Chapter 9

Molecular Geometry and Bonding

Theories

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 Molecular Shapes

• Lewis structures show bonding and lone pairs but do not

denote shape.
• However, we use Lewis structures to help us determine
shapes.
• Here we see some common shapes for molecules with two or
three atoms connected to a central atom.

Molecular
Geometries
And Bonding
Theories
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 What Determines the
Shape of a Molecule?
• The bond angles and bond lengths determine the shape and
size of molecules.
• Electron pairs repel each other.
• Electron pairs are as far apart as possible; this allows predicting
the shape of the molecule.
• This is the valence-shell electron-pair repulsion (원자가 껍질
전자쌍 반발, VSEPR) model.

Molecular
Geometries
And Bonding
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 Valence-Shell Electron-Pair Repulsion
(VSEPR) Model

“The best arrangement of a given number of

electron domains is the one that minimizes
the repulsions among them.”
(The balloon analogy in the figure to the left
demonstrates the maximum distances that
minimize repulsions.)

Molecular
Geometries
And Bonding
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 Electron Domains
• We can refer to the directions to which electrons point as
electron domains (전자 도메인).
• This is true whether there is one or more electron pairs pointing
in that direction.
• It is also true if it is a lone pair or a bond.
• The central atom in this molecule, A, has four electron domains.

Molecular
Geometries
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 Electron-Domain Geometries

• The table shows the electron-

domain geometries for two
through six electron domains
around a central atom.
• To determine the electron-
domain geometry, count the
total number of lone pairs,
single, double, and triple
bonds on the central atom.

Molecular
Geometries
And Bonding
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 Molecular Geometries

1) Draw the best Lewis structure.

2) Determine the electron-domain geometry.
3) Use the arrangement of the bonded atoms to determine the
molecular geometry. Molecular
Geometries
And Bonding
Theories
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 Linear Electron Domain

• In the linear domain, there is only one molecular geometry:

linear.
• NOTE: If there are only two atoms in the molecule, the
molecule will be linear no matter what the electron domain is.
Molecular
Geometries
And Bonding
Theories
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 Trigonal Planar Electron Domain

• There are two molecular geometries:

– Trigonal planar, if all electron domains are bonding electrons
Molecular
– Bent, if one of the domains is a lone pair Geometries
And Bonding
Theories
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 Tetrahedral Electron Domain

• There are three molecular geometries:

– Tetrahedral, if all are bonding pairs
Molecular
– Trigonal pyramidal, if one is a lone pair Geometries
And Bonding
– Bent, if there are two lone pairs Theories
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 Nonbonding Pairs and Bond Angle

• Nonbonding pairs are physically larger

than bonding pairs.
• Therefore, their repulsions are greater;
this tends to compress bond angles.

Molecular
Geometries
And Bonding
Theories
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 Multiple Bonds and Bond Angles

• Double and triple bonds

have larger electron domains
than single bonds.
• They exert a greater
repulsive force than single
bonds, making their bond
angles greater.

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry I

Formaldehyde (H2CO) is a gas at room temperature. Aqueous solutions

of formaldehyde are used to preserve biological samples. Use VESPR
theory to predict the molecular geometry of formaldehyde.

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry I
Collect and Organize

Formaldehyde (H2CO) is a gas at room temperature. Aqueous solutions

of formaldehyde are used to preserve biological samples. Use VESPR
theory to predict the molecular geometry of formaldehyde.

We are given the molecular formula of formaldehyde. The solution requires (1)
drawing the Lewis structure, (2) determining the steric number, and (3)
identifying the molecular geometry.

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry I
Analyze

Formaldehyde (H2CO) is a gas at room temperature. Aqueous solutions

of formaldehyde are used to preserve biological samples. Use VESPR
theory to predict the molecular geometry of formaldehyde.

Carbon is the likely central atom of the molecule because it has a bonding
capacity of 4 and is less electronegative than oxygen, whose bonding capacity
is 2. If there are no lone pairs of electrons, then SN = 3 and the three atoms
bonded to C are as far from each other as possible.

Molecular
Geometries
And Bonding
Theories
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 Practice: Using VESPR Theory to Predict Geometry I
Solve

Formaldehyde (H2CO) is a gas at room temperature. Aqueous solutions

of formaldehyde are used to preserve biological samples. Use VESPR
theory to predict the molecular geometry of formaldehyde.

