# Bonding Theories | General Chemistry 1

The covalent bonding is studied in this chapter: valence bond theory, molecular orbital theory, multiple bonds, hybridization and hybrid orbitals, molecular orbital diagrams.

## Valence Bond Theory

Lewis structures and VSEPR theory are used to predict molecular geometry do not provide any information about bond formation. There are 2 bonding theories in chemistry:

• Valence bond theory: chemical bonds are formed when atomic orbitals overlap
• Molecular orbital theory: quantum mechanical treatment of bonding describing the electronic structure of molecules

Valence bond theory:

Atoms share valence electrons when an incompletely filled atomic orbital (AO) of one atom overlaps with an atomic orbital of another atom. A bond forms when the resulting molecule has lower energy than the original free atoms

## Hybrid Orbitals

Hybridization

To explain bonding in some molecules, we must use the concept of hybridization, in which 2 or more atomic orbitals are combined to form the same number of hybrid orbitals with new energy and shape

Types of hybrid orbitals:

• Hybrid orbitals from s- and p-orbitals:

sp hybridization: combination of 1 s-orbital and 1 p-orbital to form 2 sp hybrid orbitals
sphybridization: combination of 1 s-orbital and 2 p-orbitals to form 3 sp2 hybrid orbitals
sp3 hybridization: combination of 1 s-orbital and 3 p-orbitals to form 4 sp3 hybrid orbitals

• Hybrid orbitals from s-, p- and d-orbitals:

sp3d hybridization: combination of 1 s-orbital, 3 p-orbitals and 1 d-orbital to form 5 sp3d hybrid orbitals
sp3d2 hybridization: combination of 1 s-orbital, 3 p-orbitals and 2 d-orbital to form 6 sp3d2 hybrid orbitals

## Hybridization and Geometry

Hybrid orbitals are not used to predict molecular geometries: the molecular geometry and bond angles of a molecule must be known in order to use hybrid-orbital theory. The number of electron domains on the central atom determines its geometry and thus its hybridization:

• 2 electron domains ⇒ linear (bond angle: 180°) ⇒ sp hybridization
• 3 electron domains ⇒ trigonal planar (bond angle: 120°) ⇒ sp2 hybridization
• 4 electron domains ⇒ tetrahedral (bond angle: 109.5°) ⇒ sp3 hybridization
• 5 electron domains ⇒ trigonal bipyramidal (bond angles: 90° & 120°) ⇒ sp3d hybridization
• 6 electron domains ⇒ octahedral (bond angle: 90°) ⇒ sp3d2 hybridization

PCl5: 5 electron domains on the central atom ⇒ sp3d hybridization
SF6: 6 electron domains on the central atom ⇒ sp3d2 hybridization

## Multiple Bonds

σ bond vs. π bond

The σ bond results from an overlap along the internuclear axis of 2s orbitals, 1s-1p orbitals, or 2p orbitals
The π bond results from an overlap located above and below the internuclear axis: side-by-side overlap of 2p orbitals
Free rotation is possible around σ-bonds while there is restricted motion around π-bonds

Types of covalent bonds:

• The single bond consists of 1 σ-bond (2 e- are shared)
• The double bond consists of 1 σ-bond and 1 π-bond (4 e- are shared)
• The triple bond consists of 1 σ-bond and 2 π-bonds (6 e- are shared)

H2 ⇒ 1 σ-bond
O2 ⇒ 1 σ-bond + 1 π-bond
N2 ⇒ 1 σ-bond + 2 π-bonds

## Molecular Orbital Theory

Molecular orbital theory:

A theory that describes the orbitals of a molecule as bonding and antibonding combinations of atomic orbitals. Atomic orbitals (AO) combine to form molecular orbitals (MO) associated with the molecule rather than individual atoms. A molecular orbital is σ if the orbital lies directly along the internuclear axis, or π if the orbital does not lie along the internuclear axis. This theory explains bond formation and the magnetic and spectral properties of molecules

Bonding MO vs. antibonding MO:

Atomic wave functions are summed to obtain molecular wave functions:

• If the wave functions reinforce each other, the AOs are in phase and their combination results in the formation of a bonding MO. A bonding molecular orbital is lower in energy than the AOs that combined to form it. The electrons in this type of MO contribute to the strength of the bond
• If wave functions cancel each other, the AOs are out of phase and their combination results in the formation of an antibonding MO (with a node). An antibonding molecular orbital is higher in energy than the AOs that combined to form it. The electrons in this type of MO impair the strength of the bond

## Molecular Orbital Diagrams

Molecular orbital diagrams show the relative energy and number of valence electrons in each molecular orbital (MO) as well as the atomic orbitals (AO) from which they are formed. The energy of the orbitals can be found on the y-axis. The AOs are arranged on the left and right sides of the diagram. Overlapping AOs produce MOs located in the middle of the diagram

How to build a molecular orbital diagram:

1. Find the valence electron configuration of each atom in the molecule. The valence electrons will be placed on the atomic orbital of that atom
2. Determine if the molecule is homonuclear or heteronuclear:
- If the molecule is homonuclear, the AOs will be symmetric
- If the molecule is heteronuclear, the AOs of the more electronegative atom will be placed lower on the diagram
3. Add the molecular orbitals using the energy and bonding properties of the overlapping atomic orbitals:
- σ orbitals are stronger than π orbitals
- Antibonding MOs are higher in energy than bonding MOs
4. Fill in the molecular orbitals with the number of valence electrons in the molecule:
- The lowest energy orbitals fill up first
- Each orbital can accommodate a maximum of 2 electrons of opposite spins
- The Hund's rule is respected

Molecular orbitals in homonuclear diatomic species

The order of energies of the molecular orbitals in homonuclear diatomic molecules od second period is different for B2, C2, and N2, than for O2, F2, and Ne2

