Chapter 8

Advanced Theories of Covalent Bonding

Shaun Williams, PhD

Hybridization and the Localized Electron Model

Exercise 1

Draw the Lewis structure for methane, $\chem{CH_4}$.

A central carbon atom singly bonded to four neighboring hydrogen atoms.

What is the shape of a methane molecule? $$ \phantom{\text{tetrahedral}} $$
What are the bond angles? $$ \phantom{109.5^\circ} $$

Hybridization and the Localized Electron Model

Exercise 1 - Answer

Draw the Lewis structure for methane, $\chem{CH_4}$.

A central carbon atom singly bonded to four neighboring hydrogen atoms.

What is the shape of a methane molecule? $$ \color{green} \text{tetrahedral} $$
What are the bond angles? $$ \color{green} 109.5^\circ $$

Concept Check 1

What is the valence electron configuration of a carbon atom?

$$ \phantom{s^2p^2} $$

Why can't the bonding orbitals for methane be formed by an overlap of atomic orbitals?

Concept Check 1 - Answer

What is the valence electron configuration of a carbon atom?

$$ s^2p^2 $$

Why can't the bonding orbitals for methane be formed by an overlap of atomic orbitals?

Because this would lead to two different types of C-H bonds and we know that methane has four identical C-H bonds that are 109.5° apart from each other (not 90° from each other).

Bonding in Methane

Assume that the carbon atom has four equivalent atomic orbitals, arranged tetrahedrally.

Hybridization

Mixing of the native atomic orbitals to form special orbitals for bonding.

$sp^3$ Hybridization

Combination of one s and three p orbitals.
Whenever a set of equivalent tetrahedral atomic orbitals is required by an atom, the localized electron model assumes that the atom adopts a set of $sp^3$ orbitals; the atom becomes $sp^3$ hybridized.
The four orbitals are identical in shape.

An Energy-Level Diagram Showing the Formation of Four $sp^3$ Orbitals

The one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

The Formation of $sp^3$ Hybrid Orbitals

A graphical representation of the one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

A graphical representation of the set of sp3 hybrid orbitals showing their tetrahedral arrangement.

Exercise 2

Draw the Lewis structure for $\chem{C_2H_4}$ (ethylene)?

Two carbon atoms doubly bonded to each other. Each carbon atom is songly bonded to two hydrogen atoms.

What is the shape of an ethylene molecule? $$ \phantom{\text{trigonal planar around each carbon atom}} $$
What are the approximate bond angles around the carbon atoms? $$ \phantom{120^\circ} $$

Exercise 2 - Answer

Draw the Lewis structure for $\chem{C_2H_4}$ (ethylene)?

Two carbon atoms doubly bonded to each other. Each carbon atom is songly bonded to two hydrogen atoms.

What is the shape of an ethylene molecule? $$ \color{green} \text{trigonal planar around each carbon atom} $$
What are the approximate bond angles around the carbon atoms? $$ \color{green} 120^\circ $$

$sp^2$ Hybridization

Combination of one $s$ and two $p$ orbitals.
Gives a trigonal planar arrangement of atomic orbitals.
One $p$ orbital is not used.
- Oriented perpendicular to the plane of the $sp^2$ orbitals.

Sigma ($\sigma$) Bond

Electron pair is shared in an area centered on a line running between the atoms.

Pi ($\pi$) Bond

Forms double and triple bonds by sharing electron pair(s) in the space above and below the $\sigma$ bond.
Uses the unhybridized p orbitals.

An Orbital Energy-Level Diagram for $sp^2$ Hybridization

The one 2s and the two 2p orbitals mix together to make three sp2 hybrid orbitals. There is also a left over unhybridized 2p orbital.

The Hybridization of the $s$, $p_x$, and $p_y$ Atomic Orbitals

A graphical representation of the one 2s and the two 2p orbitals mix together to make three sp2 hybrid orbitals and a left over 2p orbital.

$sp$ Hybridization

Combination of one $s$ and one $p$ orbital.
Gives a linear arrangement of atomic orbitals.
Two $p$ orbitals are not used.
- Needed to form the $\pi$ bonds.

The Orbital Energy-Level Diagram for the Formation of $sp$ Hybrid Orbitals on Carbon

The one 2s and the one 2p orbitals mix together to make two sp hybrid orbitals. There are also two left over unhybridized 2p orbitals.

When One $s$ Orbital and One $p$ Orbital are Hybridized, a Set of Two $sp$ Orbitals Oriented at $180^\circ$ Results

A graphical representation of the one 2s and one 2p orbitals mix together to make two sp hybrid orbitals and two left over 2p orbitals.

The Orbitals for $\chem{CO_2}$

A graphical representation carbon dioxide with the central carbon atom forming a sigma bond with each oxygen atom and a pi bond with each of the oxygen atoms.

Exercise 3

Draw the Lewis structure for $\chem{PCl_5}$?

A central phosphorus atom singly bonded to five chlorine atoms. Each chlorine atom has three lone pairs of electrons.

