Physical Chemistry Third Edition

912 21 The Electronic Structure of Polyatomic Molecules

21.71Use a computer program such as CAChe or Spartan to
find the semiempirical approximations to the SCF orbitals
for cyclooctatetraene (C 8 H 8 ), using several methods,
such as AM1, PM3, extended Hückel, and so on. Does the
molecule appear to be aromatic?

21.72Use a computer program such as CAChe or Spartan to
find the semiempirical approximations to the SCF orbitals
for 1,3,5,7-octatetraene (C 8 H 10 ), using several methods,
such as AM1, PM3, extended Hückel, and so on.

21.73Using a program that carries out molecular mechanics,
find the equilibrium conformation of each of the
following molecules. Compare the bond angles and bond
lengths with those obtained with AM1 or PM3
semiempirical methods.

a.H 2 CO

b.CHCl 3

21.74Using a program that carries out molecular mechanics,

find the equilibrium conformation of each of the

following molecules. Compare the bond angles and bond

lengths with those obtained with AM1 or PM3

semiempirical methods.

a.C 2 H 4

b.CH 3 Cl

21.75Using a program that carries out molecular mechanics,

find the equilibrium conformation oftrans-1,3-butadiene.

Compare the bond angles and bond lengths with those

obtained with AM1 or PM3 semiempirical methods.

Summary of the Chapter

In this chapter, we have discussed the quantum mechanics of electrons in polyatomic

molecules using the Born–Oppenheimer approximation, which is the assumption that

the nuclei are stationary as the electrons move. Approximate LCAOMOs for poly-

atomic molecules were constructed as linear combinations of only two atomic orbitals,

conforming to these three general criteria. In the case of the water molecule, it was

found thatsp^3 hybrid atomic orbitals could produce a satisfactory wave function with a

bond angle of 109.5◦. Thesp^2 hybrid orbitals were useful in constructing LCAOMOs

for molecules with double bonds, such as ethene, with the second bond being repre-

sented by an LCAOMO made from unhybridized 2porbitals. Thesphybrid orbitals

were used in molecules with triple bonds, such as ethyne, with two bonds represented

by LCAOMOs made from unhybridized 2porbitals.

Delocalized bonding was described in the valence-bond method by use of the concept

of resonance. In the molecular orbital description, delocalized LCAOMOs are used. For

example, in the benzene molecule, six of the electrons occupy delocalized orbitals.

A brief introduction to group theory was presented, along with two elementary

applications: Determining whether a molecule could be polar and whether it could be

optically active.

A brief survey of some of the modern semiempirical molecular orbital methods was

presented. These methods can be carried out using commercially available computer

software that is relatively easy to use.

ADDITIONAL PROBLEMS

21.76The N 2 O molecule is linear and might have either of the
two structures NNO or NON.
a.Using simple Lewis electron dot formulas, decide
which structure is more likely, using the formal charge
criterion from your general chemistry course.

b.Describe the bonding in the molecule for both of the

structures and see if you can decide on the correct

structure independently of part a.

21.77Using either the LCAOMO method or the valence-bond

method, describe the bonding in the following molecules.