triple bond con-
sists of a sigma bond and two pi bonds. Each bonding factor replaces one LCAOMO,
but nonbonding orbitals are the same in both methods. There are no analogues to
antibonding orbitals in the simple valence-bond method, so molecules with unpaired
electrons such as O 2 also cannot be well described in the simple valence-bond method.
The extended valence-bond methods mentioned in Chapter 20 are more versatile.EXAMPLE21.7
Describe the bonding in the ethyne (acetylene) molecule, using the valence-bond method.
Solution
Four electrons occupy the two carbon 1sspace orbitals. Two electrons occupy a carbon–carbon
sigma bonding factor made from a 2sphybrid on each carbon, and four electrons occupy two
carbon–hydrogen sigma bonding factors made from a 2sphybrid orbital on a carbon atom
anda1sorbital on a hydrogen atom. The last four electrons occupy two carbon–carbon pi
bonding factors, one made from the 2pxon each carbon atom and one made from the 2py
orbital on each carbon atom, making a triple carbon–carbon bond. The molecule is linear.Exercise 21.11
Using the valence-bond method, describe the bonding in the propene (propylene) molecule. Give
the bond angles around each carbon.Other Types of Hybrid Orbitals
In addition to thesp,sp^2 , andsp^3 hybrid orbitals, there are hybrid orbitals that include
dorbitals, either from the same shell as thesandporbitals or from the next lower shell.
If onedspace orbital is included in addition to the four space orbitals of thesandp
subshells, five hybrid space orbitals can be constructed. These are calledsp^3 dhybrids if
thedorbital is from the same shell as thesandporbitals ordsp^3 hybrids if thedorbital
is from the next lower shell. The symmetry axis of one orbital points along the positive
zaxis, that of another points along the negativezaxis, and three point in thexyplane
in directions 120◦from each other. This geometry is called “trigonal bipyramidal,” and
is included in the simple VSEPR theory for five charged regions. Thesp^3 dorbitals
can be used to construct sigma LCAO molecular orbitals or valence-bonding factors
for molecules such as IF 3 ,PF 5 ,SF 4 , and so on, that have five pairs of electrons in the
valence shell of the central atom.