June 10, 2009 – Class 37 and 38 Overview
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11.5 Molecular Orbital Theory.
– Bonding and antibonding molecular orbitals, properties of
molecular orbitals, bond order, molecular orbital
diagrams, diatomics of the first period elements,
molecular orbitals of the second period elements, a
special look at O2, heteronuclear diatomic molecules.
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11.6 Delocalized Electrons: Bonding in the Benzene
Molecule
– Delocalized pi bonding and resonance, delocalized
molecular orbitals, other structures with delocalized
molecular orbitals, non-bonding molecular orbitals.
Molecular Orbital Theory
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Lewis structures, VSEPR theory and valence bond
method are normally satisfactory for describing
covalent bonding and molecular structures.
They do not answer the questions:
Why is O2 paramagnetic?
Why is H2+ a stable species?
What is the explanation for
electronic (UV-vis) spectra?
These answers require another method to describe
chemical bonding.
Molecular Orbital Theory
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Molecular Orbital Theory: describes the covalent
bonds in a molecule by replacing atomic orbitals of
the component atoms by molecular orbitals
belonging to the molecule as a whole. A set or
rules is used to assign electrons to these molecular
orbitals, thereby yielding the electronic structure of
the molecule.
–
–
Molecular orbitals are mathematical functions.
Molecular orbitals may each, only accommodate two
electrons, with opposite spins.
Molecular Orbital Theory
•
Even for a seemingly simple molecule like H2, to solve
the Schrodinger equation we must make assumptions.
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–
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Atomic orbitals are isolated on atoms.
Molecular orbitals span two or more atoms.
Linear combination of atomic orbitals.
Ψ1 = φ1 + φ2
Two 1s wave functions
combine by constructive
interference.
Ψ2 = φ1 - φ2
Two 1s wave functions
combine by deconstructive
interference.
Molecular Orbital Theory
Bonding molecular orbital:
describes regions of high
electron probability or charge
density in the internuclear region
between two bonded atoms.
Antibonding molecular orbital (*):
describes regions in a molecule
in which there is a low electron
probability or charge density
between two bonded atoms.
Molecular Orbital Theory – H2
For antibonding orbitals:
Electron density is high in parts of the molecule outside the
internuclear region.
Nuclei are therefore not shielded from each other and
strong repulsions occur.
Population of these orbitals leads to bond weakening.
Molecular Orbital Theory – H2
For bonding orbitals:
Electron density is high in the internuclear region.
Nuclei are therefore shielded from each other and
repulsions are minimized.
Population of these orbitals leads to strong bonds.
Molecular Orbital Theory – H2
Molecular Orbital Theory
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Properties of molecular orbitals
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The number of molecular orbitals (MOs) formed is equal to the
number of atomic orbitals combined.
–
Of the two MOs formed when two atomic orbitals are
combined, one is a bonding MO (lower energy) and one is an
antibonding MO (higher energy).
–
In the ground state, electrons enter the lowest energy MO
available.
–
Pauli Exclusion Principle is obeyed: a maximum of two
electrons may be contained in a single MO.
–
Hund’s rule is obeyed: in the ground state, electrons enter
degnerate orbitals singly before pairing up.
Molecular Orbital Theory
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Molecular orbital diagrams show the energy levels
of the isolated atoms to the left and right of the
MOs for a molecule.
Molecular orbital diagrams for diatomics of the first period
elements
Molecular Orbital Theory
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A stable molecular species is one that has more
electrons in bonding MOs than in antibonding MOs.
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Previously, we had stated that for a single bond, the
bond order (B.O.) = 1, for a double bond B.O. = 2,
etc…we may now formally define this in terms of MOs.
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Bond order: one-half the difference between the
numbers of electrons in bonding and in antibonding
molecular orbitals in a covalent bond.
# e- in bonding MOs - # e- in antibonding MOs
Bond Order =
2
Molecular Orbital Theory
Problem: Calculate the bond order for the diatomic
molecules of the first-period elements and state
whether these should be stable species.
Molecular orbitals of the second period elements
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•
•
First period elements use only 1s orbitals for formation
of molecular orbitals.
Second period elements have 2s and 2p orbitals
available.
p orbital overlap:
– End-on overlap is best – sigma bond (σ).
– Side-on overlap is good – pi bond (π).
Molecular orbitals of the second period elements
(a) The addition of two 2p orbitals,
in phase, along the internuclear
axis to form a s2p MO.