The Lewis structure for formaldehyde is:

SN = 3 and there are no lone pairs of electrons on the central atom. Therefore,
the molecular geometry is trigonal planar.

Molecular
Geometries
And Bonding
Theories
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 Expanding beyond the Octet Rule

• Remember that some elements can break the octet rule and
make more than four bonds (or have more than four electron
domains).
• The result is two more possible electron domains:
- five = trigonal bipyramidal
- six = octahedral
(as was seen in the slide on electron-domain geometries).

Molecular
Geometries
And Bonding
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 Trigonal Bipyramidal Electron Domain

• There are two distinct

positions in this geometry:
– Axial
– Equatorial
• Lone pairs occupy
equatorial positions.

Molecular
Geometries
And Bonding
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 Trigonal Bipyramidal Electron Domain

• There are four

distinct molecular
geometries in this
domain:
– Trigonal
bipyramidal
– Seesaw
– T-shaped
– Linear

Molecular
Geometries
And Bonding
Theories
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 Octahedral Electron Domain

• All positions are

equivalent in the
octahedral domain.
• There are three
molecular geometries:
– Octahedral
– Square pyramidal
– Square planar

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry II

The Lewis structure of SF4 is

What is its molecular geometry and the angles between the SF bonds?

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry II
Collect and Organize
The Lewis structure of SF4 is

What is its molecular geometry and the angles between the SF bonds?

We are given the Lewis structure of SF4. From it we can determine the steric
number of the central atom in the molecule and its electron-pair geometry.

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry II
Analyze
The Lewis structure of SF4 is

What is its molecular geometry and the angles between the SF bonds?

Four atoms are bonded to the central S atom, which also has one lone pair of
electrons, so SN = 5.

Molecular
Geometries
And Bonding
Theories
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Practice: Using VESPR Theory to Predict Geometry II
Solve
The Lewis structure of SF4 is

What is its molecular geometry and the angles between the SF bonds?

With a steric number of 5 for its central atom, the electron-pair geometry of SF4 is
trigonal bipyramidal. The presence of one lone pair of electrons on the S atom
means that its molecular geometry is seesaw.

The equatorial lone pair slightly reduces the bond angles from their normal values
of 90° between the axial and equatorial bonds, 120° between the two equatorial
bonds, and 180° between the two axial bonds.
Molecular
Geometries
And Bonding
Theories
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 Shapes of Larger Molecules

For larger molecules, look at the geometry about each atom

rather than the molecule as a whole.
Molecular
Geometries
And Bonding
Theories
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What is the approximate bond angle around the
central carbon atom in acrolein?

A. 180°

B. 120°

C. 109.5°

D. 90°

Molecular
Geometries
And Bonding
Theories
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What is the approximate bond angle around the
central carbon atom in acrolein? [ANSWER]

A. 180°

B. 120° [CORRECT ANSWER]

C. 109.5°

D. 90°

Molecular
Geometries
And Bonding
Theories
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 Comparison of the
Polarity of Two Molecules
A NONPOLAR molecule A POLAR molecule

Molecular
Geometries
And Bonding
Theories
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Practice: Predicting the Polarity of a Substance

Does formaldehyde, CH2O, have a permanent dipole?

Molecular
Geometries
And Bonding
Theories
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Practice: Predicting the Polarity of a Substance
Collect and Organize

Does formaldehyde, CH2O, have a permanent dipole?

To predict whether a molecule has a permanent dipole, we need to determine

whether there is asymmetry in its structure, particularly in the way polar bonds in
the molecule are oriented relative to one another. Bond polarity depends on the
difference in the electronegativity of the bonded pair of atoms. Looking at the
Lewis structure, we see that formaldehyde has a trigonal planar structure:

Molecular
Geometries
And Bonding
Theories
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Practice: Predicting the Polarity of a Substance
Analyze

Does formaldehyde, CH2O, have a permanent dipole?

The electronegativities of the elements are

H = 2.1 C = 2.5 O = 3.5
Given the differences in the electronegativities of the atoms it is
likely that formaldehyde has a permanent dipole moment.

Molecular
Geometries
And Bonding
Theories
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Practice: Predicting the Polarity of a Substance
Solve

Does formaldehyde, CH2O, have a permanent dipole?

Each of the bonds in the molecule has a bond dipole directed toward the oxygen
atom.

