Unit 9 - Molecular

Geometry
 Molecular Shape
Chemical/Physical Properties Related to
Molecular Shape
Lewis Structures
Show atoms and bonds, but not spatial
orientations (3-D)
Molecular Models
Show orientations and bond angles; help us
understand physico-chemical properties

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Lewis Structures vs Models

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 Molecular Shape
Bond Angle:
Angle defined
by covalent bonds
between three adjacent
atoms
Molecular Geometry:
Shape defined
by lowest energy
3-D arrangement O−C−O angle H−O−H angle
of atoms
= 180⁰ (linear) = 104.5⁰ (bent)
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 Valence-Shell Electron-Pair Repulsion Theory
(VSEPR)
VSEPR Theory:
• Geometric arrangement of electron pairs around
atoms based on minimizing repulsion energy
Electron Pair Geometry:
• Spatial arrangement of bonding e− pairs and lone pairs
(non-bonding) of valence electrons
Molecular Geometry:
• Defined by relative arrangement of atoms (bonding
pairs) in molecule
• Bond angles depend on e− pair repulsion

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 Predicting a VSEPR Structure
1. Draw the Lewis structure
2. Determine the steric number (SN)
of the central atom
SN = (number of atoms bonded to central atom)
+ (number of lone pairs on central atom)
3. Use the SN to determine the geometry
around the central atom
4. Optimize molecular structure by determining the
number of lone pairs and bonding pairs of
electrons

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 Electron Pair Repulsions
Electron Pair Repulsion Order:
• Lone pair—Lone pair = greatest repulsion
• Lone pair—Bonding pair is next
• Bonding pair—Bonding pair = least repulsion
• Double bonds exert more repulsion than single bonds

Bond angles around central atom decrease as

repulsive forces increase

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 Geometric Forms: SN = 2
Electron Pair Geometry Molecular Geometry
Linear Linear

Examples: CO2, BeF2, HCN, C2H2

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 Geometric Forms: SN = 3
Electron Pair Geometry Molecular Geometry
Trigonal Planar If 3 bonding, 0 non-bonding
Trigonal Planar

BF3

If 2 bonding, 1 non-bonding
Bent

NO2-

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 Geometric Forms: SN = 4
Electron Pair Geometry Molecular Geometry
Tetrahedral If 4 bonding, 0 non-bonding
Tetrahedral

If 3 bonding, 1 non-bonding
Trigonal Pyramidal

If 2 bonding, 2 non-bonding
Bent

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 Geometric Forms: SN = 5
Electron Pair Geometry Molecular Geometry
Trigonal Bipyramidal If 5 bonding, 0 non-bonding
Trigonal Bipyramidal

If 4 bonding, 1 non-bonding
Seesaw

If 3 bonding, 2 non-bonding
T-Shaped

If 2 bonding, 3 non-bonding
Linear

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 Molecular Geometry: SN = 5
Seesaw

SF4
T-Shaped

ClF3
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 Geometric Forms: SN = 6
Electron Pair Geometry Molecular Geometry
Octahedral If 6 bonding, 0 non-bonding
Octahedral
If 5 bonding, 1 non-bonding
Square Pyramidal

If 4 bonding, 2 non-bonding
Square Planar
If 3 bonding, 3 non-bonding
T-Shaped
If 2 bonding, 4 non-bonding
Linear
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 Molecular Geometry: SN = 6
Square Pyramidal

IF5
Square Planar

XeF4
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 Molecular Geometry: SN = 4

Tetrahedral Trigonal pyramid Bent

Note: Bond angles decrease as

number of lone pairs increases
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Atoms Lone Steric
Electron Geometry Molecular geometry
Bonded Pairs Number
6 0 6 Octahedral Octahedral
5 1 6 Octahedral Square pyramidal
4 2 6 Octahedral Square planar
5 0 5 Trig. Bipyramidal Trig. Bipyramidal
4 1 5 Trig. Bipyramidal See-saw
3 2 5 Trig. Bipyramidal T-shaped
4 0 4 Tetrahedral Tetrahedral
3 1 4 Tetrahedral Trig. Pyramidal
2 2 4 Tetrahedral Bent
3 0 3 Trig. Planar Trig. Planar
2 1 3 Trig. Planar Bent
2 0 2 Linear Linear
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 Practice: Molecular Geometry

Determine the molecular geometry of:

a) SeCl4 b) PSCl3

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 Problem to Consider
Predict the molecular geometry and bond angles in SiF5─

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 Dipole Moment and Molecular Geometry
The dipole moment is a measure of the degree of charge
separation in a molecule
Measurements are based on the fact that polar molecules
are oriented by an electric field. This orientation affects
the capacitance of the charged plates that create the
electric field.