Electron density is located
between the nuclei leading to
bond formation.
(b) The addition of two 2p orbitals,
out of phase, forming a s*2p
MO.
This orbital has a nodal plane
perpendicular to the
internuclear axis (as do all
antibonding orbitals!)
Molecular orbitals of the second period elements
(c) The addition of two 2p orbitals,
in phase, perpendicular to the
internuclear axis to form a p2p
MO.
Electron density is located
between the nuclei contributing
to multiple bond formation.
(d) The addition of two 2p orbitals,
out of phase, forming a p*2p
MO.
This orbital also has a nodal
plane perpendicular to the
internuclear axis (as do all
antibonding orbitals!)
Molecular orbitals of the second period elements
Molecular orbitals of the second period elements
For diatomics of the second period elements with Z = 7 or less, the energy
difference between the s and p orbitals is small, and both produce regions of
electron density between the nuclei (through s2s and s2p MOs). This leads to
mixing of the s2s and s2p MOs.
This leads to the following molecular orbital energy level scheme.
Molecular orbitals of the second period elements
Molecular orbitals of the second period elements
For diatomics of the second period elements with Z = 8 or greater, the energy
difference between the s and p orbitals is large, and little s and p orbital
mixing takes place.
This leads to the following molecular orbital energy level scheme.
Molecular orbitals of the second period elements
Molecular Orbital Theory
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A special look at O2
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Experimentally, O2 is
paramagnetic.
–
The experimentally
determined bond
length of O2 is
consistent with double
bond character.
–
Molecular orbital
theory explains both
observations!
(FINALLY!)
Molecular Orbital Theory
Problem: Write a molecular orbital diagram and determine
the bond order for:
(a) Ne2+
(b) C22Problem: Using energy level diagrams for the MO’s of N2,
N2+, O2 and O2+, explain the following data, which
shows that removing an electron from N2 weakens the
bond and lengthens it but removing an electron from O2
strengthens the bond and shortens it.
Molecular Orbital Theory - Heteronuclear diatomic molecules
For heterodiatomics, the energy of
the bonding orbital is closer to that of
the more electronegative atom and
energy of the antibonding orbital is
closer to that of the less
electronegative atom.
The atoms involved must not be too
far apart so that the order of the
energy levels is not too different than
that of the homodiatomics.
When deciding what MO energy
level diagram to use, if either of the
atoms is O or F, use the splitting
pattern for Z ≥ 8.
Molecular Orbital Theory
Problem: Write a molecular orbital diagram and determine
the bond order for:
(a) CN(b) BN
Delocalized Electrons: Bonding in the Benzene Molecule
(a) Lewis structure for C6H6 showing (b) Kekule structures for
benzene
alternate carbon-to-carbon single
and double bonds.
(c) A space filling
model
Delocalized Electrons: Bonding in the Benzene Molecule
Valence Bond Method
(a) Carbon atoms use sp2 and p (b) The overlap in sidewise
fashion of 2p orbitals produces
orbitals. Each carbon atom
three p bonds.
forms three s bonds, two with
neighboring C atoms in the
hexagonal ring and a third with
an H atom.
(c) Because the
three p bonds are
delocalized around
the benzene ring,
the molecule is often
represented through
a hexagon with an
inscribed circle.
Delocalized Electrons: Bonding in the Benzene Molecule
Molecular Orbital Theory
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Delocalized molecular orbital: describes a region of
high electron probability or charge density that extends
over three or more atoms.
Molecular orbital representation of p
bonding in benzene.
A computer-generated model of the
benzene molecule.
The planar s bond framework is
clearly visible.
The p orbitals above and below the C
and H plane are highlighted
Delocalized Electrons: Bonding in the Benzene Molecule
Molecular Orbital Theory
p MO for bonding in benzene.
Each C in C6H6 has one p electron
available for p-bonding, consistent
with the number of e- present in the
bonding orbitals.
Other structures with delocalized molecular orbitals
sp2 hybridize orbitals on each oxygen, leaving 3 p
orbitals.
14 of the 18 electrons occupy these orbitals.
The three p orbitals form 3 molecular orbitals and
there are four electrons to occupy these orbitals.
Other structures with delocalized molecular orbitals
The molecule
has one σ bond
between each
pair of O atoms
and a p bond
delocalized over
two pairs of O
atoms for a bond
order of 1.5.
Non-bonding
MOs have the
same energy as
the atomic
orbitals from
which they
came, but
neither add nor
detract from
bond formation