Chapter 9
Molecular Geometry
Bonding Theories
Molecular Shape
• A bond angle is the
angle defined by lines
joining the centers of
two atoms to a third
atom to which they are
covalently bonded
• The molecular
geometry or shape is
defined by the lowest
energy arrangement of
its atoms in threedimensional space.
VSEPR
Valence-Shell Electron-Pair Repulsion Theory
The geometric arrangement of atoms bonded to a
given atom is determined principally by
minimizing electron pair repulsions of bonding and
non-bonding electrons.
Central Atoms without Lone Pairs
Steric number (SN) is
the number of volumes
of space occupied by
electrons surrounding
a central atom
Geometric Forms
Predicting a VSEPR Structure
1. Draw Lewis structure.
2. Determine the steric number of the
central atom.
3. Use the SN to determine the geometry
around the central atom.
4. The name for molecular structure is
determined by the number of volumes
of space occupied by bonding
electrons.
Examples
• What is the molecular geometry of BF3?
• What is the molecular geometry of CH4
Examples
• What is the molecular geometry of BF3?
Lewis Structure (exception to Law of Octaves)
F
B
F
F
• What is the molecular geometry of CH4
Examples
• What is the molecular geometry of BF3?
Lewis Structure (exception to Law of Octaves)
F
B
F
F
Bond Angles = 120°
Trigonal Planar
• What is the molecular geometry of CH4
Examples
• What is the molecular geometry of BF3?
Lewis Structure (exception to Law of Octaves)
F
B
F
F
Bond Angles = 120°
Trigonal Planar
• What is the molecular geometry of CH4
H
H
C
H
H
Examples
• What is the molecular geometry of BF3?
Lewis Structure (exception to Law of Octaves)
F
B
F
F
Bond Angles = 120°
Trigonal Planar
• What is the molecular geometry of CH4
H
H
C
H
Bond Angles = 120°
H
Tetrahedral
Central Atoms with Lone Pairs
• Electron-pair geometry describes the arrangement
of atoms and lone pairs of electrons about a
central atom.
 The electron-pair geometry will always be one of the
five geometries presented previously.
• The molecular geometry in these molecules
describes the shape of the atoms present (it
excludes the lone pairs).
Lone Pairs
• Lone pairs of electrons occupy more space
around a central atom than do bonding electrons.
• Lone pair-lone pair repulsion is the largest.
• Lone pair-bonding pair repulsion is the next
largest.
• Bonding pair-bonding pair repulsion is the smallest.
• In structures with lone pairs on the central atom,
the bond angles are a little smaller than predicted
based on the electron-pair geometry.
SN = 3, Electron-pair Geometry = Trigonal Planar
No. of Bonded
Atoms
No. of Lone
Pairs
Molecular
Geometry
Bond Angles
3
0
Trigonal Planar
120o
Bent
<120o
Like 119.6o
2
1
Non-bonding Electrons & Shape
H
H
B
B
H
H
H
H
Angles = 120
Angles < 120
Trigonal Planar
Bent
SN = 4, Electron-pair Geometry = Tetrahedral
No. of Bonded
Atoms
No. of Lone
Pairs
Molecular
Geometry
Bond Angles
4
0
Tetrahedral
109.5o
3
1
Trigonal
Pyramidal
<109.5o
2
2
Bent
<109.5o
Non-bonding Electrons & Shape
Non-bonding Electrons & Shape
Tetrahedral
Trigonal Pyramid
v-shape
SN = 5, Electron-pair Geometry = Trigonal
Bipyramidal
No. of Bonded
Atoms
No. of Lone
Pairs
Molecular
Geometry
Bond Angles
5
0
Trigonal
Bipyramidal
120o & 90o
4
1
Seesaw
<120o & 90o
3
2
T-shaped
<120o & 90o
2
3
Linear
180o
The lone pairs of electrons are always found in the trigonal
planar part of the structure to minimize repulsion.
SN = 6, Electron-pair Geometry = Octahedral
No. of Bonded
Atoms
No. of Lone
Pairs
Molecular
Geometry
Bond Angles
6
0
Octahedral
90o
5
1
Square
Pyramidal
<90o
4
2
Square Planar
90o
3
3
2
4
Although these arrangements
are possible, we will not
encounter any molecules with
these arrangements.
Hybrid Orbitals
You may have noticed that the electron pairs in molecules
have different orientations in space compared to atomic
orbitals. Wave equations mathematically generated
volumes of space where electrons spend most of their time,
but what about molecules?