What is the shape of phosphorus pentachloride? $$ \phantom{\text{trigonal bipyramidal}} $$
What are the bond angles? $$ \phantom{90^\circ \text{ and } 120^\circ} $$

Exercise 3 - Answer

Draw the Lewis structure for $\chem{PCl_5}$?

A central phosphorus atom singly bonded to five chlorine atoms. Each chlorine atom has three lone pairs of electrons.

What is the shape of phosphorus pentachloride? $$ \color{green} \text{trigonal bipyramidal} $$
What are the bond angles? $$ \color{green} 90^\circ \text{ and } 120^\circ $$

$dsp^3$ Hybridization

Combination of one $d$, one $s$, and three $p$ orbitals.
Gives a trigonal bipyramidal arrangement of five equivalent hybrid orbitals.

The Orbitals Used to Form the Bonds in $\chem{PCl_5}$

A graphical representation phosphorus pentachloride with the central phosphorus atom forming a sigma bond with each chlorine atom.

Exercise 3

Draw the Lewis structure for $\chem{XeF_4}$?

A central xenon atom with two lone electron pairs is singly bonded to four fluorine atoms. Each fluorine atom has three lone pairs of electrons.

What is the shape of an xenon tetrafluoride? $$ \phantom{\text{octahedral}} $$
What are the bond angles? $$ \phantom{90^\circ \text{ and } 180^\circ} $$

Exercise 3 - Answer

Draw the Lewis structure for $\chem{XeF_4}$?

A central xenon atom with two lone electron pairs is singly bonded to four fluorine atoms. Each fluorine atom has three lone pairs of electrons.

What is the shape of an xenon tetrafluoride? $$ \color{green} \text{octahedral} $$
What are the bond angles? $$ \color{green} 90^\circ \text{ and } 180^\circ $$

$d^2sp^3$ Hybridization

Combination of two $d$, one $s$, and three $p$ orbitals.
Gives an octahedral arrangement of six equivalent hybrid orbitals.

How is the Xenon Atom in $\chem{XeF_4}$ Hybridized

A graphical representation of the two d orbitals, one 2s and the three 2p orbitals mix together to make four sp3 hybrid orbitals.

Using the Localized Electron Model

Draw the Lewis structure(s).
Determine the arrangement of electron pairs using the VSEPR model.
Specify the hybrid orbitals needed to accommodate the electron pairs.

The Molecular Orbital Model

Regards a molecule as a collection of nuclei and electrons, where the electrons are assumed to occupy orbitals much as they do in atoms, but having the orbitals extend over the entire molecule.
The electrons are assumed to be delocalized rather than always located between a given pair of atoms.
The electron probability of both molecular orbitals is centered along the line passing through the two nuclei.
- Sigma ($\sigma$) molecular orbitals (MOs)
In the molecule only the molecular orbitals are available for occupation by electrons.

Combination of Hydrogen 1s Atomic Orbitals to form MOs

A graphical representation of subtracting the 1s orbitals on the two atoms to form the antibonding MO (called MO1) and adding the two 1s orbitals to form the bonding MO (MO2). The antibonding MO has a node between the atoms while the bonding MO does not.

Relative Stabilities

$\chem{MO_1}$ is lower in energy than the $s$ orbitals of free atoms, while $\chem{MO_2}$ is higher in energy than the $s$ orbitals.
- Bonding molecular orbital – lower in energy
- Antibonding molecular orbital – higher in energy

MO Energy-Level Diagram for the $\chem{H_2}$ Molecule

A graphical representation of the relative energies of the bonding and antibonding orbitals showing the bonding MO at a lower energy than the antibonding orbital.

Description of Bonding

The molecular orbital model produces electron distributions and energies that agree with our basic ideas of bonding.
The labels on molecular orbitals indicate their symmetry (shape), the parent atomic orbitals, and whether they are bonding or antibonding.
Molecular electron configurations can be written in much the same way as atomic electron configurations.
Each molecular orbital can hold 2 electrons with opposite spins.
The number of orbitals are conserved.

Bond Order

Larger bond order means greater bond strength. $$ \text{Bond order} = \frac{\left( \text{# of bonding }e^- \right) - \left( \text{# of antibonding }e^- \right)}{2} $$

Example: $\chem{H_2}$

In the H2 molecule, two electrons are in the lower energy bonding orbital and the higher energy antibonding orbital is empty.

$$ \text{Bond order}=\frac{2-0}{2} = 1 $$

Example: $\chem{H_2^-}$

In the H2 negative 1 ion, two electrons are in the lower energy bonding orbital and one electron is in the higher energy antibonding orbital.

$$ \text{Bond order}=\frac{2-1}{2} = \frac{1}{2} $$

Bonding on Homonuclear Diatomic Molecules

Homonuclear Diatomic Molecules

Composed of 2 identical atoms.
Only the valence orbitals of the atoms contribute significantly to the molecular orbitals of a particular molecule.

