Chemistry
Second Edition
Julia Burdge
Lecture PowerPoints
Jason A. Kautz
University of Nebraska-Lincoln
9
Chemical Bonding II:
Molecular Geometry and
Bonding Theories
Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1
9
Chemical Bonding II: Molecular Geometry and
Bonding Theories
9.1 Molecular Geometry
The VSEPR Model
Electron-Domain Geometry and Molecular Geometry
Deviation from Ideal Bond Angles
Geometry of Molecules with More Than One Central Atom
9.2 Molecular Geometry and Polarity
9.3 Valence Bond Theory
9.4 Hybridization of Atomic Orbitals
Hybridization of s and p Orbitals
Hybridization of s, p, and d Orbitals
9.5 Hybridization of Molecules Containing Multiple Bonds
9.6 Molecular Orbital Theory
Bonding and Antibonding Molecular Orbitals
σ Molecular Orbitals
Bond Order
π Molecular Orbitals
Molecular Orbital Diagrams
9.7 Bonding Theories and Descriptions
of Molecules with Delocalized Bonding
9.1
Molecular Geometry
Molecular shape can be predicted by using the valence-shell electronpair repulsion (VSEPR) model.
ABx
A is the central atom surrounded by x B atoms
x can have integer values of 2 to 6.
Molecular Geometry
The basis of the VSEPR model is that electrons repel each other.
Electrons are found in various domains.
Lone pairs
Single bonds
2 double bonds
Double bonds
Triple bonds
1 single bond
3 single bonds
1 double bond
1 lone pair
1 lone pair
2 electron domains
(central atom)
3 electron domains
(central atom)
4 electron domains
(central atom)
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.
2 electron domains
Linear
3 electron domains
Trigonal planar
Molecular Geometry
4 electron domains
Tetrahedral
5 electron domains
Trigonal bipyramidal
6 electron domains
Octahedral
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.
180°
120°
Linear
109.5°
Trigonal planar
90°
120°
Tetrahedral
Trigonal bipyramidal
90°
Octahedral
Molecular Geometry
AB5 molecules contain two different bond angles between adjacent
bonds.
Axial positions; perpendicular
to the trigonal plane
90°
Equatorial positions; three bonds
arranged in a trigonal plane.
120°
Trigonal bipyramidal
Molecular Geometry
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.
••
•• ••
••
O =O− O
Molecular Geometry
Molecular Geometry
Molecular Geometry
The steps to determine the electron-domain and molecular geometries
are as follows:
Step 1: Draw the Lewis structure of the molecule or polyatomic ion.
Step 2: Count the number of electron domains on the central atom.
Step 3: Determine the electron-domain geometry by applying the VSEPR
model.
Step 4: Determine the molecular geometry by considering the positions
of the atoms only.
Molecular Geometry
Determine the shape of SF4.
Solution:
Step 1: Draw the Lewis structure of the molecule or polyatomic ion.
S
F
6x1=6
7 x 4 = 28
34 total valence electrons
4 bonds x 2 e– = 8 e–
34 – 8 = 26 e– left over
Molecular Geometry
Determine the shape of SF4.
Solution:
Step 2: Count the number of electron domains on the central atom.
4 single bonds
1 lone pair
5 electron domains
Molecular Geometry
Determine the shape of SF4.
Solution:
Step 3: Determine the electron-domain geometry by applying the VSEPR
model.
5 electron domains
Trigonal bipyrimidal electron
domain geometry
Molecular Geometry
Determine the shape of SF4.
Solution:
Step 4: Determine the molecular geometry by considering the positions
of the atoms only.
5 electron domains
Trigonal bipyrimidal electron
domain geometry
See-saw shape
Molecular Geometry
Some electron domains are better than others at repelling neighboring
domains.
Lone pairs take up more space than bonded pairs of electrons.
Multiple bonds repel more strongly than single bonds.
Molecular Geometry
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:
Central C atom
No. of electron domains:
4
Electron-domain geometry: tetrahedral
Molecular geometry:
tetrahedral
bent
9.2
Molecular Geometry and Polarity
Molecular polarity is one of the most important consequences of
molecular geometry.
