Geometry 10/27/2011
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Molecular and Bonding Theories
7.1 VSEPR Model
7.2 Molecular Geometry and Polarity
7.4 Hybridization of Atomic Orbitals
7.5 Hybridization of Molecules Containing Multiple Bonds
7.6 Molecular Orbital Theory
Molecular Geometry
The VSEPR Model
Molecular shape can be predicted by using the valence-shell
electron-pair repulsion (VSEPR) model.
Electrons, being negatively charged, repel each other and are most
stable when they are separated as much as possible.
Electrons are found in various domains.
ABx
A is the central atom surrounded by x B atoms.
Lone pairs
Single bonds
Double bonds
Triple bonds
x can have integer values of 2 to 6.
1 single bond
3 single bonds
1 double bond
2 double bonds
1 lone pair
1 lone pair
2 electron domains
(on central atom)
Electron-Domain Geometry and Molecular Geometry
The basis of the VSEPR model is that electrons repel each other.
Electrons will arrange themselves to be as far apart as possible.
Arrangements minimize repulsive interactions.
3 electron domains
(on central atom)
4 electron domains
(on central atom)
Electron-Domain Geometry and Molecular Geometry
4 electron domains
Tetrahedral
2 electron domains
Linear
5 electron domains
Trigonal bipyramidal
3 electron domains
Trigonal planar
6 electron domains
Octahedral
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Electron-Domain Geometry and Molecular Geometry
The electron domain geometry is the arrangement of electron domains
around the central atom.
The molecular geometry is the arrangement of bonded atoms.
In an ABx molecule, a bond angle is the angle between two adjacent
A-B bonds.
AB5 molecules contain
two different bond
angles between adjacent
bonds.
Axial positions:
perpendicular to the
trigonal plane
120
180
109.5
Electron-Domain Geometry and
Molecular Geometry
90
Linear
Equatorial positions:
three bonds arranged in a
trigonal plane.
Trigonal planar
120
Tetrahedral
90
120
90
Octahedral
Trigonal bipyramidal
Electron-Domain Geometry and
Molecular Geometry
Electron-Domain Geometry and Molecular Geometry
Number of
e- domains
Number of
lone pairs
Class
2
0
AX2
Linear
Linear
CO2
0
AX3
Trigonal
planar
Trigonal
planar
H2CO
1
AX2E
Bent
SO2
0
When the central atom in an ABx molecule bears one or more lone
pairs, the electron-domain geometry and the molecular geometry are
no longer the same.
AX4
Tetrahedral
CH4
3
e- domain
geometry
Molecular
geometry
Tetrahedral
Number of
e- domains
Class
0
AX5
1
AX4E
2
AX4E2
T-shaped
e- domain
geometry
Molecular
geometry
AX4E3
Linear
ICl2-
0
AX6
Octahedral
Bent
NH3
H2O
S F6
Example
Trigonal
bipyramidal
Trigonal
bipyramidal
PCl5
Seesaw
S F4
Electron-Domain Geometry and
Molecular Geometry
Draw the Lewis structure of the molecule or polyatomic
ion.
Count the number of electron domains on the central
atom.
Determine the electron-domain geometry by applying the
VSEPR model.
Octahedral
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AX3E
AX2E2
ClF3
3
5
Number of
lone pairs
1
Trigonal
pyramidal
2
4
Example
1
AX5E
Square
pyramidal
BrF5
2
AX4E2
Square
planar
XeF4
Determine the molecular geometry by considering the
positions of the atoms only.
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Deviation from Ideal Bond Angles
Some electron domains are better than others at repelling neighboring
domains.
Lone pairs take up more space than bonded pairs of electrons.
Geometry of Molecules with More Than
One Central Atom
The geometry of more complex molecules can be determined by
treating them as though they have multiple central atoms.
Central O atom
No. of electron domains: 4
Electron-domain geometry: tetrahedral
Molecular geometry: bent
Multiple bonds repel more strongly than single bonds.
Central C atom
No. of electron domains: 4
Electron-domain geometry: tetrahedral
Molecular geometry: tetrahedral
Geometry of Molecules with More Than One Central
Atom
Molecule Polarity
Determine the shape around each of the central atoms in
acetone, (CH3)2C=O.
tetrahedral
tetrahedral
trigonal planar
>1200
The HCl bond is polar. The bonding electrons
are pulled toward the Cl end of the molecule.
The net result is a polar molecule.
