Notes on Covalent Bonding: Orbitals

Covalent Bonding: Orbitals

9.1 Hybridization and the Localized Electron Model

• Overview: Discussed the localized electron model, focusing on atomic orbitals and hybridization to explain molecular structures and bonding.

Main Concepts

• Localized Electron Model: Molecules are viewed as collections of atoms bound by shared electrons. Lewis structures represent valence electron arrangement and VSEPR model predicts molecular geometry.

• Hybridization: A modification of the localized electron model to explain the use of non-native orbitals in bonding.

Types of Hybridization

sp3 Hybridization

• Example: Methane (CH₄)

• Characteristics: 1 2s and 3 2p orbitals combine to form 4 equivalent sp³ orbitals arranged tetrahedrally, with bond angles of 109.5°.

• Lewis Structure of Methane:

  • Each H-atom forms a sigma bond with an sp³ orbital of carbon.

sp2 Hybridization

• Example: Ethylene (C₂H₄)

• Characteristics: Involves 1 2s and 2 2p orbitals forming 3 sp² orbitals in a trigonal planar arrangement with bond angles of 120°.

• Double Bond Explanation: One sigma bond formed by sp² orbitals and one pi bond formed by the unhybridized p orbital.

• Molecular Geometry: Each carbon in ethylene forms sigma bonds with hydrogen atoms and is bonded to another carbon through sigma and pi bonds.

sp Hybridization

• Example: Carbon Dioxide (CO₂)

• Characteristics: 1 2s and 1 2p orbital combine to form 2 sp orbitals which align linearly at 180°.

• Double Bonds: Each C=O bond consists of one sigma bond from the sp hybrid orbitals and one pi bond from unhybridized p orbitals.

dsp³ Hybridization

• Example: Phosphorus Pentachloride (PCl₅)

• Characteristics: 1 d orbital, 1 s orbital, and 3 p orbitals combine to form 5 dsp³ orbitals in a trigonal bipyramidal arrangement.

d²sp³ Hybridization

• Example: Sulfur Hexafluoride (SF₆)

• Characteristics: 2 d orbitals, 1 s orbital, and 3 p orbitals combine to form 6 d²sp³ orbitals in an octahedral arrangement.

9.2 The Molecular Orbital Model

• Comparison to Localized Electron Model: The molecular orbital model accounts for delocalization of electrons and can describe magnetic properties more effectively.

Basic Features of Molecular Orbitals:

1. Formation from Atomic Orbitals: Molecular orbitals are derived from atomic orbitals of bonded atoms.

2. Electron Capacity: Each molecular orbital can hold two electrons with opposite spins.

3. Bonding and Antibonding Orbitals:

   • Bonding MO: Lower energy, favors bonding (i.e., H₂).

   • Antibonding MO: Higher energy, disfavor bonding.

4. Bond Order Calculation:

   • Formula: Bond order = (Number of bonding electrons - Number of antibonding electrons) / 2.

Example of H₂ Molecule:

• The lowest energy state observed is lower than two separate H atoms.

• Energy comparison favors molecule formation with bond order calculated as follows:

  • Bond order = (2 bonding electrons - 0 antibonding electrons) / 2 = 1.

Homonuclear Diatomic Molecules:

• Discussed O₂, N₂, F₂, and their respective molecular orbital configurations.

• Highlighted differences in paramagnetism (O₂) versus diamagnetism (N₂).

9.3 Bonding in Homonuclear Diatomic Molecules

• Review of homonuclear diatomic molecules where bonding principles of symmetry and electron configurations lead to specific bond orders and stability predictions.

• Paramagnetism and its relation to unpaired electrons in molecular orbitals were emphasized, specifically in O₂.

9.4 Bonding in Heteronuclear Diatomic Molecules

• The principle of using molecular orbital diagrams adapted from homonuclear examples to describe heteronuclear cases like NO or HF

Example - Hydrogen Fluoride:

• In HF, the molecular orbitals are arranged differently due to differing electronegativities leading to bond polarity.

9.5 Combining the Localized Electron and Molecular Orbital Models

• Exploring ways to reconcile the localized electron model's assumptions of electron localization with the molecular orbital concept of delocalization.