Hybrid Orbitals
You may have noticed that the electron pairs in molecules
have different orientations in space compared to atomic
orbitals. Wave equations mathematically generated
volumes of space where electrons spend most of their time,
but what about molecules? This brings us to the concept
of hybrid orbitals, combinations of atomic orbitals, or
molecular orbitals (from wave equations of electrons in
molecules)
Hybrid Orbitals
Hybridization is a concept you might be familiar
with. For example a grapefruit is a hybrid of
what two fruits?
Hybrid Orbitals
Hybridization is a concept you might be familiar
with. For example a grapefruit is a hybrid of
what two fruits?
Hybrid Orbitals
Hybridization is a concept you might be familiar
with. For example a grapefruit is a hybrid of
what two fruits? Lemon and orange
Hybrid Orbitals
How about a nectarine?
Hybrid Orbitals
How about a nectarine? Plumb and a peach.
Hybrid Orbitals
How about a nectarine? Plumb and a peach.
Broccoaflower? Broccoli and cauliflower
Hybrid Orbitals
How about a nectarine? Plumb and a peach.
Broccoaflower? Broccoli and cauliflower
And a Cocapoo?
Hybrid Orbitals
How about a nectarine? Plumb and a peach.
Broccoaflower? Broccoli and cauliflower
And a Cocapoo? Cocker spaniel and poodle
Hybrid Orbitals
On to Chemistry! How about an s-orbital and a porbital? Yes, sp orbital.
Hybrid Orbitals
On to Chemistry! How about an s-orbital and a porbital? Yes, sp orbital.
How about one s-orbital and two p-orbitals?
Hybrid Orbitals
On to Chemistry! How about an s-orbital and a porbital? Yes, sp orbital.
How about one s-orbital and two p-orbitals? Yes an
sp2 orbital.
Hybrid Orbital Notation
In order to construct hybrid orbital notation, we
need to separate the central atom from the
surrounding electrons, usually the central atom is the
largest, the most electronegative, or the one that
there is one of.
Hybrid Orbital Notation
In order to construct hybrid orbital notation, we
need to separate the central atom from the
surrounding electrons, usually the central atom is the
largest, the most electronegative, or the one that
there is one of. When constructing a hybrid orbital
diagram, all of the valence electrons of the central
atom are used and only the single electrons of the
atoms attached to the central atom are use.
Hybrid Orbital Example
Suppose we want to make a diagram of SF6
First we separate the central atom from the other atoms.
The central atom is A and the other atoms are called X’s
A
SF6
X’s
Hybrid Orbital Example
Suppose we want to make a diagram of SF6
First we separate the central atom from the other atoms.
The central atom is A and the other atoms are called X’s
A
SF6
X’s
Then we generate a set of degenerate hybrid orbitals to
house the valence electrons
Hybrid Orbital Example
Suppose we want to make a diagram of SF6
First we separate the central atom from the other atoms.
The central atom is A and the other atoms are called X’s
A
SF6
X’s
Then we generate a set of degenerate hybrid orbitals to
house the valence electrons F
F
F
F
F
F
F
Insert single electrons into the degenerate hybrid orbitals
Hybrid Orbital Example
Suppose we want to make a diagram of SF6
First we separate the central atom from the other atoms.
The central atom is A and the other atoms are called X’s
A
SF6
X’s
Then we generate a set of degenerate hybrid orbitals to house
the valence electrons F
F
F
F
F
F
F
Insert single electrons into the degenerate hybrid orbitals
Double up the single electrons with the valence electrons
from the A atom
Hybrid Orbital Example
F
F
F
S
F
F
F
Shape: Octahedral
Angles: 90 deg.
Hybrid: sp3d2
Polarity: Nonpolar
Practice
What are the molecular geometries of
the ions: SCN- and NO2- ?
Polar Bonds and Polar Molecules
• Two covalently bonded atoms with different
electronegativities have partial electric charges
of opposite sign creating a bond dipole.
• A molecule is called a polar molecule when it
has polar bonds and a shape where the bond
dipoles don’t offset each other.
Examples
Measuring Polarity
• The permanent dipole moment () is a
measured value that defines the extent of
separation of positive and negative charge
centers in a covalently bonded molecule.
Atomic Orbitals and Bonds
•
•
A tetrahedral molecule requires that four
orbitals of the central atom must overlap
with an orbital of an outer atom to form
a bond.
The central atom would use its s orbital
and its three p orbitals, but these
orbitals would not yield the 109° bond
angles observed in the tetrahedral
molecule.