<1200
The orientation of
polar molecules in
an electric field.
+
HF
Electrical Charge
HF
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Electrical Charge
Electrical Charge
Lightning is produced when liquid
and ice particles collide, and build
up large electrical fields in the
clouds until a giant "spark" occurs
between them: a lightning bolt.
Thunder is the sound made as the
air around a lightning bolt rapidly
heats (50,000 F) and cools to
cause a shock wave that can be
heard as thunder.
Vector Addition
Molecule Polarity
= +
= +
No net dipole moment
= +
= +
= +
= + +
Molecule Polarity
The OC bond is polar.
The bonding electrons are pulled equally toward both O
ends of the molecule.
The net result is a nonpolar molecule.
Polarity of Molecules
For a molecule to be polar it
must
have polar bonds
Draw the Lewis structure and
determine the molecular
geometry
electronegativity difference
bond dipole moments
Net dipole moment
have an unsymmetrical
shape
Determine whether the bonds in
the molecule are polar
bond dipole moments dont
cancel out (vector addition)
The HO bond is polar. Both sets of bonding
electrons are pulled toward the O end of the
molecule. The net result is a polar molecule.
Determine whether the polar
bonds add together to give a net
dipole moment
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Molecular Geometry and Polarity
The polarity of a molecule made up of three or more atoms depends
on:
1. the polarity of the individual bonds
2. the molecular geometry
Molecular Geometry and Polarity
Phosphorous pentachloride
PCl5
The bonds are polar
Boron trifluoride
BF3
The bonds in BF3 are polar
No net dipole moment
No net dipole moment
The molecule is non polar.
The molecule is non polar.
Molecular Geometry and Polarity
Molecular Geometry and Polarity
Dipole moments can be used to distinguish between structural isomers.
Difluoromethane
CH2F2
trans-dichloroethylene
The bonds are polar
Non polar
Net dipole moment
The molecule is polar.
cis-dichloroethylene
polar
Valence Bond Theory
A covalent bond forms when the orbitals of two atoms overlap and
the overlap region, which is between the nuclei, is occupied by a
pair of electrons.
The two electrons shared in the region of orbital overlap must be of
opposite spin.
Orbital overlap and spin pairing in three diatomic
molecules
Hydrogen, H2
Formation of a bond results in a lower potential energy for the
system.
The greater the orbital overlap, the stronger (more stable) the
bond.
The valence atomic orbitals in a molecule are different from those in
isolated atoms.
Hydrogen fluoride, HF
Fluorine, F2
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Hybrid Orbitals
Hybridization of Atomic Orbitals
Hybridization or mixing of atomic orbitals can account for
observed bond angles in molecules that could not be
described by the direct overlap of atomic orbitals.
CO2
The number of hybrid orbitals obtained equals the
number of atomic orbitals mixed.
Types of Hybrid Orbitals
sp
sp2
sp3
sp3d
sp3d2
Geometry
Hybridization of s and p Orbitals
Mixing of one s orbital and one p orbital to yield two sp hybrid orbitals
oriented 180 degree to each other.
2 non hybrid p orbitals
remain, oriented at 90
to the sp hybrids.
2p
Hybridization of s and p Orbitals
Mixing of one s orbital and two p orbitals to yield three sp2 orbitals
orbitals lying on a plane, 120 from each other.
2p
2p
One non hybrid p orbital is
oriented perpendicularly to the
plane defined by the sp2 orbitals
2p
sp2
sp
2s
2s
Hybridization of s and p Orbitals
Mixing of one s orbital and three p orbitals to yield four sp3 orbitals
oriented towards the corners of a tetrahedron, with angles of 109.5
between each other.
Hybridization of s and p Orbitals
Determine the number and type of hybrid orbitals necessary to
rationalize the bonding in CH4.
Step 1: Draw the Lewis structure
Step 2: The number of electron domains on the central atom is the
number of hybrid orbitals necessary to account for the molecules
geometry.
2p
sp3
2s
4 electron domains
4 hybrid orbitals required
hybridization: sp3
Hybrid sp3 orbitals on C
overlap with 1s orbitals on H.
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Hybridization of s, p and d Orbitals
The sp3d hybrid orbitals in PCl5
Determine the number and type of hybrid orbitals necessary to
rationalize the bonding in PCl5.
Mixing of one s, three p and one d orbital to yield five sp3d orbitals.
Step 1: Draw the Lewis structure
Step 2: Count the number of electron domains on the central atom.