Molecular
Geometries
And Bonding
Theories
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 Valence-Bond Theory

• In valence-bond theory, electrons

of two atoms begin to occupy the
same space.
• This is called “overlap” of orbitals.
• The sharing of space between two
electrons of opposite spin results
in a covalent bond.

Molecular
Geometries
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 Valence-Bond Theory

• Increased overlap brings the atoms together until a balance is

reached between the like charge repulsions and the electron-
nucleus attraction.
• Atoms can’t get too close because the internuclear repulsions
get too great.

Molecular
Geometries
And Bonding
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 Hybrid Orbitals

• Hybrid orbitals form by “mixing” of atomic orbitals to create

new orbitals of equal energy, called degenerate orbitals.
• This process is called hybridization.
• When two orbitals “mix” they create two orbitals;
when three orbitals mix, they create three orbitals; and so on.

Molecular
Geometries
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Theories
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 Be—sp Hybridization

• When we look at the orbital diagram for beryllium (Be), we see

that there are only paired electrons in full sublevels.
• Be makes electron-deficient compounds with two bonds for Be.
Why?
sp hybridization (mixing of one s orbital and one p orbital).

Molecular
Geometries
And Bonding
Theories
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 sp Orbitals

• Mixing the s and p orbitals yields two degenerate orbitals that

are hybrids of the two orbitals.
– The sp hybrid orbitals each have two lobes like a p orbital.
– One of the lobes is larger and more rounded, as is the s
orbital.

Molecular
Geometries
And Bonding
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 Position of sp Orbitals

• These two degenerate orbitals would align themselves 180°

from each other.
• This is consistent with the observed geometry of Be
compounds (like BeF2) and VSEPR: linear.

Molecular
Geometries
And Bonding
Theories
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 Boron—Three Electron Domains
Gives sp2 Hybridization
Using a similar model for boron leads to three degenerate sp2
orbitals.

Molecular
Geometries
And Bonding
Theories
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 Carbon: sp3 Hybridization

With carbon,
we get four degenerate
sp3 orbitals.

Molecular
Geometries
And Bonding
Theories
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 What Happens with Water?

• Discussion with H2O and the angle question: Why is it 104.5°

instead of 90°?
• Oxygen has two bonds and two lone pairs—four electron
domains.
• The result is sp3 hybridization!

Molecular
Geometries
And Bonding
Theories
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 Hypervalent Molecules

• The elements that have more than an octet

• Valence-bond model would use d orbitals to make more than
four bonds.
• This view works for period 3 and below.
• Theoretical studies suggest that the energy needed would be
too great for this.
• A more detailed bonding view is needed than we will use in this
course.

Molecular
Geometries
And Bonding
Theories
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 Hybrid Orbital Summary

1) Draw the Lewis structure.

2) Use VSEPR to determine the electron-domain geometry.
3) Specify the hybrid orbitals needed to accommodate these
electron pairs.

Molecular
Geometries
And Bonding
Theories
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 Types of Bonds

• How does a double or triple bond form?

• It can’t, if we use only hybridized orbitals.
• However, if we use the orbitals that are not hybridized, we can
have a “sideways” overlap.
• Two types of bonds:
– Sigma (σ) bond
– Pi (π) bond

Molecular
Geometries
And Bonding
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 Sigma () and Pi () Bonds

• Sigma bonds are characterized by

– head-to-head overlap.
– cylindrical symmetry of electron density about the
internuclear axis.
• Pi bonds are characterized by
– sideways overlap.
Molecular
– electron density above and below the internuclear axis.
Geometries
And Bonding
Theories
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 Bonding in Molecules

• Single bonds are always σ-bonds.

• Multiple bonds have one σ-bond; all other bonds are π-bonds.

Molecular
Geometries
And Bonding
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 Localized or Delocalized Electrons

• Bonding electrons (σ or π) that are specifically shared between

two atoms are called localized electrons.
• In many molecules, we can’t describe all electrons that way
(resonance); the other electrons (shared by multiple atoms) are
called delocalized electrons.

Molecular
Geometries
And Bonding
Theories
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 Benzene

The organic molecule benzene (C6H6) has six -bonds and a p

orbital on each C atom, which form delocalized bonds using one
electron from each p orbital.

