Bonding Theories | General Chemistry 1

Bonding theories:

Lewis structures and VSEPR theory, while useful for predicting molecular geometry, do not provide any information about bond formation. In chemistry, two primary bonding theories describe how atoms form bonds:

• Valence Bond Theory: Chemical bonds are formed when atomic orbitals overlap.
• Molecular Orbital Theory: A quantum mechanical treatment of bonding that describes 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. The strength of the bond is determined by the extent of orbital overlap; greater overlap results in a stronger bond.

• Bond types and directionality: Bonds involving s-orbitals are non-directional, whereas bonds involving p, d, and f orbitals are directional, influencing the geometry of the molecule.

• Lower energy state: The formation of a covalent bond via orbital overlap results in a molecule with a lower potential energy compared to the separate atoms, making the bonded state more stable.

 Hydrogen Molecule (H₂):

The bond forms due to the overlap of two 1s orbitals, each containing one electron, resulting in a stable molecule with a σ bond.

Hybridization

To explain bonding in some molecules, we must use the concept of hybridization, where two or more atomic orbitals combine to form the same number of hybrid orbitals with new energies and shapes. Hybridization helps in understanding the geometry and bonding properties of molecules.

Hybrid orbitals from s- and p-orbitals:

• sp hybridization: combination of 1 s-orbital and 1 p-orbital to form 2 sp hybrid orbitals.
• sp² hybridization: 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.

Hybrid orbitals are not used to predict molecular geometries; rather, the molecular geometry and bond angles of a molecule must be known to use hybrid-orbital theory effectively. The number of electron domains around 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

 σ bond vs. π bond

• σ bond: Formed by the head-on overlap of orbitals along the internuclear axis.
  It can result from the overlap of two s orbitals, an s orbital with a p orbital, or two p orbitals.
  It allows free rotation around the bond axis.
• π bond: Formed by the side-by-side overlap of two p orbitals.
  The overlap occurs above and below the internuclear axis.
  It restricts rotational motion due to the nature of the side-by-side overlap.

Types of covalent bonds:

• A single bond consists of 1 σ bond (2 e^- are shared between the atoms).
• A double bond consists of 1 σ bond and 1 π bond (4 e^- are shared). The presence of a π bond restricts rotation, resulting in a fixed planar structure around the bond, as seen in alkenes.
• A triple bond consists of 1 σ bond and 2 π bonds (6 e^- are shared). The addition of a second π bond further restricts rotational motion and results in a linear geometry, as seen in alkynes.

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

Molecular orbital theory:

Molecular orbital theory describes the orbitals of a molecule as bonding and antibonding combinations of atomic orbitals (AOs). In this theory, atomic orbitals combine to form molecular orbitals (MO) that are associated with the entire molecule rather than individual atoms.

• The number of MOs formed equals the number of AOs combined.
• Molecular orbitals can be classified as σ or π depending on their orientation relative to the internuclear axis: σ orbitals lie directly along the internuclear axis, while π orbitals do not lie along the internuclear axis, involving side-by-side overlap.
• MO Theory explains not only bond formation but also the magnetic and spectral properties of molecules.

Bonding MO vs. antibonding MO:

Molecular orbitals are formed by the linear combination of atomic wave functions:

• Bonding molecular orbital: An MO formed when the atomic wave functions reinforce each other (in-phase combination). It is lower in energy than the atomic orbitals (AOs) that combined to form it. Electrons in bonding MOs contribute to bond strength and stability.
• Antibonding molecular orbital: An MO formed when atomic wave functions cancel each other (out-of-phase combination), resulting in a node between nuclei. It is higher in energy than the AOs that combined to form it. Electrons in antibonding MOs weaken the bond and decrease stability.

Overview:

Molecular orbital diagrams show the relative energies and number of valence electrons in each molecular orbital (MO), as well as the atomic orbitals (AOs) from which they are formed. The energy levels of the orbitals are displayed on the y-axis, with the AOs arranged on the left and right sides of the diagram. The MOs, resulting from the overlap of AOs, are located in the middle.

Molecular orbitals in homonuclear diatomic species

The relative energy levels of MOs for homonuclear diatomic molecules are determined by the combination of AOs from each atom:

• B₂, C₂, N₂: The π_2p orbitals are lower in energy than the σ_2p orbital due to less effective overlap in the case of lighter atoms.
• O₂, F₂, Ne₂: The σ_2p orbital is lower in energy than the π_2p orbitals due to more effective overlap in the case of heavier atoms.

How to build a molecular orbital diagram:

1. Determine Valence Electron Configuration:
   Identify the valence electron configuration of each atom in the molecule. These electrons will be placed in the atomic orbitals of each atom.
2. Identify Molecule Type:
   - Homonuclear molecules: The AOs will be symmetric (e.g., O₂, N₂).
   - Heteronuclear molecules: The AOs of the more electronegative atom will be placed lower on the diagram (e.g., CO).
3. Add Molecular Orbitals:
   - σ Orbitals: Formed from head-on overlap of AOs, generally stronger and lower in energy.
   - π Orbitals: Formed from side-by-side overlap of AOs.
   - Antibonding MOs: Higher in energy than the corresponding bonding MOs.
4. Fill Molecular Orbitals with Electrons:
   - Fill from the lowest to the highest energy orbitals.
   - Each orbital can accommodate a maximum of two electrons with opposite spins.
   - Follow Hund's rule: Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.

Bond order:

Bond order is a measure of the stability of a bond within a molecule. The higher the bond order, the more stable the molecule. It can be determined using a molecular orbital (MO) diagram and is calculated using the formula:
 

• H₂ ⇒ one σ bond ⇒ Bond order = 1
• O₂ ⇒ one σ bond and one π bond ⇒ Bond order = 2
• N₂ ⇒ one σ bond and two π bond ⇒ Bond order = 3

Paramagnetic vs. Diamagnetic

The magnetic properties of a molecule are determined by the presence or absence of unpaired electrons in its molecular orbitals:

• Paramagnetic species: Contains unpaired electrons and is weakly attracted to a magnetic field.
• Diamagnetic species: It does not contain unpaired electrons and is weakly repelled by a magnetic field.

• Oxygen molecule (O₂) is paramagnetic due to the presence of unpaired electrons in its π*2p antibonding orbitals.
• Nitrogen molecule (N₂) is diamagnetic because all electrons are paired in its molecular orbitals.