The particle-in-a-box model can be used to describe the energy of an
electron confined within a three-dimensional region of nanoscale
dimension. This is known as quantum confinement, and examples
involving quantum confinement in solid nanoparticles are given in
Chapter 9.
5.4.2 Conjugation in organic molecules
The free electron model can be applied to conjugated organic molecules.
In fact, the model can help us explain why the absorption wavelength
increases as the length of the molecule increases. We will use the term
conjugation length to describe the length of the alternating double- and
single-bonded hydrocarbon chain in which the electrons are delocalized
over. First let’s review some background on the structure of conjugated
organic molecules.
As briefly mentioned in the last section, a conjugated system has three sp
2
hybridized orbitals on every carbon atom, which form covalent bonds
with nearby atoms. This accounts for the s-bonding in the molecule. The
leftover unhybridized p z orbital combines with other p z orbitals to form a
delocalized π MO that spans the length of the molecule. For example,
ethylene has two atomic p z orbitals, f 1 and f 2 . From these two atomic
orbitals, two MOs, y 1 and y 2 *, are formed by taking linear combinations.
The bonding MO, y 1 , results from the in-phase combination of the wave
functions of the two p orbitals, whereas the antibonding orbital, y 2 *,
results from the out-of-phase combination. The overlap results in two
new MOs—one bonding orbital with an energy lower than either of the
original p orbitals and one antibonding orbital with an elevated energy.
The relative energies of these MOs are illustrated in Figure 5.18. It must be
pointed out that only the π MOs are shown in the figure. These MOs result
from the overlap between unhybridized p-orbitals on the carbons. The
MOs resulting from s-bonds are not shown since this is not relevant to
our discussion of conjugation.
In terms of shape, the bonding MO has electron density above and below
the line connecting the two carbon atoms. There is no node between
these atoms. In contrast, the antibonding MO has a node between the
two carbons. The antibonding MO has electron density concentrated
near each of the two carbon atoms, but zero electron density between
these atoms. The presence of a node means no bond, thus the term
antibonding MO.
CHAPTER 5: Intermolecular Interactions and Self-Assembly
170
electron confined within a three-dimensional region of nanoscale
dimension. This is known as quantum confinement, and examples
involving quantum confinement in solid nanoparticles are given in
Chapter 9.
5.4.2 Conjugation in organic molecules
The free electron model can be applied to conjugated organic molecules.
In fact, the model can help us explain why the absorption wavelength
increases as the length of the molecule increases. We will use the term
conjugation length to describe the length of the alternating double- and
single-bonded hydrocarbon chain in which the electrons are delocalized
over. First let’s review some background on the structure of conjugated
organic molecules.
As briefly mentioned in the last section, a conjugated system has three sp
2
hybridized orbitals on every carbon atom, which form covalent bonds
with nearby atoms. This accounts for the s-bonding in the molecule. The
leftover unhybridized p z orbital combines with other p z orbitals to form a
delocalized π MO that spans the length of the molecule. For example,
ethylene has two atomic p z orbitals, f 1 and f 2 . From these two atomic
orbitals, two MOs, y 1 and y 2 *, are formed by taking linear combinations.
The bonding MO, y 1 , results from the in-phase combination of the wave
functions of the two p orbitals, whereas the antibonding orbital, y 2 *,
results from the out-of-phase combination. The overlap results in two
new MOs—one bonding orbital with an energy lower than either of the
original p orbitals and one antibonding orbital with an elevated energy.
The relative energies of these MOs are illustrated in Figure 5.18. It must be
pointed out that only the π MOs are shown in the figure. These MOs result
from the overlap between unhybridized p-orbitals on the carbons. The
MOs resulting from s-bonds are not shown since this is not relevant to
our discussion of conjugation.
In terms of shape, the bonding MO has electron density above and below
the line connecting the two carbon atoms. There is no node between
these atoms. In contrast, the antibonding MO has a node between the
two carbons. The antibonding MO has electron density concentrated
near each of the two carbon atoms, but zero electron density between
these atoms. The presence of a node means no bond, thus the term
antibonding MO.
CHAPTER 5: Intermolecular Interactions and Self-Assembly
170