Valence-Bond Theory
• Valence-bond theory assumes that
covalent bonds form when orbitals on
different atoms overlap or occupy the
same region of space.
• A sigma () bond is a covalent bond in
which the highest electron density lies
between the two atoms along the bond
axis connecting them.
Examples
Valence Bond Theory
• Hybridization is the mixing of atomic
orbitals to generate new sets of orbitals
that are then available to overlap and
form covalent bonds with other atoms.
• A hybrid atomic orbital is one of a set of
equivalent orbitals about an atom
created when specific atomic orbitals
are mixed.
Tetrahedral Geometry: sp3 Hybrid Orbitals
A tetrahedral orientation of valence electrons is
achieved by forming four sp3 hybrid orbitals form one
s and three p atomic orbitals.
Other
3
sp
Hybrid Examples
2
sp
Hybridization
• In a covalent pi () bond, electron density is
greatest above and below the bonding axis.
sp Hybridization
• Pi bonds will not exist between two atoms
unless a sigma bond forms first.
The Bonding in Carbon Dioxide
The carbon atom
is sp hybridized
and these orbitals
form the two
sigma bonds. The
 bonds are
rotated 90° from
one another.
2
3
d sp
Hybridization
dsp3 Hybridization
Practice
What are the hybridizations of the
central atoms of the ions: SCN- and
NO2- ?
Delocalization of Electrons
• The electrons in the
 system with
alternating single
and double bonds
can be delocalized
over several atoms
or even an entire
molecule.
Chirality
• “Handedness”: right glove doesn’t fit the
left hand.
• Mirror-image object is different from the
original object
chapter 6
Examples of Handed Objects
•
•
•
•
•
Your hands, from the previous slide
Gloves
Scissors
Screws
Golf clubs
chapter 6
HANDED MOLECULES
Handed molecules are called chiral molecules. A chiral
molecule has a non-superimposable mirror image. For
example your hands are non-superimposable mirror
images, this is where the word handed comes from.
Molecules that are superimposable on their mirror image
are called achiral.
How about molecules?
• Chemical substances can be handed
• Handed substances are said to be chiral
• Molecules, that are chiral are
nonsuperimposable on their mirror image
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
• Enantiomers: nonsuperimposable mirror
images, and are different molecules.
chapter 6
Chirality in Molecules
• cis isomers are achiral (not chiral).
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
• Enantiomers: nonsuperimposable
mirror images, different molecules.
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
• Enantiomers: nonsuperimposable
mirror images, different molecules.
• One enantiomeric form of limonene
smells like oranges, while its mirror
image smells like lemons.
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
• Enantiomers: nonsuperimposable mirror images,
different molecules.
• One enantiomeric form of limonene smells like
oranges, while its mirror image smells like lemons.
• The one enantiomer of carvone is the essence of
caraway, and the other, the essence of spearmint.
• Most molecules in the plant and animal world are
chiral and usually only one form of then
enantiomer is found.
chapter 6
Chirality in Molecules
• The cis isomer is achiral.
• The trans isomer is chiral.
• Enantiomers: nonsuperimposable mirror images,
different molecules.
• One enantiomeric form of limonene smells like
oranges, while its mirror image smells like lemons.
• The one enantiomer of carvone is the essence of
caraway, and the other, the essence of spearmint.
• Most molecules in the plant and animal world are
chiral and usually only one form of then
enantiomer is found.
• Nineteen of the twenty known amino acids are
chiral, and all of them are classified as left
handed.
chapter 6
Chirality in Molecules
How can we tell if a molecule is chiral or not?
Simply divide the molecule in half, if both haves
are the same then the molecule is achiral, if
they are different then the molecule is chiral.
The line dividing the molecule in half is called
an internal mirror plane. An example is on the
next slide.
Mirror Planes of Symmetry
• If two groups are the same, carbon
is achiral. (animation)
• A molecule with an internal mirror
plane cannot be chiral.*
Caution! If there is no
plane of symmetry,
molecule may be chiral
or achiral. See if
mirror image can be
superimposed.
chapter 6
Problems with Bonding Theories
• Lewis structure and valence bond theory help us
understand the bonding capacities of elements.
• VSEPR and valence bond theories account for the
observed molecular geometries.
• None of these models enables us to explain why O2 is
attracted to a magnetic field while N2 is repelled
slighty.
Molecular Orbital (MO) Theory
• The wave functions of atomic orbitals of atoms
are combined to create molecular orbitals
(MOs) in molecules.
 Each MO is associated with an entire molecule, not
just a single atom. MOs are spread out, or
delocalized over all the atoms in a molecule.