3d
3p
Five electron domains
3d
sp3d
Five hybrid orbitals required
The sp3d2 hybrid orbitals in SF6
Hybridization in Molecules Containing
Multiple Bonds
Mixing of one s, three p and two d orbital to yield six sp3d2 orbitals.
Valence theory bond and hybridization can be used to
describe the bonding in molecules containing double and
triple bonds.
3d
3p
3d
Each carbon has three electron domains:
2 single bonds
1 double bond
sp3d2
Expect sp2 hybridization
ethylene (C2H4)
Hybridization in Molecules Containing
Multiple Bonds
One unhybridized atomic 2p
orbital gives rise to multiple
bonds
Hybridization in Molecules Containing
Multiple Bonds
A sigma () bond forms when sp2 hybrid orbitals on the C atoms overlap.
In a sigma bond, the shared electron density lies directly along the
internuclear axis.
ethylene (C2H4)
Three equivalent sp2 hybrid orbitals
explain three bonds around carbon
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Hybridization in Molecules Containing
Multiple Bonds
The ethylene molecule contains five sigma bonds:
1 between the two carbon atoms (sp2 and sp2 overlap)
4 between the C and H atoms (sp2 and 1s overlap)
Hybridization in Molecules Containing
Multiple Bonds
Sigma () bonds are concentrated along the internuclear axis, and exhibit
free rotation around the bond axis.
Hybridization in Molecules Containing
Multiple Bonds
The remaining unhybridized p orbital is perpendicular to the plane in
which the atoms of the molecule lie.
The unhybridized p orbitals overlap in a sideways fashion to form a pi
(p) bond.
Hybridization in Molecules Containing
Multiple Bonds
Pi (p) bonds form from overlap of parallel p orbitals on adjacent
atoms, have a nodal plane that contains the internuclear axis and
restrict free rotation around the bond axis.
All three Lewis structures represent the same molecule.
cis-1,2-dichloroethylene
Hybridization in Molecules Containing
Multiple Bonds
The acetylene molecule is linear with sp hybridized carbons.
acetylene (C2H2)
Hybridization in Molecules Containing Multiple
Bonds
Formation of the CC pi bond in acetylene:
3 sigma bonds:
1 between the two carbon atoms (sp and sp)
2 between the C and H atoms (sp and 1s)
2 pi bonds
2 between the two carbon atoms (2p and 2p)
trans-1,2-dichloroethylene
acetylene (C2H2)
3 sigma bonds:
1 between the two carbon atoms (sp and sp)
2 between the C and H atoms (sp and 1s)
2 pi bonds
2 between the two carbon atoms (2p and 2p)
Two unhybridized atomic 2p orbitals
gives rise to 2 pi bonds
Two equivalent sp hybrid orbitals
give rise to 2 sigma bonds
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MO Theory
A molecule is viewed on a quantum mechanical level as a
collection of nuclei surrounded by delocalized molecular orbitals.
Atomic wave functions are summed to obtain molecular wave
functions.
If wave functions reinforce each other, a bonding MO is formed
(region of high electron density exists between the nuclei).
If wave functions cancel each other, an antibonding MO is formed
(a node of zero electron density occurs between the nuclei).
Molecular Orbital Theory
Lewis structures and valence bond theory fail to predict some
important properties of molecules.
Paramagnetism is a result of a molecules electron configuration.
Species that contain one or more unpaired electrons are paramagnetic.
Paramagnetic species are attracted to magnet fields.
The Lewis structure for O2
shows no unpaired electrons.
O2 exhibits paramagnetism.
Molecular Orbital Theory
Lewis structures and valence bond theory fail to predict some
important properties of molecules.
Species that contain paired electrons are diamagnetic.
Diamagnetic species are weakly repelled by magnetic fields.
Nitrogen, N2, is diamagnetic.
Bonding and Antibonding Molecular
Orbitals
H2 is the simplest homonuclear diatomic molecule.
Valence bond theory:
H2 forms when from the overlap of the 1s orbitals.
Molecular orbital theory:
H2 forms when the 1s orbitals combine to give molecular
orbitals.
Molecular orbitals result from the constructive and
destructive combination of atomic orbitals.
Molecular Orbital Theory
Another bonding theory is needed to describe the paramagnetism of O2.
In molecular orbital theory, the atomic orbitals combine to form new
orbitals that are the property of the entire molecule.
The new orbitals are called molecular orbitals.