A diatomic molecule is polar when the electronegativites of the two atoms
are different.
••
H−F
••
δ−
••
••
••
H−F
••
δ+
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
Carbon dioxide, CO2
The bonds in CO2 are polar, the molecule is nonpolar
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
Water, H2O
The bonds in H2O are polar, the molecule is polar
Molecular Geometry and Polarity
Dipole moments can be used to distinguish between structural isomers.
trans-dichloroethylene
nonpolar
cis-dichloroethylene
polar
9.3
Valence Bond Theory
According to valence bond theory, atoms share electrons when atomic
orbitals overlap.
(1) A bond forms when single occupied atomic orbitals on two atoms
overlap.
(2) The two electrons shared in the region of orbital overlap must be of
opposite spin.
(3) Formation of a bond results in a lower potential energy for the system.
Valence Bond Theory
The H−H bond in H2 forms when the singly occupied 1s orbitals of the
two H atoms overlap:
Valence Bond Theory
The F−F bond in F2 forms when the singly occupied 2p orbitals of the two
F atoms overlap:
Valence Bond Theory
The H−F bond in HF forms when the singly occupied 1s orbital on the H
atom overlaps with the single occupied 2p orbital of the F atom:
9.4
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.
Hybridization of Atomic Orbitals
BeCl2
Lewis theory and VSEPR theory predict Cl−Be−Cl bond angle of 180°
2 electron domains
Linear molecular geometry
A ground state beryllium atom can not form two bonds; there are no
unpaired electrons.
Hybridization of Atomic Orbitals
BeCl2
An excited state configuration for Be has two unpaired electrons and can
form to bonds.
The two bonds formed would not be equivalent.
Hybridization of Atomic Orbitals
BeCl2
Experimentally the bond in BeCl2 bonds are identical in length and
strength.
Mixing of one s orbital and one p orbital to yield two sp orbitals.
Hybridization of Atomic Orbitals
BeCl2
The 2s orbital and one of the 2p orbitals on Be combine to form two sp
hybrid orbitals.
Like any two electron domains, the hybrid orbitals on Be are 180° apart.
Hybridization of Atomic Orbitals
BeCl2
The hybrid orbitals on Be each overlap with a singly occupied 3p orbital
on a Cl atom.
The energy required to form an excited state Be atom is more than
compensated for by the energy given off when a bond forms.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in BF3
Step 1: Draw the Lewis structure:
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in BF3
Step 2: The number of electron domains on the central atom is the
number of hybrid orbitals necessary to account for the
molecule’s geometry.
Three electron domains
Three hybrid orbitals required
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in BF3
Step 3: Draw the ground-state orbital diagram for the central atom.
Step 4: Maximize the number of unpaired electrons by promotion.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in BF3
Step 5: Combine the necessary number of atomic orbitals to generate
the required number of hybrid orbitals.
Step 6: Place electrons in the hybrid orbitals, putting one electron in
each orbital before pairing any electrons.
Hybridization of Atomic Orbitals
Mixing of one s orbital and two p orbitals to yield three sp2 orbitals.
Hybridization of Atomic Orbitals
Hybrid orbitals on boron overlap with 2p orbitals on fluorine.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in CH4.
Step 1: Draw the Lewis structure:
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in CH4.
Step 2: The number of electron domains on the central atom is the
number of hybrid orbitals necessary to account for the
molecule’s geometry.
Four electron domains
Four hybrid orbitals required
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in CH4.
Step 3: Draw the ground-state orbital diagram for the central atom.
Step 4: Maximize the number of unpaired electrons by promotion.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in CH4.
Step 5: Combine the necessary number of atomic orbitals to generate
the required number of hybrid orbitals.
Step 6: Place electrons in the hybrid orbitals, putting one electron in
each orbital before pairing any electrons.
Hybridization of Atomic Orbitals
Mixing of one s orbital and three p orbitals to yield four sp3 orbitals.
Hybridization of Atomic Orbitals
Hybrid orbitals on carbon overlap with 1s orbitals on hydrogen.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in PCl5.
Step 1: Draw the Lewis structure:
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in PCl5.