MOs for H2
• The two 1s orbitals may be added or subtracted to
yield two MOs.
Types of MOs
• Electrons in bonding orbitals serve to hold
atoms together in molecules by increasing the
electron density between nuclear centers.
• Electrons in antibonding orbitals in a molecule
destabilize the molecule because they do not
increase the the electron density between
nuclear centers.
Bond Types
• A sigma, , bond is a covalent bond in which
the highest electron density lies along the bond
axis.
• A pi, , bond is formed by the mixing of atomic
orbitals that are not oriented along the bonding
axis in a molecule.
Bond Order
Bond Order = 1/2 (# bonding electrons - # antibonding
electrons)
The bond order is zero in He2 and the molecule is not stable.
MO Guidelines
1.
The total number of MO formed equals the number of atomic
orbitals used in the mixing process.
2.
Orbitals with similar energy and shape mix more effectively
than do those that are different.
3.
Orbitals of different principal quantum numbers have different
sizes and energies resulting in less effective mixing.
4.
A MO can accommodate two electrons with opposite spin.
5.
Electrons are placed in MO diagrams according to Hund’s
rule.
Combinations of Atomic Orbitals
MO Diagrams for N2 and O2
MO Scheme for N2
Figure 9.27
• Electron configuration for
N2: 2s22s*22p22p4
• Bond order = 1/2 (8 - 2) = 3
 N2 has three bonds
 N2 has no unpaired
electrons
MO Scheme for O2
• Electron configuration
for O2: 2s22s*22p22p4
2p*2
• Bond order = 1/2 (8 - 4)
=2
 O2 has two bonds
 O2 has two unpaired
electrons in 2p*
Paramagnetism / Diamagnetism
• Paramagnetism - atoms or molecules
having unpaired electrons are attracted
to magnetic fields
• Diamagnetism - atoms or molecules
having all paired electrons are repelled
by magnetic fields
Other Diatomic Molecules
• The 2s and 2p interactions are strong in Li2
through N2 but weaker in O2 through Ne2.
Other Diatomic Molecules
• The MO diagram illustrates
how the effective nuclear
charge alters the diagram.
• The odd electron is more
likely to be found on nitrogen
since its in an orbital closer
in energy to the atomic
orbitals of the nitrogen atom.
Comparison of Theories
• MO theory may provide the most complete
picture of covalent bonding, but it is also the
most difficult to apply to large molecules and it
does not account for molecular shape.
THE END
ChemTour: Partial Charges and
Bond Dipoles
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PC | Mac
Students learn that covalent bonds often include unequal
distribution of electrons leading to partial charges on atoms,
bond dipole moments, and molecule polarity. Interactive
Practice Exercises ask students to calculate dipole
moments of polar molecule.
ChemTour: Greenhouse Effect
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This unit explores how excess carbon dioxide and CFCs in
the atmosphere contribute to global warming.
ChemTour: Vibrational Modes
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This tutorial illustrates the three vibrational modes: bending,
symmetric stretching, and asymmetric stretching. Students
learn that molecules can absorb specific wavelengths of
infrared radiation by converting this energy into molecular
vibrations.
ChemTour: Hybridization
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This tutorial animates the formation of hybrid orbitals from
individual s and p orbitals, shows examples of their
geometry, and describes how they can produce single,
double, and triple bonds. Includes Practice Exercises.
ChemTour: Chemistry of the
Upper Atmosphere
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This ChemTour examines how particles of the upper
atmosphere absorb and emit electromagnetic radiation.
ChemTour: Molecular Orbitals
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This animated tutorial offers a patient explanation of
molecular orbital theory, an alternative to the bonding theory
depicted by Lewis dot structures. Includes Practice
Exercises.
Ethylene, which has the molecular formula C2H4, is a
rigid molecule in which all 6 atoms lie in a plane.
Which of the following molecules also has a rigid planar
structure?
A) H2C=C=CH2
Planar Hydrocarbons
B) H2C=C=C=CH2
C) Neither
Consider the following arguments for each answer and
vote again:
A. A combination of 3 carbons and 4 hydrogens can
form the rigid planar molecule H2C=C=CH2.
B. The orientations of the π bonds in H2C=C=C=CH2
alternate in such a way as to create a planar structure.
C. The hybridization of the atomic orbitals on the
carbons prevents the retention of a planar structure in
molecules longer than C2H4.
Planar Hydrocarbons
What is the bond order of the N-O bond in nitrate, NO3-?