Molecular orbitals have characteristics similar to atomic and hybrid orbitals:
specific shapes
specific energies
accommodate a maximum of 2 electrons each
electron filling follows the Pauli exclusion principle
the number of molecular orbitals obtained equals the number of
orbitals combined
Molecular Orbital Theory
Constructive combination of the two 1s orbitals gives rise to a molecular
orbital that lies along the internuclear axis.
Constructive combination increases the electron density between the two
nuclei.
This molecular orbital is
referred to as a bonding
molecular orbital.
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Bonding and Antibonding Molecular
Orbitals
Bonding and Antibonding Molecular
Orbitals
Destructive combination of the two 1s orbitals gives rise to a molecular
Molecular orbitals that lie along the internuclear axis are referred to as
molecular orbitals.
Electron density in this molecular orbital pulls the two nuclei in opposite
directions.
Examples:
1s bonding molecular orbital from the combination of two 1s orbitals
*1s antibonding molecular orbital from the combination of two 1s
orbitals
orbital that lies along the internuclear axis, but does not lie between the
two nuclei.
The asterisk distinguishes an antibonding molecular orbital from a
bonding orbital.
This molecular orbital is referred
to as an antibonding
molecular orbital.
Molecular Orbitals
Bond Order
Molecular orbitals have specific energies.
The bond order indicates how stable a molecule is.
Electrons in bonding molecular orbitals stabilize the molecule and are
lower in energy than the isolated atomic orbitals.
The higher the bond order, the more stable a molecule is.
Electrons in antibonding molecular orbitals destabilize the molecule
and are higher in energy than the isolated atomic orbitals.
=
Bond Order
Bond Order
He2
H2
=
#
#
2
=
=
=
# #
2
2 0
=1
2
According to molecular orbital theory,
H2 is a stable molecule.
# #
2
2 2
=0
2
According to molecular orbital theory,
He2 is NOT a stable molecule and
does not exist.
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p Molecular Orbitals
p Molecular Orbitals
p atomic orbitals also form molecular orbitals by both constructive and
destructive combination.
The orientations of px, py, and pz give rise to two different types of
molecular orbitals:
p atomic orbitals also form molecular orbitals by both constructive and
destructive combination.
molecular orbitals electron density above and below the
internuclear axis
s molecular orbitals electron density along the internuclear axis
bonding and antibonding s
molecular orbitals
px orbitals point towards each other
Molecular Orbital Theory
Molecular orbitals resulting from the combination of p atomic orbitals are
higher in energy than those resulting from the combination of s atomic
orbitals.
Molecular Orbital Diagrams
Filling molecular orbital diagrams follows the same rules as
the filling of atomic orbitals.
Lower energy orbitals fill first.
Each orbital can accommodate a maximum of two
electrons with opposite spin.
Hunds rule is obeyed.
This order of orbital energies assumes
no mixing of s and p orbitals.
This is found in O2, F2, Ne2.
This order of orbital energies assumes
some mixing of s and p orbitals.
This arrangement of orbitals is found
in Li2, B2, C2 and N2.
Molecular Orbital Diagrams
Molecular orbital diagrams for second-period homonuclear diatomic molecules.
Bonding Theories and Descriptions of
Molecules with Delocalized Bonding
Lewis Theory
Strength:
qualitative prediction of bond strength and bond length
Weakness:
two dimensional model, real molecules are three dimensional
fails to explain why bonds form
Valence-Shell Electron-Pair Repulsion Model
Strength:
predict the shape of many molecules and polyatomic ions
Weakness:
fails to explain why bonds form (based on Lewis theory)
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Bonding Theories and Descriptions of
Molecules with Delocalized Bonding
Valence Bond Theory
Strength:
covalent bonds form when atomic orbitals overlap
Weakness:
fails to explain the bonding in many molecules
Bonding Theories and Descriptions of
Molecules with Delocalized Bonding
Molecular Orbital Theory
Strength:
accurately predict the magnetic and other properties of molecules
Weakness:
complex
Hybridization of Atomic Orbitals
Strength:
an extension of valence bond theory. Using hybrid orbitals it is
possible to explain the bonding and geometry of more molecules
Weakness:
fails to predict some important properties, such as magnetism
Bonding Theories and Descriptions of
Molecules with Delocalized Bonding
Some molecules are best described using a combination of models.
Benzene, C6H6, is represented with two resonance structures:
The p bonds in benzene are delocalized -- spread out over the entire
molecule.
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