Requirements for Polar Molecule:

1. Molecule must contain polar bonds (i.e., covalent
bond between atoms with ΔEN)
2. Orientation of polar bonds results in charge
separation from one part of the molecule to another
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 Example: CO vs. CO2

Polar but linear shape results in partial

Polar bond… no other bond
to cancel; polar!
bonds… charges canceling out; nonpolar!

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 Polar Bonds and Polar Molecules

Bond Dipole:
• Separation of
charge within a
covalent bond

Polar Molecule:
• Have nonzero
dipole moments
• Vectors of bond
dipoles sum > zero
Polar!
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 Dipole Moment and Molecular Geometry
Dipole moment arrow with + on partial
plus side (or least electronegative atom)
Geometry example: CO2 is linear, and
H2O is bent.
+
+ + + O +
O C O
H H
The vectors add to zero (cancel) For H2O, a net vector points up
for CO2 Water has a dipole moment
Its dipole moment is zero = polar
= nonpolar
Note: Any geometry with polar bonds and any
asymmetry in the arrangement of electron pairs
would have a nonzero dipole moment. These
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molecules are considered polar.
 Dipole Moment and Molecular Geometry
Polar molecules experience attractive forces between molecules; in response,
they orient themselves in a d+ to d- manner.
Attraction between molecules impacts molecular properties
Example: The attractive forces due to the polarity lead the molecule to have a
higher boiling point.
Example: Molecular polarity affects solubility in water.
We can see this illustrated with two compounds:

There is no net polarity; this The net polarity is down; this

is a nonpolar molecule is a polar molecule

Boiling point 48°C Boiling point 60°C 25

 Problem to consider
Which of the following molecules would be expected to
have a zero dipole moment?

a. GeF4

b. SF2

c. XeF2

d. H2O

e. AsF3
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 Measuring Polarity
Dipole moment (μ):
Measured value defining extent of separation of + and −
charge centers in a molecule
(Units = debyes (D); 1 D = 3.34 × 10−30 coul∙m )

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 Atomic Orbitals and Bonds
Bond electron density holding two atoms together.
Atomic Orbitals / Tetrahedral Geometry:
• Requires overlap of four orbitals of the central
atom with orbitals of outer atoms
• Available orbitals (one s + three p) not oriented to
yield 109° bond angles observed in tetrahedral
geometry!
• Need new theory to explain orientation
of bonds in molecules
Valence Bond Theory (Linus Pauling)
Bond = overlap between 2 atomic or hybrid orbitals 29
 Valence-Bond Theory
Assumes that covalent bonds form when
orbitals on different atoms overlap
Hybridization: mixing of atomic orbitals
to generate new sets of orbitals that form
covalent bonds with other atoms
Hybrid atomic orbital: one of a set of equivalent
orbitals created when specific atomic orbitals
are mixed

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 Hybrid orbitals
Hybrid orbitals are named by using the atomic orbitals that
combined:
• one s orbital + one p orbital gives two sp orbitals
• one s orbital + two p orbitals gives three sp2 orbitals
• one s orbital + three p orbitals gives four sp3 orbitals
• one s orbital + three p orbitals + one d orbital gives five sp3d orbitals
• one s orbital + three p orbitals + two d orbitals gives six sp3d2 orbitals
Hybrid orbitals have definite directional characteristics, as described
below
Hybrid Orbitals Geometric Arrangement Number of Orbitals Example
sp Linear 2 Be in BeF2
sp2 Triognal Planar 3 B in BF3
sp3 Tetrahedral 4 C in CH4
sp3d Trigonal bipyramidal 5 P in PCl5
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sp3d2 Octahedral 6 S in SF6
 Orbital Overlap: Sigma Bonds
Sigma (σ) bond: covalent bond having highest
electron density between the two atoms along
the bond axis

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 Hybrid orbitals
• First, the paired 2s electron is promoted (excited) to the
unfilled orbital. Now each orbital has one electron.
• Second, these orbitals are hybridized, giving four sp3 hybrid
orbitals.