Paramagnetism

Paramagnetism – substance is attracted into the inducing magnetic field.
- Unpaired electrons ($\chem{O_2}$)
Diamagnetism – substance is repelled from the inducing magnetic field.
- Paired electrons ($\chem{N_2}$)

Apparatus Used to Measure the Paramagnetism of a Sample

The pan of a balance is connected to a hanging sample tube which is houses in glass tubing. The sample tube is suspended between the poles of an electromagnet.

Molecular Orbital Summary of Second Row Diatomic Molecules

A summary of the molecular orbital diagrams for B2, C2, N2, O2, and F2.

Bonding in Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecules

Composed of 2 different atoms.

Heteronuclear Diatomic Molecule: $\chem{HF}$

The $2p$ orbital of fluorine is at a lower energy than the $1s$ orbital of hydrogen because fluorine binds its valence electrons more tightly.
- Electrons prefer to be closer to the fluorine atom.
Thus the $2p$ electron on a free fluorine atom is at a lower energy than the $1s$ electron on a free hydrogen atom.

Orbital Energy-Level Diagram for the $\chem{HF}$ Molecule

In the HF molecule, two electrons are in the lower energy bonding orbital and the higher energy antibonding orbital is empty.

The diagram predicts that the $\chem{HF}$ molecule should be stable because both electrons are lowered in energy relative to their energy in the free hydrogen and fluorine atoms, which is the driving force for bond formation.

Heteronuclear Diatomic Molecule: HF (cont.)

The $\sigma$ molecular orbital containing the bonding electron pair shows greater electron probability close to the fluorine.
The electron pair is not shared equally.
This causes the fluorine atom to have a slight excess of negative charge and leaves the hydrogen atom partially positive.
This is exactly the bond polarity observed for $\chem{HF}$.

Combining the Localized Electron and Molecular Orbital Models

Delocalization

Describes molecules that require resonance.
In molecules that require resonance, it is the $\pi$ bonding that is most clearly delocalized, the $\sigma$ bonds are localized.
$p$ orbitals perpendicular to the plane of the molecule are used to form $\pi$ molecular orbitals.
The electrons in the $\pi$ molecular orbitals are delocalized above and below the plane of the molecule.

Resonance in Benzene

The two resonance structures of the benzene molecule with alternating single/double bonds around the ring of six carbon atoms.

The Sigma System for Benzene

There is a sigma bond between each neighboring carbon atoms in the six membered carbon atom ring. There is also sigma bonds to the hydrogen atoms.

The Pi System for Benzene

There are p orbitals above and below the plane of the ring on each carbon atom. These p orbitals bond to form a ringed pi system.

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Chapter 8 Advanced Theories of Covalent Bonding

Hybridization and the Localized Electron Model

Exercise 1

Hybridization and the Localized Electron Model

Exercise 1 - Answer

Concept Check 1

Concept Check 1 - Answer

Bonding in Methane

Hybridization

\(sp^3\) Hybridization

An Energy-Level Diagram Showing the Formation of Four \(sp^3\) Orbitals

The Formation of \(sp^3\) Hybrid Orbitals

Exercise 2

Exercise 2 - Answer

\(sp^2\) Hybridization

Sigma (\(\sigma\)) Bond

Pi (\(\pi\)) Bond

An Orbital Energy-Level Diagram for \(sp^2\) Hybridization

The Hybridization of the \(s\), \(p_x\), and \(p_y\) Atomic Orbitals

\(sp\) Hybridization

The Orbital Energy-Level Diagram for the Formation of \(sp\) Hybrid Orbitals on Carbon

When One \(s\) Orbital and One \(p\) Orbital are Hybridized, a Set of Two \(sp\) Orbitals Oriented at \(180^\circ\) Results

The Orbitals for \(\chem{CO_2}\)

Exercise 3

Exercise 3 - Answer

\(dsp^3\) Hybridization

The Orbitals Used to Form the Bonds in \(\chem{PCl_5}\)

Exercise 3

Exercise 3 - Answer

\(d^2sp^3\) Hybridization

How is the Xenon Atom in \(\chem{XeF_4}\) Hybridized

Using the Localized Electron Model

The Molecular Orbital Model

Combination of Hydrogen 1s Atomic Orbitals to form MOs

Relative Stabilities

MO Energy-Level Diagram for the \(\chem{H_2}\) Molecule

Description of Bonding

Bond Order

Example: \(\chem{H_2}\)

Example: \(\chem{H_2^-}\)

Bonding on Homonuclear Diatomic Molecules

Homonuclear Diatomic Molecules

Paramagnetism

Apparatus Used to Measure the Paramagnetism of a Sample

Molecular Orbital Summary of Second Row Diatomic Molecules

Bonding in Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecules

Heteronuclear Diatomic Molecule: \(\chem{HF}\)

Orbital Energy-Level Diagram for the \(\chem{HF}\) Molecule

Heteronuclear Diatomic Molecule: HF (cont.)

Combining the Localized Electron and Molecular Orbital Models

Delocalization

Resonance in Benzene

The Sigma System for Benzene

The Pi System for Benzene

Chapter 8

Advanced Theories of Covalent Bonding