Lecture Notes on Molecular Orbital Theory

Introduction

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Quick Clicker Question Recap

• Clicker Questions: Engaging students in real-time problem-solving.

Phosphorus-Hydrogen Molecule

• Phosphorus: 5 valence electrons.
• Hydrogen: Each has 3 electrons, total of 8.
• Molecular Geometry: Tetrahedral but bond angles less than 109.5 degrees due to lone pair repulsions.

Lewis Structure Importance

• Structure: Helps determine parent geometry and bond angles.

Molecular Orbital Theory (MO Theory)

Course Overview

• Topics: Atomic structure, atomic orbitals, bonding, molecular structure, and reactions.
• Excitement: Focus on structure of molecules and reactions.

MO Theory Basics

• Concept: Valence electrons are delocalized around molecules, not individual atoms.
• Electron Delocalization: Use of molecular orbitals (MOs) and wave functions.
• Linear Combination of Atomic Orbitals (LCAO): Combines atomic orbitals to form molecular orbitals.
  • Types of MOs: Bonding and antibonding MOs.
  • Principle: N atomic orbitals produce N molecular orbitals.

S-Orbitals and MO Formation

• Simple Molecules: Identical atoms forming molecular orbitals.
• Bonding Orbitals: Constructive interference leading to lower energy.
  • Example: H₂ molecule.
  • Sigma (σ) Orbitals: Symmetric around bond axis.
• Antibonding Orbitals: Destructive interference leading to higher energy.
  • *Sigma Star (σ)**: High energy, results in nodes between nuclei.

MO Energy Diagram

• Energy Levels: Bonding orbitals are lower, antibonding orbitals are higher.
• Electron Configuration: Describes electron occupancy in MOs.
  • Example: H₂ has σ(1s)² configuration.

Practical Examples

Helium and Dihelium (He₂)

• MO Diagram Exercise: For helium, 2 electrons in bonding, 2 in antibonding.
• Bond Order: Calculation showing no net energy gain, He₂ unlikely to exist.
• Real Data: Experimental dissociation energy supports MO theory predictions.

Lithium (Li₂) and Beryllium (Be₂)

• MO Diagrams: Considering both 1s and 2s orbitals.
• Bond Order Calculation: Using formula $$\frac{1}{2}(\text{bonding electrons} - \text{antibonding electrons})$$
• Stability: Li₂ exists, Be₂ is very weak.

P-Orbitals and PI (π) Orbitals

• Formation: Combining px and py orbitals.
• Bonding and Antibonding: Constructive and destructive interference.
• Energy Levels: Placement depends on atomic number (Z).

Complete MO Diagrams

Pz Orbitals

• Constructive Interference: Leads to σ₂p_z bonding orbitals.
• Destructive Interference: Leads to σ*₂p_z antibonding orbitals.
• Arrangement: Depends on Z-value; changes order of orbitals.

Examples with Complete MO Diagrams

• Molecular Oxygen (O₂)
  • Electron Configuration: Shows π orbitals lower for Z ≥ 8.
  • Bond Order Calculation: Bond order = 2, indicating a double bond.
  • Properties: Bi-radical nature, paramagnetic.
• Molecular Nitrogen (N₂)
  • Electron Configuration: Shows triple bond character.
  • Bond Order Calculation: Bond order = 3, very strong bond.

Important Insights

• Molecular Stability: Bond order and electron arrangements affect stability.
• Life on Earth: O₂ and N₂ play critical roles, explained by MO theory.
• Real-World Applications: Chemical reactions, research in breaking strong molecular bonds like N₂.

Closing Remarks

• Quiz Review: Concepts of bonding and antibonding orbitals, bond order, and Sigma vs. Pi orbitals.
• Next Topics: More on Pz orbitals and their role in molecular bonding structures.

Summary

• Molecular Orbital Theory: Provides a comprehensive understanding of how atoms combine to form stable or unstable molecules.
• Future Directions: Will further study reactions, thermodynamics, and more complex molecules.