Molecular
Geometries
And Bonding
Theories
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 Molecular Orbital (MO) Theory

• Wave properties are used to describe the energy of the

electrons in a molecule.
• Molecular orbitals have many characteristics like atomic
orbitals:
– Maximum of two electrons per orbital
– Electrons in the same orbital have opposite spin
– Definite energy of orbital
– Can visualize electron density by a contour diagram

Molecular
Geometries
And Bonding
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 More on MO Theory

• They differ from atomic orbitals because they represent the

entire molecule, not a single atom.
• Whenever two atomic orbitals overlap, two molecular orbitals
are formed: one bonding, one antibonding.
• Bonding orbitals are constructive combinations of atomic
orbitals.
• Antibonding orbitals are destructive combinations of atomic
orbitals.
They have a new feature unseen before:
A nodal plane occurs where electron density equals zero.
Molecular
Geometries
And Bonding
Theories
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 Molecular Orbital (MO) Theory

• Whenever there is direct overlap of orbitals, forming a bonding

and an antibonding orbital, they are called sigma (σ)
molecular orbitals.
• The antibonding orbital is distinguished with an asterisk as σ*.
Here is an example for the formation of a hydrogen molecule
from two atoms.

Molecular
Geometries
And Bonding
Theories
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 MO Diagram

• An energy-level diagram, or MO diagram, shows how orbitals

from atoms combine to form molecular orbitals.
• In H2 the two electrons go into the bonding molecular orbital
(lower in energy).
• Bond order = ½(# of bonding e’s – # of antibonding e’)
= ½ (2 – 0) = 1 bond.

Molecular
Geometries
And Bonding
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 Can He2 Form? Use MO Diagram
and Bond Order to Decide!

• Bond order = ½ (2 – 2) = 0 bonds.

• Therefore, He2 does not exist.

Molecular
Geometries
And Bonding
Theories
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 Guiding Principles for the Formation of
Molecular Orbitals
1) The number of MOs formed equals the number of AOs
combined.
2) AOs combine with AOs of similar energy.
3) The effectiveness with which two AOs combine is proportional
to their overlap.
4) Each MO can accommodate at most two electrons with
opposite spin. (They follow the Pauli exclusion principle.)
5) When MOs of the same energy are populated, one electron
enters each orbital (same spin) before pairing.
(They follow Hund’s rules.)
Molecular
Geometries
And Bonding
Theories
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 MOs, Bonding, and Core Electrons

• Li2 (g) occurs at high

temperatures.
• Lewis structure: Li — Li.
• The MO diagram is on the right.
• Notice that core electrons don’t
play a major part in bonding, so
we usually don’t include them in
the MO diagram.

Molecular
Geometries
And Bonding
Theories
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 MOs from p-Orbitals

• p-orbitals also undergo

overlap.
• They result in either direct or
sideways overlap.

Molecular
Geometries
And Bonding
Theories
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 MO Diagrams for the Second
Period p-Block Elements
• There are σ and σ* orbitals
from s and p atomic orbitals.
• There are π and π* orbitals
from p atomic orbitals.
• Since direct overlap is
stronger, the effect of raising
and lowering energy is
greater for σ and σ*.

Molecular
Geometries
And Bonding
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 s and p Orbital Interactions (Mixing)

• In some cases, s orbitals can interact with the pz orbitals more

than the px and py orbitals.
• It raises the energy of the pz orbital and lowers the energy of
Molecular
the s orbital. Geometries
• The px and py orbitals are degenerate orbitals. And Bonding
Theories
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 MO Diagrams for Diatomic Molecules
of Second Period Elements

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Geometries
And Bonding
Theories
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 MO Diagrams and Magnetism

• Diamagnetism is the result of all electrons in every orbital

being spin-paired. These substances are weakly repelled by a
magnetic field.
• Paramagnetism is the result of the presence of one or more
unpaired electrons in an orbital.
• Is oxygen (O2) paramagnetic or diamagnetic?
Look back at the MO diagram! It is paramagnetic.

Molecular
Geometries
And Bonding
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 Paramagnetism of Oxygen

• Lewis structures would not predict that O2 is paramagnetic.

• The MO diagram clearly shows that O2 is paramagnetic.
• Both show a double bond (bond order = 2).

Molecular
Geometries
And Bonding
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 Heteronuclear Diatomic Molecules

• Diatomic molecules can consist of

atoms from different elements.
• How does a MO diagram reflect
differences?
• The atomic orbitals have different
energy, so the interactions change
slightly.
• The more electronegative atom has
orbitals lower in energy, so the
bonding orbitals will more resemble
them in energy.
Molecular
Geometries
And Bonding
Theories
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