Chemical Bonding

Chapter 14: Introduction to Chemical Bonding

Recommended Textbook Problems

  • Chapter 13 - Bonding: General Concepts
    • Lewis Structures and Resonance: 63, 67, 73, 75, 77
    • Formal Charge: 85, 87, 89
  • Chapter 14 - Covalent Bonding: Orbitals
    • The LE Model and Hybrid Orbitals: 13, 15, 21, 23, 27
    • The MO Model: 35, 39, 43, 45, 51

Chemical Bonding and Lewis Theory

  • Lewis Theory:
    • Works reasonably well for light atoms in main-group compounds (s and p block elements).
    • Emphasizes the electron pair bond and octets.
    • Based on chemical reactivity and structure patterns, not on a fundamental physical model.
    • Many exceptions noted for main-group elements.
    • Fails for transition metals and rare Earth elements (d+f block).
  • Historical Context:
    • Lewis formulated his concepts without a complete description of bonding at the time.
  • Quantum Mechanics:
    • The 1920s/30s saw the discovery and development of quantum mechanics.
    • First applied to atoms and then molecules, providing a complete physical description of bonding.

The Schrödinger Equation: A Simplified Overview

  • Schrödinger Equation:
    • HΨ = EΨ
    • Where:
      • H is the Hamiltonian operator (contains kinetic energy T and potential energy V terms).
      • Ψ is the wavefunction.
      • E is the energy of a given state.
  • Interactions in H_2:
    • Potential energy terms: electron-electron repulsion, proton-proton repulsion, electron-proton attraction.
    • Kinetic energy terms.
  • Orbitals:
    • Energy is the only observable; therefore, there are orbitals when describing electrons.
  • Wavefunction:
    • Ψ has no physical meaning itself.
    • Ψ^2 gives a probability distribution.
  • Utility:
    • A very useful tool for tackling chemical bonding.

Review of Atomic Orbitals and Orbital Phases

  • Quantum Numbers:
    • Principal quantum number n: 1, 2, 3, … (energy level)
    • Angular momentum quantum number l: 0, 1, …, n-1 (shape)
    • Magnetic quantum number m_l: -l, …, +l (direction/orientation)
    • Electron spin quantum number m_s: +1/2, -1/2
  • Example: Oxygen Atom
    • Electron configuration: 1s^2 2s^2 2p^4
    • 2p orbitals: 2px, 2py, 2p_z
  • Pauli Exclusion Principle:
    • No two electrons can have the same four quantum numbers.
  • Orbital Phase:
    • Phase is important! (+ + = constructive interference, + - = destructive interference)

Two Major Approximations of the Schrödinger Equation

  • Challenge:
    • The Schrödinger equation is too complex mathematically to be solved for molecules larger than H_2.
    • Need to make approximations.
  • Approximations to be Discussed:
    • Molecular Orbital (MO) theory: delocalized view of chemical bonding.
      • Bonding without bonds.
    • Valence Bond (VB) theory: localized view of bonding.

Molecular Orbital Theory: The Basic Idea

  • Helium Atom Example:
    • Pull nucleus apart. Approach He_2^{2+} as H-H.
  • Molecular Orbitals:
    • Molecular orbitals are solutions to the molecular problem.
  • Linear Combination of Atomic Orbitals (LCAO):
    • A way to make MO theory useful.
    • Example:
      • Ψ1 = 1s + 1s = σg + σ_g (same phase, constructive)
      • Ψ2 = 1s - 1s = σu + σ_u (opposite phase, destructive)
  • Key Principles:
    • Number of atomic orbitals (AO's) in = Number of molecular orbitals (MO's) out.
    • For atomic orbitals to combine, they must be of similar energy and symmetry.
    • Overlap: O + O →
      σ, O + O_{out
      of
      phase} → π

Molecular Orbital Symmetry and Labels

  • Symmetry Requirement:
    • Orbitals must have the same symmetry to combine.
  • Defining MO Symmetry:
    • Symmetry is determined by how the orbital 'looks' following rotation about a bond.
  • Symmetry Labels:
    • σ: symmetric with a full 360° rotation (sigma).
    • π: antisymmetric with a 180° rotation (pi).
    • By definition, the atomic z-axis is oriented along the bond.