MO energy levels for O2, F2 and Ne2

MO energy levels for B2, C2 and N2

Bond order:

A measure of the strength of a bond. The higher the bond order, the stronger the bond. It can be determined using a molecular orbital diagram:

Bond order = $\frac{1}{2}$ [number of e- in bonding orbitals - number of e- in antibonding orbitals]

Paramagnetic vs. Diamagnetic

A paramagnetic species contains unpaired electrons. It is weakly attracted by a magnetic field
A diamagnetic species does not contain unpaired electrons. It is weakly repelled by a magnetic field

Lewis structures and VSEPR theory are used to predict molecular geometry but do not provide any information about bond formation

There are 2 bonding theories in chemistry:

• Valence bond theory: chemical bonds are formed when atomic orbitals overlap
• Molecular orbital theory: quantum mechanical treatment of bonding describing the electronic structure of molecules

Valence bond theory states that atoms share valence electrons when an incompletely filled atomic orbital (AO) of one atom overlaps an atomic orbital of another atom. A bond forms when the resulting molecule has lower energy than the original free atoms

To explain bonding in some molecules, we must use the concept of hybridization, in which 2 or more atomic orbitals are combined to form the same number of hybrid orbitals with new energy and shape

• sp hybridization: combination of 1 s-orbital and 1 p-orbital to form 2 sp hybrid orbitals
• sphybridization: combination of 1 s-orbital and 2 p-orbitals to form 3 sp2 hybrid orbitals
• sp3 hybridization: combination of 1 s-orbital and 3 p-orbitals to form 4 sp3 hybrid orbitals
• sp3d hybridization: combination of 1 s-orbital, 3 p-orbitals and 1 d-orbital to form 5 sp3d hybrid orbitals
• sp3d2 hybridization: combination of 1 s-orbital, 3 p-orbitals and 2 d-orbital to form 6 sp3d2 hybrid orbitals

The number of electron domains on the central atom determines its geometry and thus its hybridization:

• 2 electron domains ⇒ linear (bond angle: 180°) ⇒ sp hybridization
• 3 electron domains ⇒ trigonal planar (bond angle: 120°) ⇒ sp2 hybridization
• 4 electron domains ⇒ tetrahedral (bond angle: 109.5°) ⇒ sp3 hybridization
• 5 electron domains ⇒ trigonal bipyramidal (bond angles: 90° & 120°) ⇒ sp3d hybridization
• 6 electron domains ⇒ octahedral (bond angle: 90°) ⇒ sp3d2 hybridization

The σ bond results from an overlap along the internuclear axis of 2s orbitals, 1s-1p orbitals, or 2p orbitals, whereas the π bond results from an overlap located above and below the internuclear axis: side-by-side overlap of 2p orbitals. Free rotation is possible around σ-bonds while there is restricted motion around π-bonds

There are 3 different types of covalent bonds:

• The single bond consists of 1 σ-bond (2 e- are shared)
• The double bond consists of 1 σ-bond and 1 π-bond (4 e- are shared)
• The triple bond consists of 1 σ-bond and 2 π-bonds (6 e- are shared)

Molecular orbital theory describes the orbitals of a molecule as bonding and antibonding combinations of atomic orbitals. Atomic orbitals (AO) combine to form molecular orbitals (MO) associated with the molecule rather than individual atoms. A molecular orbital is σ if the orbital lies directly along the internuclear axis, or π if the orbital does not lie along the internuclear axis. This theory explains bond formation and the magnetic and spectral properties of molecules

• If the wave functions reinforce each other, the atomic orbitals (AO) are in phase and their combination results in the formation of a bonding molecular orbital (MO). A bonding MO is lower in energy than the AOs that combined to form it. The electrons in this type of MO contribute to the strength of the bond
• If the wave functions cancel each other, the AOs are out of phase and their combination results in the formation of an antibonding MO (with a node). An antibonding MO is higher in energy than the AOs that combined to form it. The electrons in this type of MO impair the strength of the bond

Molecular orbital diagrams show the relative energy and number of valence electrons in each molecular orbital (MO) as well as the atomic orbitals (AO) from which they are formed. The energy of the orbitals can be found on the y-axis. The AOs are arranged on the left and right sides of the diagram. Overlapping AOs produce MOs located in the middle of the diagram

1. Find the valence electron configuration of each atom in the molecule. The valence electrons will be placed on the atomic orbital of that atom
2. Determine if the molecule is homonuclear or heteronuclear:
- If the molecule is homonuclear, the AOs will be symmetric
- If the molecule is heteronuclear, the AOs of the more electronegative atom will be placed lower on the diagram
3. Add the molecular orbitals using the energy and bonding properties of the overlapping atomic orbitals:
- σ orbitals are stronger than π orbitals
- Antibonding MOs are higher in energy than bonding MOs
4. Fill in the molecular orbitals with the number of valence electrons in the molecule:
- The lowest energy orbitals fill up first
- Each orbital can accommodate a maximum of 2 electrons of opposite spins
- The Hund's rule is respected

The order of energies of the molecular orbitals in homonuclear diatomic molecules od second period is different for B2, C2, and N2, than for O2, F2, and Ne2

MO energy levels for O2, F2 and Ne2

MO energy levels for B2, C2 and N2

Bond order is a measure of the strength of a bond. The higher the bond order, the stronger the bond. It can be determined using a molecular orbital diagram:

Bond order =  [number of e- in bonding orbitals - number of e- in antibonding orbitals]

A paramagnetic substance is a substance with unpaired electrons and therefore weakly attracted by a magnetic field while a diamagnetic substance is a substance without unpaired electrons (not attracted by a magnetic field)