A) 1
Bond Order of Nitrate
B) 11/3
C) 2
Consider the following arguments for each answer and
vote again:
A. The majority of the bonds in NO3- are single bonds,
so the bond order is 1.
B. The N-O bond is twice as likely to be a single bond as
it is to be a double bond, so the bond order should be
11/3.
C. The bond order is dictated by the strongest bond,
which in NO3- is a double bond.
Bond Order of Nitrate
Which of the following species is not
paramagnetic in its ground state?
A) NO+
Bond Order of Nitrate
B) NO
C) NO-
Consider the following arguments for each answer
and vote again:
A. NO+ is isoelectronic with N2, which has no unpaired
electrons and hence is not paramagnetic.
B. NO has no electrical charge and thus cannot be
paramagnetic.
C. By pairing an additional electron with the one
unpaired electron in NO, a diamagnetic anion, NO-, is
formed.
Bond Order of Nitrate
According to Valence Shell Electron Pair
Repulsion (VSEPR) theory, 4 objects
around a central atom will have the
tetrahedral arrangement shown to the left
with bond angles of ~109.5º. Which of the
following compounds has a bond angle of
~109.5º?
A) SF2
B) SF3-
Molecular Geometry of SF , SF -, and SF
C) SF4
Please consider the following arguments for each answer and
vote again:
A. SF2 consists of a sulfur atom surrounded by 2 lone electron
pairs and bonded to 2 fluorine atoms, therefore, it has an
approximately tetrahedral bond angle.
B. The tetrahedral VSEPR arrangement of SF3- is formed by a
sulfur atom surrounded by 3 fluorine atoms and by the
additional electron (from the negative charge).
C. Sulfur tetrafluoride is the only molecule with a central atom
(sulfur) surrounded by 4 additional atoms (4 fluorines) and so
is the only molecule with a bond angle of ~109.5º.
Molecular Geometry of SF , SF -, and SF
Which of the following is true of the
bond angle (θ1) in BrF2+ compared to
the bond angle (θ2) in ICl2-?
A) θ1 = θ2
B) θ1 > θ2
Bond Angles of BrF2 and ICl2
C) θ1 < θ2
Please consider the following arguments for each
answer and vote again:
A. Both BrF2+ and ICl2- consist of a central halogen
atom bonded to two halogen atoms, and therefore
should have the same arrangement of atoms.
B. ICl2- has 1 more lone pair of electrons than BrF2+,
which forces the chlorine atoms closer together.
C. ICl2-, with 3 lone pairs, is linear whereas BrF2+, with
2 lone pairs, is bent.
Bond Angles of BrF2 and ICl2
Boron trifluoride (BF3), which has the
structure shown to the left, is capable of
reacting with an unknown compound to
form a new compound without breaking
any bonds. Which of the following
could be the unknown compound?
A) BF3
Reaction of Boron Trifluoride
B) CH4
C) NH3
Please consider the following arguments for each
answer and vote again:
A. BF3 can dimerize to BF3-BF3 by forming a boronboron single bond.
B. By forming a boron-carbon bond, the carbon atom in
CH4 will increase its steric number to 5, thus
expanding its octet to compensate for boron's
incomplete octet.
C. The nitrogen lone electron pair can form a nitrogenboron bond yielding BF3-NH3, isoelectronic with
CH3-CH3.
Reaction of Boron Trifluoride
Pictured to the left is the planar
molecule ethylene, C2H4, which does
not have a permanent electric dipole
moment.
If chlorine atoms were substituted for two hydrogen
atoms, how many of the possible structures would also
not possess a dipole moment?
A) 0
B) 1
Dipole Moments of Dichloroethylene
C) 2
Consider the following arguments for each answer
and vote again:
A. Chlorine atoms always draw electron density away
from carbon atoms, so all possible structures will
possess a dipole moment.
B. Only if the chlorine atoms are diagonally opposite
will the two carbon-chlorine dipole moments cancel
each other.
C. So long as the two chlorine atoms are on different
carbon atoms, no permanent dipole moment will
form.
Dipole Moments of Dichloroethylene
For which central atom "X" does the
anion pictured to the left have a square
planar geometry?
A) C
Molecular Geometry of XF
2-
B) S
C) Xe
Please consider the following arguments for each
answer and vote again:
A. CF42- forms a structure in which the 4 fluorine
atoms form a square plane with one negative charge
on either side of the plane.
B. With 2 lone electron pairs on the sulfur in SF42-, its
steric number is 6.
C. To maximize fluorine-fluorine distances, the 4
fluorine atoms in XeF42- will lie in a plane.
Molecular Geometry of XF
2-