Important Molecules: Benzene (C₆H₆) and Nitrate Ion (NO₃⁻)

• Benzene's equilibrated bond characteristics are described using both models where the localized model assisted in illustrating resonance and the delocalized model explained overall stability in bonding.

Summary of Hybridization Requirements:

• Concluded by summarizing requisite hybridizations for molecular geometries and the utility of theoretical models in predicting molecular behavior.

Covalent Bonding: Orbitals

9.1 Hybridization and the Localized Electron Model

• Localized Electron Model: Uses Lewis structures and VSEPR to predict molecular geometry based on shared electron pairs.

• Hybridization: Atomic orbitals (s, p, d) combine to form new, degenerate hybrid orbitals that explain observed molecular geometries and equivalent bond strengths.

Types of Hybridization

sp³ Hybridization

• Formation: One 2s + three 2p orbitals $\rightarrow$ four sp³ orbitals.

• Characteristics: Tetrahedral geometry (e.g., CH₄), $109.5^{\circ}$ bond angles. Forms 4 sigma bonds.

sp² Hybridization

• Formation: One 2s + two 2p orbitals $\rightarrow$ three sp² orbitals; one 2p orbital unhybridized.

• Characteristics: Trigonal planar geometry (e.g., C₂H₄), $120^{\circ}$ bond angles.

• Double Bond: One sigma bond (sp²-sp²) and one pi bond (sideways overlap of unhybridized p orbitals).

sp Hybridization

• Formation: One 2s + one 2p orbital $\,\rightarrow$ two sp orbitals; two 2p orbitals unhybridized.

• Characteristics: Linear geometry (e.g., CO₂, C₂H₂), $180^{\circ}$ bond angles.

• Triple/Double Bonds: Central atom forms two sigma bonds. Unhybridized p orbitals form two pi bonds for a triple bond or two separate pi bonds for two double bonds.

dsp³ Hybridization

• Formation: One d + one s + three p orbitals $\,\rightarrow$ five dsp³ orbitals.

• Characteristics: Trigonal bipyramidal geometry (e.g., PCl₅).

d²sp³ Hybridization

• Formation: Two d + one s + three p orbitals $\,\rightarrow$ six d²sp³ orbitals.

• Characteristics: Octahedral geometry (e.g., SF₆).

9.2 The Molecular Orbital Model

• Overview: Electrons are delocalized in molecular orbitals (MOs) that span the entire molecule. Explains paramagnetism and delocalized bonding.

Basic Features of Molecular Orbitals:

1. Formation: MOs form from the linear combination of atomic orbitals. (#MOs = #AOs).

2. Electron Capacity: Each MO holds up to two electrons with opposite spins.

3. Bonding MOs (lower energy): Concentrates electron density between nuclei, favors bonding.

4. Antibonding MOs (higher energy): Has a node between nuclei, disfavors bonding (denoted by $*$).

5. Bond Order: $(\text{Number of bonding electrons} - \text{Number of antibonding electrons}) / 2$

   • $>0$: stable bond. $0$: no net bond.

Example of H₂ Molecule:

• Two H 1s AOs combine to form one bonding ($1\sigma$) and one antibonding ($1\sigma^*$) MO.

• Two electrons fill $1\sigma$. Bond order = $(2-0)/2 = 1$.

Homonuclear Diatomic Molecules:

• MO configurations predict magnetic properties.

• O₂: Has two unpaired electrons in $\pi_{2p}^*$ MOs, explaining its paramagnetism.

• N₂: All electrons are paired, making it diamagnetic.

9.3 Bonding in Homonuclear Diatomic Molecules

• MO diagrams predict bond order, length, energy, and magnetic properties based on electron configuration.

9.4 Bonding in Heteronuclear Diatomic Molecules

• MO diagrams apply, but atomic orbital energies differ due to electronegativity (e.g., in HF, F's 2p orbital is lower in energy than H's 1s).

9.5 Combining the Localized Electron and Molecular Orbital Models

• Localized Model: Good for sigma framework and basic geometry.

• Molecular Orbital Model: Essential for delocalized pi bonding and resonance structures.

• Example (Benzene, C₆H₆): Sigma bonds (sp² hybridized C atoms) form the ring; unhybridized p orbitals form delocalized pi MOs above and below the ring, explaining equivalent C-C bonds and extra stability.