Step 2: The number of electron domains on the central atom is the
number of hybrid orbitals necessary to account for the
molecule’s geometry.
Five electron domains
Five hybrid orbitals required
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in PCl5.
Step 3: Draw the ground-state orbital diagram for the central atom.
Step 4: Maximize the number of unpaired electrons by promotion.
Hybridization of Atomic Orbitals
Determine the number and type of hybrid orbitals necessary to rationalize
the bonding in PCl5.
Step 5: Combine the necessary number of atomic orbitals to generate
the required number of hybrid orbitals.
Step 6: Place electrons in the hybrid orbitals, putting one electron in
each orbital before pairing any electrons.
Hybridization of Atomic Orbitals
Hybrid orbitals on phosphorus overlap with 3p orbitals on chlorine.
Hybridization of Atomic Orbitals
9.5
Hybridization in Molecules Containing Multiple
Bonds
Valence bond theory and hybridization can be used to describe the
bonding in molecules containing double and triple bonds.
Each carbon has three electron domains:
2 single bonds
1 double bond
Expect sp2 hybridization
ethylene (C2H4)
Hybridization in Molecules Containing Multiple Bonds
Maximize unpaired electrons on carbon by promotion:
Hybridize the required number of atomic orbitals (one for each electron
domain on carbon)
Hybridization in Molecules Containing Multiple Bonds
Hybridization scheme for a the carbon atoms in ethylene:
One unhybridized atomic 2p
orbital gives rise to multiple
bonds
ethylene (C2H4)
Three equivalent sp2 hybrid orbitals
explain three bonds around carbon
Hybridization in Molecules Containing Multiple Bonds
A sigma (σ) bond forms when sp2 hybrid orbitals on the C atoms
overlap.
Hybridization in Molecules Containing Multiple Bonds
A sigma (σ) bond occurs when electron density is concentrated directly
along the internuclear axis.
internuclear axis
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)
ethylene (C2H4)
Unhybridized 2p orbitals, NOT involved
in sigma bonding (no overlap)
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 (π)
bond.
Hybridization in Molecules Containing Multiple Bonds
A pi (π) bond occurs when the regions of electron density are
concentrated above and below the plane of the molecule.
internuclear axis
Hybridization in Molecules Containing Multiple Bonds
A sigma and a pi bond together constitute a double bond.
ethylene (C2H4)
Hybridization in Molecules Containing Multiple Bonds
Sigma bonds exhibit free rotation around the bond axis.
All three Lewis structures represent the same molecule.
Hybridization in Molecules Containing Multiple Bonds
Pi bonds restrict free rotation around the bond axis.
cis-1,2-dichloroethylene
trans-1,2-dichloroethylene
There are two isomers of 1,2-dichloroethylene
Hybridization in Molecules Containing Multiple Bonds
The acetylene molecule is linear with sp hybridized carbons.
acetylene (C2H2)
Promotion of an electron maximizes the number of unpaired electrons:
Hybridization in Molecules Containing Multiple Bonds
The acetylene molecule is linear with sp hybridized carbons.
3 sigma bonds:
1 between the two carbon atoms (sp and sp)
2 between the C and H atoms (sp and 1s)
acetylene (C2H2)
2 pi bonds
2 between the two carbon atoms (2p and 2p)
The 2s orbital and one of the 2p orbitals then mix to form two sp hybrid
orbitals:
Hybridization in Molecules Containing Multiple Bonds
The acetylene molecule is linear with sp hybridized carbons.
acetylene (C2H2)
Two unhybridized atomic 2p orbitals
gives rise to 2 pi bonds
Two equivalent sp hybrid orbitals
give rise to 2 sigma bonds
Hybridization in Molecules Containing Multiple Bonds
Formation of the C−C sigma bond in acetylene:
acetylene (C2H2)
3 sigma bonds:
1 between the two carbon atoms (sp and sp)
2 between the C and H atoms (sp and 1s)
Hybridization in Molecules Containing Multiple Bonds
Formation of the C−C pi bond in acetylene:
acetylene (C2H2)
2 pi bonds
2 between the two carbon atoms (2p and 2p)
9.6
Molecular Orbital Theory
Lewis structures and valence bond theory fail to predict some important
properties of molecules.
