Extended Pi Bonding
In symmetry-based molecular orbital diagrams for the multiatom molecules water, ozone, and methane,
we'll combine group orbitals with the valence orbitals of the central atom. The group orbitals are linear
combinations of atomic orbitals from all the atoms bonded to the central atom.
In the simpler bonding models, chemical bonds are regions
of electron overlap between only 2 atoms. The molecular
orbital approach shows us how the chemical bonds affect
the entire molecule. This model of bonding gives results
that are in good agreement with the observations of electron
density and electron energy levels we obtain from
spectroscopy. Molecular orbital diagrams give a good,
qualitative picture of bonding in molecules.
Outline
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Resonance in Lewis Structures
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Pi Bonds over 3 Atoms
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Conjugated Multiple Bonds
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Homework
At right you see the resonance structures for benzene, a hydrocarbon
with alternating C-C and C=C bonds. The electron density map
shows that the pi electron density (green) is in a ring around the
molecule.
Resonance in Lewis Structures
For some molecules, there are two or more equally valid Lewis structures. Some examples are below.
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When there are two equivalent Lewis structures, the bonding of the molecule is likely to be an average of
the two.
Think about the molecular orbital diagram of each of these molecules. After forming sigma bonding and
sigma antibonding orbitals, three contiguous atoms have a remaining p orbital. These p orbitals are
pointing in the same direction, let's call that the x direction.
The Lewis structures show a double bond between either the first 2 atoms or the second 2 atoms. The two
structures differ only in the pi bonding.
Can we illustrate pi bonding that extends over 3 or more atoms in a molecular orbital diagram?
First, consider the hybridization of the oxygen atoms in ozone.
After forming the sigma bonds with the 2sp2 hybrid orbitals between the atoms, each oxygen atom has a
remaining 2p orbital for pi bonding.
Pi Bonds over 3 Atoms
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Ozone
Let's look at the molecular orbital diagram of ozone. We'll use the hybrid orbital approximation. Each
oxygen atom combines its 2s, 2pz and 2py orbitals to make three 2sp2 hybrid orbitals.
•
O1 uses one 2sp2 orbital to combine with one 2p2 orbital of O2, making a sigma bonding and
sigma antibonding orbital
•
O3 uses one 2sp2 orbital to combine with a second 2sp2 orbital of O2, making another sigma
bonding and sigma antibonding orbital
•
Two 2sp2 orbitals on O1, one 2sp2 orbital on O2, and two 2sp2 orbitals on O3 are non-bonding.
The 2px orbital on O1, the 2px orbital on O2, and 2px orbital on O3 combine to form three pi symmetry
orbitals.
The p orbitals in the picture above indicate electron density in those orbitals.
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π1, bonding all the way across the 3 atoms
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π2, non-bonding, zero pi electron density on the second atom
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π3, antibonding, the mathematical sign of the wavefunction changes with every atom, repulsive
interaction between atoms
The full molecular orbital diagram with the electrons is below.
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Nitrogen Dioxide
Nitrogen dioxide has one fewer electron than ozone. Because of
this, the highest energy orbital that is occupied by electrons, the
π2 orbital, has only one electron.
At right are the molecular orbitals for nitrogen dioxide.
The nitrogen atom is less electronegative than the oxygen atoms
so its atomic orbitals are a little higher in energy.
Because one of the non-bonding orbitals is localized on the N
atom, it is a little higher in energy than the four non-bonding
orbitals localized on the two oxygen atoms.
Because there is one 2px orbital on each atom available for pi
bonding, there are three pi symmetry molecular orbitals.
Each oxygen atom contributes is 6 valence electrons and the
nitrogen contributes 5 electrons.
The total, 11 electrons, fills orbitals from low energy to higher
energy.
The π2 orbital has only 1 electron.
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Allyl Radical
In CH2CHCH2, 5 of the carbon 2sp2 hybrid orbitals
combine with the 5 hydrogen 1s orbitals to form 5 C-H σ
bonding orbitals and 5 C-H σ antibonding orbitals. These
levels are colored blue in the figure.
The remaining four carbon 2sp2 hybrid orbitals (one each on
the end carbons and two on the middle carbon) combine to
form 2 C-C σ bonding orbitals and 2 C-C σ antibonding
orbitals. These levels are black in the figure.
The 2px orbitals (one from each carbon atom) combine to
form the three pi orbitals. These are green in the figure.
There are a total of 17 electrons, 4 from each carbon and 1
from each hydrogen atom.
Conjugated Multiple Bonds
When each adjacent atom in a row of have a p orbital with the same orientation, a px orbital for example,
the p orbitals will combine to make pi orbitals that extend over all those atoms. The atoms in such a set
have a conjugated pi system.
For a conjugated set of n atoms:
1.
n atomic p orbitals forms a set of n pi symmetry molecular orbitals
2.
average energy of the pi molecular orbitals equals the average energy of the p orbitals
3.
as n increases, the energy difference between the pi molecular orbitals decreases
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Why is this important? When molecules contain pi bonding orbitals, the highest occupied molecular
orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are typically pi symmetry
molecular orbitals.
Molecules are colored when they absorb visible light. In unsaturated molecules, an electron is promoted
from one pi orbital to another. The difference in energy between these orbitals determines the wavelength
of light that the molecule can absorb.
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The molecules in the table above are all colorless. The energy between the HOMO and LUMO pi orbitals
is above the visible light region. They absorb light in the shorter wavelength ultraviolet region of the
spectrum.
The beta-carotene molecule, with 26 interacting p orbitals, does absorb visible light. You've seen that
ozone acts as a bleach, converting the orange molecule to a colorless one. This is because it breaks the pi
system. Instead of 26 interacting p orbitals with an energy gap in the visible region, there is a 14 p orbital
unit and a 10 p orbital unit. These pi systems have a HOMO-LUMO energy gap in the ultraviolet.
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