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 Tetrahedral: sp3 Hybrid Orbitals

Tetrahedral orientation of bonding orbitals

results from “hybridization” of the s and p
orbitals

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Other sp3 Hybrid Examples

Note:
Lone pairs
(non-
bonding)

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 Trigonal Planar: sp2 Hybridization
Mixing of one s and two p orbitals:

Unhybridized orbitals used to form double bonds

(“pi” bond) 36
 Trigonal Planar: sp2 Hybridization

pi (π) bond:
electron density is concentrated above/below the
bonding axis

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 Linear: sp Hybridization
Mixing of one s and one p orbital:
Unhybridized orbitals
used to form triple
bond (= one σ and
two π bonds)

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 Carbon Dioxide: Multiple π Bonds
Carbon: sp hybridized
• sp orbitals = σ bonds
• unhybridized orbitals = π bonds

Oxygen: sp2 hybridized

• one sp2 orbital = σ bond
• two sp2 orbitals = lone pairs
• unhybridized orbital = π bond

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 Octahedral: sp3d2 Hybridization

Formed by mixing one s, two d, and three p

orbitals. All six hybridized orbitals used to form
sigma bonds

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 Trigonal Bipyramid: sp3d Hybridization

Formed by mixing one s, one d, and three p

orbitals - all five hybrid orbitals used to form
sigma bonds

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 Hybrid orbitals
To obtain the bonding description about any
atom in a molecule:
1. Write the Lewis electron-dot formula.
2. Use VSEPR to determine the electron arrangement
about the atom.
3. From the arrangement, deduce the hybrid orbitals.
4. Assign the valence electrons to the hybrid orbitals
one at a time, pairing only when necessary.
5. Form bonds by overlapping singly occupied hybrid
orbitals with singly occupied orbitals of another atom.

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Summary of Hybridization

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 A Problem to consider
Describe the bonding in XeF4 using hybrid
orbitals
– From the Lewis formula for a molecule,
determine its geometry about the central atom
using the VSEPR model.
– The Lewis formula of XeF4 is

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 A Problem to consider
Describe the bonding in XeF4 using hybrid
orbitals.
– The xenon atom has four single bonds and two lone
pairs. It will require six orbitals to describe the bonding.
– From this geometry, determine the hybrid orbitals on
this atom, assigning its valence electrons to these
orbitals one at a time.
– This suggests that you use sp3d2 hybrid orbitals on
xenon.

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 A Problem to consider
Describe the bonding in XeF4 using hybrid
orbitals.
– Each Xe-F bond is formed by the overlap of a
xenon sp3d2 hybrid orbital with a singly occupied
fluorine 2p orbital.
– You can summarize this as follows:

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 A Problem to consider

5d

5p

5s
Xe atom (ground state)
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 A Problem to consider

5d

sp3d2

lone pairs Xe-F bonds

Xe atom (in XeF4)

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 Practice: Hybrid Orbitals
What are the hybridizations of the central atoms
of the ions: SCN− and NO2− ?

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 Description of Multiple Bonds

One hybrid orbital is required for each bond

(whether a single or a multiple bond) and for
each lone pair.

Multiple bonding involves the overlap of one

hybrid orbital and one (for a double bond) or
two (for a triple bond) nonhybridized p orbitals.

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 Description of Multiple Bonds
To describe a multiple bond, we need to distinguish
between two kinds of bonds.
• A σ (sigma) bond is a “head-to-head” overlap of
orbitals with a cylindrical shape about the bond axis.
This occurs when two “s” orbitals overlap or “p”
orbitals overlap along their axis.

• A π (pi) bond is a “side-to-side” overlap of parallel

“p” orbitals, creating an electron distribution above
and below the bond axis.

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1 | 54
 Multiple Bonding - Ethene
– Two of the sp2 hybrid orbitals of each carbon overlap with
the 1s orbitals of the hydrogens.
– The remaining sp2 hybrid orbital on each carbon overlap to
form a s bond.
– The remaining “unhybridized” 2p orbitals on each of the
carbon atoms overlap side-to-side forming a p bond.

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Hybrid orbitals overlap
to form a σ bond.
Unhybridized p orbitals
overlap to form a π
bond.

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 sp Hybrid Orbitals
p
s
p

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 Bond Rotation
Because the orbitals that form the s bond point along
the internuclear axis, rotation around that bond does not
require breaking the interaction between the orbitals

But the orbitals that form the p bond interact above and
below the internuclear axis, so rotation around the axis
requires the breaking of the interaction between the
orbitals

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Bond Rotation

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 Bond Rotation
The description of a p bond helps to explain the cis-
trans isomers of 1,2-dichloroethene.