Paramagnetic species are attracted to magnet fields.
Paramagnetism is a result of a molecules electron configuration.
Species that contain one or more unpaired electrons are paramagnetic.
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.
Diamagnetic species are weakly repelled by magnetic fields.
Species that contain paired electrons are diamagnetic.
Nitrogen, N2, is diamagnetic.
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 news 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
H2 is the simplest homonuclear diatomic molecule.
Valence bond theory:
H2 forms when from the overlap of the 1s orbitals.
Molecular obrital 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
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.
Molecular Orbital Theory
Destructive combination of the two 1s orbitals gives rise to a molecular
orbital that lies along the internuclear axis, but does not lie between the
two nuclei.
Electron density in this molecular orbital pulls the two nuclei in opposite
directions.
This molecular orbital is
referred to as an antibonding
molecular orbital.
Molecular Orbital Theory
Molecular orbitals that lie along the internuclear axis are referred to as σ
molecular orbitals.
Examples:
σ1s bonding molecular orbital from the combination of two 1s orbitals
σ*1s antibonding molecular orbital from the combination of two 1s orbitals
The asterisk distinguishes an antibonding molecular orbital from a bonding
orbital.
Molecular Orbital Theory
Molecular orbitals have specific energies.
Electrons in bonding molecular orbitals stabilize the molecule and are lower
in energy than the isolated atomic orbitals.
Electrons in antibonding molecular orbitals destabilize the molecule are
higher in energy than the isolated atomic orbitals.
Molecular Orbital Theory
The bond order indicates how stable a molecule is
The higher the bond order, the more stable a molecule is.
No. of e in bonding orbitals  No. of e in antibonding orbitals
bond order =
2
Molecular Orbital Theory
H2
No. of e in bonding orbitals  No. of e in antibonding orbitals
bond order =
2
bond order 
2  0
1
2
According to molecular orbital theory, H2 is a
stable molecule.
Molecular Orbital Theory
He2
No. of e in bonding orbitals  No. of e in antibonding orbitals
bond order =
2
bond order 
2  2
0
2
According to molecular orbital theory, He2 is
NOT a stable molecule and does not exist.
Molecular Orbital Theory
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:
σ molecular orbitals – electron density along the internuclear axis
px orbitals point towards each other
bonding and antibonding σ
molecular orbitals
Molecular Orbital Theory
p atomic orbitals also form molecular orbitals by both constructive and
destructive combination.
π molecular orbitals – electron density above and below the internuclear
axis.
Molecular Orbital Theory
Molecular orbitals resulting from the combination of p atomic orbitals are
higher than those resulting from the combination of s atomic orbitals.
This order of orbital energies assumes no
mixing of s and p orbitals.
s orbitals only interact with s orbitals
p orbitals only interact with p orbitals
This is found in O2, Fe2, Ne2.
Molecular Orbital Theory
Molecular orbitals resulting from the combination of p atomic orbitals are
higher than those resulting from the combination of s atomic orbitals.
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 Theory
Filling molecular orbital diagrams follows the same rules as the filling of
atomic orbitals.
1) Lower energy orbitals fill first
2) Each orbital can accommodate a maximum of two electrons with
opposite spin.
3) Hund’s rule is obeyed.
Molecular Orbital Theory
Molecular orbital diagrams for second-period homonuclear diatomic
molecules.
9.7
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).
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.
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
Molecular Orbital Theory
Strength:
accurately predict the magnetic and other properties of
molecules
Weakness: complex
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 π bonds in benzene are delocalized -- spread out over the entire
molecule.
Bonding Theories and Descriptions of Molecules
with Delocalized Bonding
The π bonds in benzene are delocalized -- spread out over the entire
molecule.
9
Chapter Summary: Key Points
Molecular Geometry
The VSEPR Model
Bond Angles
Molecular Polarity
Valence Bond Theory
Hybridization
Multiple Bonding
Molecular Orbital Theory
Bonding Molecular Orbitals
Antibonding Molecular Orbitals
Bond Order
Molecular Orbital Diagrams
Delocalized Bonding