# 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 but tell us nothing about bond formation. There are 2 bonding theories:

• Valence bond theory ⇒ bonds are formed when atomic orbitals overlap
• Molecular orbital theory ⇒ quantum mechanical treatment of bonding

Valence bond theory:

Atoms share valence electrons when an atomic orbital (AO) on one atom overlaps with an atomic orbital on the other. A bond forms when the resulting molecule is lower in energy than the original free atoms

## Hybrid Orbitals

Hybridization

To explain the bonding in some molecules, we need to employ the concept of hybridization, in which 2 or more atomic orbitals are combined to form the same number of hybrid orbitals

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: we must need to know molecular geometry and bond angles in a molecule to be able to use hybrid-orbital analysis. The number of electron domains on the central atom determines its geometry and therefore its hybridization:

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

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

Types of covalent bonds:

Single bond consists of 1 σ-bond (2 e- are shared
Double bond consists of 1 σ-bond and 1 π-bond (4 e- are shared)
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 in a molecule as bonding and antibonding combinations of atomic orbitals. Atomic orbitals (AO) combine to form new molecular orbitals (MO) associated with the molecule rather than with 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 the formation of bonds and the magnetic and spectral properties of molecules

Bonding MO vs. antibonding MO:

Atomic wave functions are summed to obtain molecular wave functions:

• If 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. Electrons in this type of MO contribute to the strength of a 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. Electrons in this type of MO detract from the strength of a 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 is on the y axis. The AOs are arranged to the left and right of the diagram. Overlapping AOs produce MOs located in the middle of the diagram

How to build 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 this 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 molecular orbitals using 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 of the molecule:
Lower energy orbitals fill first
Each orbital can accommodate a maximum of 2 electrons with opposite spins
Hund's rule is obeyed

Molecular orbitals in homonuclear diatomic species

The order of energies of molecular orbitals in second-period homonuclear diatomic molecules is different for B2, C2, and N2, than it is 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