The overlap of the parallel p orbitals restricts the

rotation around the C=C bond. This fixes the geometric
positions of Cl: either on the same side (cis) or on
different sides (trans) of the C=C bond.
H H H Cl

C C C C

Cl Cl Cl H
cis trans
1 | 60
 Problems with Bonding Theories

Lewis structures /valence bond theory:

• Modeled bonding capacities of elements,
but did not account for molecular shapes.
VSEPR + valence bond theories:
• Account for observed molecular geometries, but
not magnetic properties.
• For example, O2 is attracted to a magnetic field
(paramagnetic) while N2 is repelled slightly
(diamagnetic).
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 Molecular Orbital (MO) Theory

The wave functions of atomic orbitals in atoms are

combined to create molecular orbitals (MOs) in
molecules.

The number of molecular orbitals formed is equal

to the number of atomic orbitals combined.

Molecular orbitals spread out over entire molecule

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 Types of Molecular Orbitals
Bonding orbitals:
• Hold atoms together by increasing electron density
between nuclear centers in molecules.
• Are lower in energy (more stable) than atomic orbitals
from which they are formed.
Antibonding orbitals:
• Destabilize the molecule because they do not increase
electron density between nuclear centers.
• Are higher in energy (less stable) than atomic orbitals from
which they are formed.

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 Molecular Orbital Diagrams
MO Diagram:
• Energy level diagram for molecular orbitals; shows
formation of bonding / antibonding orbitals.
Sigma (σ) Bond:
• Covalent bond with the highest electron density
along the bond axis.
pi (π) Bond:
• Formed by mixing of atomic orbitals not oriented
along the bonding axis in a molecule.
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 Molecular Orbital Diagram: H2

The two 1s orbitals may be added or subtracted

to yield two sigma MOs (1 bonding/1 antibonding).

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 Bond Order and Stability

Bond Order = (½ number of bonding e-) – (½ number antibonding e-)

Bond order in H2- = 1/2 Bond order in He2 = 0

(Stable) (Not Stable)
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 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.

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MO Diagrams for N2 and O2

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 MO Scheme for O2
Electron configuration for O2:
σ2s2σ2s*2σ2p2π2p4 π2p*2
Bond order = ½(8 − 4) = 2
• O2 has two bonds
• O2 has two unpaired
electrons in π2p*

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MO Scheme for N2
• Electron configuration for
N2: σ2s2σ2s*2σ2p2π2p4
• Bond order = 1/2 (8 − 2)
=3
• N2 has three bonds.
• N2 has no unpaired electrons.

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Paramagnetism and Diamagnetism
Paramagnetism:
Atoms or molecules having unpaired electrons are
attracted to magnetic fields.
• Example: O2
Diamagnetism:
Atoms or molecules having all paired electrons are
repelled by magnetic fields.
• Example: N2

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 Other Diatomic Molecules

MO Theory predicts both magnetic properties and

stability of diatomic molecules 72
Comparing theoretical bond order and experimental
data

1 | 73
 MO for Heteroatomic Molecules

Effective nuclear charge alters

the diagram; atomic orbitals
for O are lower in energy.

The odd electron is more likely

to be found on N since it is in
an orbital closer in energy to
the atomic orbitals of the
nitrogen atom.

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 MO Theory: Summary
Advantages:
• Provides the most complete picture of covalent
bonding, including bond types
and bond orders
• Accounts for magnetic properties
Disadvantage:
• The most difficult to apply to large molecules;
does not account for molecular shape

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 Hydrogen Bonding
Hydrogen Bond: Special class of dipole-dipole
interactions due to strength

One polar molecule is attracted to H- from another

polar molecular that is covalently bonded to strongly
electronegative atom (N, O, or F)
10 | 76
 Hydrogen Bonding in DNA
H-bonding in complementary nucleotide bases

10 | 77
 Learning Objectives
● Describe the formation of covalent bonds in terms of atomic overlap
● Apply valence bond theory in terms of hybrid and unhybridized atomic orbitals
● Determine the hybrid orbitals in a species based on the molecular geometry
● Distinguish between σ bonds and π bonds and be able to determine the number of
each in a molecule
● Describe multiple bonds in terms of atomic overlap
● Explain the concept of resonance in terms of π bonding
● Describe molecular orbital configurations and apply molecular orbital theory to
determine magnetic behavior and bond order/stability
● Describe bonding vs antibonding orbitals
● Calculate bond order based on molecular orbital diagrams

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