Molecular Geometry and
Bonding Theories
Chapter 9, Part 4
November 30th, 2004
Bond Order
• Defined as:
Bond order = ½(# of bonding electrons - # of antibonding electrons)
• For a single bond: bond order = 1.
• For a double bond: bond order = 2.
• For a triple bond: bond order = 3.
• Sometimes fractional bond orders are
possible.
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SecondSecond-row Diatomic Molecules
• Molecular Orbitals for Li2 and Be2:
– Each 1s orbital combines with another 1s orbital to
produce one σ1s and one σ1s*, both of which are
occupied by electrons.
– Each 2s orbital combines with another 2s to
produce one σ2s and one σ2s*, molecular orbitals.
– The energies of the 1s and 2s orbitals are
sufficiently different preventing any cross-mixing
(meaning there is no 1s + 2s mixing).
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Is Starship Enterprise powered by
Dilithium?
Dilithium?
• In the Li2 molecule there are in all 6 electrons:
– 2 electrons in σ1s
– 2 electrons in σ1s*
– 2 electrons in σ2s
– 0 electrons in σ2s*
• Since the 1s AOs are completely filled, the σ1s
and σ1s* MOs are also completely filled. The
core electrons are generally ignored in MO
diagrams.
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The Be2 Molecule
• Each Be2 molecule has a total of 8 electrons:
– 2 electrons are in the σ1s
– 2 electrons are in the σ1s*
– 2 electrons are in the σ2s
– 2 electrons are in the σ2s*
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2
MOs from 2p orbitals
• The p orbitals can overlap in 2 ways:
– End-on so that the resulting MO has electron
density on the axis between the nuclei (a σ MO).
– Sideways, so that the resulting MO has electron
density above and below the axis between the
nuclei (a π type MO).
• Thus 6 p orbitals (set of 3/atom) will produce 6
MOs: σ, σ*, π, π *, π and π*.
• A maximum of 2 p bonds can be produced
from the p orbitals.
• The relative energies of these 6 orbitals can
change.
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Molecular
Orbitals from 2p
Atomic Orbitals
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Configurations for B2 to Ne2
• Since 2s orbitals are lower in
energy than 2p, σ2s MOs are
lower in energy than σ2p
MOs.
• There is greater overlap
between the 2px orbitals
(they point directly at each
other) making the σ2p MO
lower in energy than the π2p
MOs.
• There is greater overlap
between 2pz orbitals so the
σ*2p MO is higher in energy
than the π*2p MO.
• The π2p and π*2p MOs are
doubly degenerate.
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3
Configurations for B2 to Ne2
• As the atomic number decreases, interactions
between a 2s orbital from one atom and a 2p
orbital become more likely.
– As the 2s-2p interaction increases, the σ2s MO
lowers in energy and the σ2p MO increases in
energy.
– For B2, C2 and N2 the σ2p MO is higher in energy
than the π2p MO.
– For O2, F2 and Ne2, the σ2p MO is lower in energy
than the π2p.
– Due to these differences the MOS now look like:
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Configurations for B2 to Ne2
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4
Magnetic Properties of Matter
• Most substance can be classified as
diamagnetic, meaning they are repelled
slightly by strong magnets.
• Diamagnetism occurs in substances whose
atoms or ions have paired electrons.
• Many metals and other compounds that are
attracted by strong magnets are called
paramagnetic.
• Paramagnetism occurs in substances whose
atoms or ions have unpaired electrons.
• The Lewis structure of O2 shows no unpaired
electrons. Why is O2 still paramagnetic?
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Why is O2 Paramagnetic?
• The MO diagram of O2 shows 2 unpaired electrons
in the π*2p MO.
• The MO diagram predicts both the bond order and
the paramagnetism of O2.
• Experimentally O2 has a short bond length (1.21 Å)
and high bond dissociation energy (495 kJ/mol)
suggesting a double bond.
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